value capture theory: a strategic management review · value capture theory: a strategic management...

Strategic Management JournalStrat. Mgmt. J., 38: 17–41 (2017)

Published online EarlyView in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/smj.2592Received 30 April 2014; Final revision received 27 February 2016

VALUE CAPTURE THEORY: A STRATEGICMANAGEMENT REVIEW

JOSHUA GANS and MICHAEL D. RYALL*Rotman School of Management, University of Toronto, Toronto, Ontario, Canada

Research summary: This article provides the first review of a growing line of scholarly workin strategy that we refer to as “value capture theory.” The common thread in this work is itsuse of cooperative game theory as a general, mathematical foundation upon which to build adeep understanding of firm performance in market settings. Our review: (1) describes the primaryelements of the theory; (2) highlights important blindspots that it resolves with respect to existingtheoretical approaches; (3) calls attention to several of its novel insights; and (4) summarizesa myriad of applications and empirical studies that have appeared in recent years using valuecapture theory.

Managerial summary: Traditionally, theoretical claims in strategic management have beensupported by informal, qualitative reasoning. Recently, however, a new line of theoretical workbased upon mathematical methods, known as “value capture theory,” has been gaining inpopularity. This article reviews the recent advances in this line with a particular emphasis upona number of its important insights, several of which challenge longstanding propositions fromthe traditional line. For managers, the formal nature of value capture theory is well-aligned withdata-driven analyses of strategic situations. Copyright © 2016 John Wiley & Sons, Ltd.

INTRODUCTION

Understanding persistent heterogeneity in firmperformance is, perhaps, the central objective inthe field of strategy.1 The seminal contributionof Brandenburger and Stuart (1996) initiated aunique stream of work designed to deepen ourunderstanding of this phenomenon through the

Keywords: value creation; value capture; competition;cooperative game theory*Correspondence to: Michael D. Ryall, 105 St. GeorgeSt., Toronto, ON M5S 3E6, Canada. E-mail: [email protected] As evidence for this assertion, we note that an adequate reviewof the existing empirical literature on this topic would require aseparate article of its own. For example, a partial list of relevantempirical analyses on the extent to which above-average profitspersist includes: Cubbin and Geroski (1987), Dosi, Lechevalier,and Secchi (2010), Jacobsen (1988), Knott (2003), McGahanand Porter (2003), Mueller (1977, 1986), Roberts (2001), Rumelt(1991), Waring (1996), Wiggins and Ruefli (2002), and Madsenand Walker (2015).

Copyright © 2016 John Wiley & Sons, Ltd.

development of a mathematical theory of valuecreation and capture under competition. Since then,this literature has quietly and steadily grown to thepoint where it now represents a substantial bodyof work. Due to its mathematical nature, the col-lection of findings build upon each other, therebycreating a coherent, interlocking set of theoreticalclaims. These claims reveal subtleties of compe-tition that were not previously apparent, pushingstrategy scholars to rethink some fundamentalideas about value capture under competition. Whatis more, recent advances in empirical methodshave opened the door to empirical investigationof these claims. Finally, it is important to notethat the theory of interest is entirely publishedin strategic management journals. This has notbeen an exercise of locating technical resultsoutside the field and importing them into strategyvia reinterpretation and analogy. Rather, thiswork contains novel propositions of its own, with

18 J. Gans and M. D. Ryall

implications extending well beyond the boundariesof strategy.

Thus, we presently find ourselves in a situationin which a stream of literature has developed to thepoint that a general, scholarly audience is likely tofind the insights it offers of substantial interest, yetit is early enough in the process that these insightsare not broadly disseminated. In other words, thetime seems just right for a review of this streamaimed at a general audience. The purpose of thisarticle is to provide such a review. Our specific goalsinclude identifying the major issues this researchis intended to address, explaining the mathematicalframework upon which it is built, highlightingthe central theoretical insights thus far obtained,describing notable applications (both theoreticaland empirical), and concluding with some thoughtsabout open issues and future directions.

The scope of our review includes papers (1)published in management journals that (2) presentnovel mathematical propositions using cooperativegame theory. By adopting this unifying theme, thescope of our article is manageable, permits a coher-ent discussion, and allows us to treat key ideas witha reasonable degree of depth. Moreover, by restrict-ing attention to management publications, weprovide a sense of the novelty and substance of thestream within our own field.2 Our intended audienceincludes those looking for an overview of the cen-tral concepts and latest results associated with thisline of work as well as those considering enteringand contributing to it. Therefore, this article is con-structed to be self-contained within the content con-straint of a single journal article—the formalism,relevant assumptions, associated interpretations,and important results to date are all covered, albeitconcisely, with citations to more in-depth sourcesfor those interested in pursuing them.

This being a literature review, it is also worthpointing out that the issues elaborated below werethe product of a discovery process: theorists builtmodels that seemed sensible; based on these mod-els, formal propositions were proven; mathemati-cal claims led to insights about value capture undercompetition in the real world; these insights led toa grasp of the kinds of issues that the dominant

2 Unfortunately, this scope does imply, on the one hand, passingover a number of thought-provoking, qualitative papers in strategythat adopt ideas from cooperative game theory and, on the otherhand, ignoring potentially interesting papers published in otherfields (most notably, economics). Stuart (2001) provides an earlyprecursor to this article.

paradigms missed. This article proceeds in reverseorder: we summarize the (now) apparent issues;then, we present the formalism and trace the lineof results derived from it; this should spark insightsin the reader regarding value capture under compe-tition; which, cumulatively, should lead to a deeperunderstanding not only of this line of work but alsoto new questions for future inquiry.

A MOTIVATING EXAMPLE

To provide context for our survey, it is useful tobegin not with the literature but with an examplethat motivates value capture theory and the contri-butions it can make. The example is intended tobe illustrative rather than the model of a specificstrategic situation.

Status quo configuration

Any formal model of an industry usually startswith a benchmark or what we will call a statusquo configuration upon which changes can becompared. For our example, suppose there is anindustry that consists of value networks composedof some finite numbers of agents. By “valuenetwork” we mean a collection of agents connectedto one another via chains of transactions that, takentogether, ultimately result in the production ofeconomic value. The network includes all agentsinvolved in the production of value, from the mostupstream resource providers all the way downthrough the final consumer. An example of a valuenetwork would be the agents engaged in the Applemobile computing ecosystem, including those whoprovide platform elements, mobile carriers whoprovide access to communications and the Internet,app developers, the content providers and theconsumers and end-users themselves. The Applevalue network competes with others built aroundSamsung, Google, etc.

Suppose there are exactly two such networks,A and B. Further, assume that—adding up theutility enjoyed by end-users and subtracting allof the economic costs associated with creatingand delivering the products to those end-users(including costs relating to the transactionsthemselves)—Network A creates economic valueof $200 million and Network B creates economicvalue of $180 million. This is the situation depictedin the first panel of Figure 1 (Configuration #1).

Copyright © 2016 John Wiley & Sons, Ltd. Strat. Mgmt. J., 38: 17–41 (2017)DOI: 10.1002/smj

Survey of Value Capture Theory 19

Value Network A$200

Value Network B$180

Value Network A$150

Value Network B$180

Value Network A$150

Value Network B$210

F forms a trivial value network$0

Figure 1. Three industry configurations

Assume this configuration is actually the oneobserved operating in the world and, hence, referto it as the “Status Quo.” In aggregate, the industryproduces $380 million in economic value. Finally,suppose our interest is in understanding the per-formance of a focal firm F, which is presentlyoperating in Network A. For instance, to continueour mobile example, F may be Adobe, whichprovides specialized Flash software.

Although this setup is “simple” in the sense that itcontains only two value networks, it is worth point-ing out a number of simplifying assumptions thatwere not imposed. We did not limit the number ofagents (beyond being finite), exclude transactionscosts, restrict consideration to two-sided markets,exclude buyers, represent buyers as a linear demandcurve, impose special functional forms on produc-tion functions, exclude positive externalities, andso on. This level of generality is a feature of themathematical approach we describe in more detailbelow.

Competitive upper bound

In the second panel of Figure 1 (Configuration #2),we indicate the chains of transactions that wouldarise were all agents in the market to forgo trans-actions with F; for instance, deciding not to sup-port Adobe’s software. In our example, the valueproduced by Network A drops to $150 million,while Network B continues to create $180 millionin value. Of course, F can create no value on itsown. In this case, the aggregate value produced inthe industry would drop from $180 to $330 million,a decrease of $50 million. This difference—theincremental value produced as a result of F’s pres-ence in the market—is called its added value (tothe market as a whole), symbolically, avF = 50. Itis easy to see that, in a noncoercive market setting,whatever amount of the $380 million F ultimatelycaptures, it cannot be more than $50 million. Why?Because were F to insist upon a share greater thanthis, the other agents in the market could implement



Configuration #2, which would yield them morevalue than producing $380 million and giving Fmore than $50 million.

By now, the notion of added-value and its roleas a limiter of value capture is well known withinstrategy (see, Brandenburger and Nalebuff, 1996;Gans, 2005). Even so, there are a few points worthhighlighting. First, as shown in the figure, Con-figuration #2 contemplates a different collectionof transactions to those at work in Configuration#1. Computing added value goes beyond the sim-ple removal of transactions with a given agent, toinclude a complete assessment of the new collec-tion of transactions that would actually arise in theirplace. Second, it illustrates a general feature ofadded value. An agent’s added value can be com-puted with respect to any group (the quantity ofvalue produced when the group includes that agentless the quantity produced without it. When theadded value being computed is with respect to a sta-tus quo value network that includes the agent, thatadded value represents an upper bound on its abil-ity to capture value. As we see from the figure, F’sadded values to Network A and to the market as awhole coincide at $50.3

Finally, added value provides an importantinsight into the nature of competition. Compe-tition in markets means vying for transactionpartners. To engage in the transactions that produce$380 million, other transactions must be forgone.In particular, in order to ensure that the transactionsdepicted in Configuration #1 actually arise, Fmust offer enough value to all of the agents withwhom it transacts to persuade them not to engagein the transactions depicted in Configuration #2.The latter transactions provide F’s transactionpartners with a valuable alternative to dealing withF—an alternative against which F must, in effect,compete.

Competitive lower bound

Now consider the third panel of Figure 1, Config-uration #3. Here, F deals with Network B, witha resultant increase in the value it produces from$180 to $210 million. Thus, F’s added value withrespect to Network B is $30 million. Note the impli-cation: the agents in Network B are willing to give

3 The two need not be equal, though an agent’s added value to themarket as a whole is never greater than its added value to a distinctvalue network.

F a share of up to $30 million (at which point theyare indifferent to F’s inclusion) in order to effectthe transactions depicted in Configuration #3. Thisillustrates an often-overlooked aspect of competi-tion: F’s transaction partners must offer it enoughvalue to ensure that F remains in Network A ratherthan abandoning them to transact with Network B.How much must they offer F to remain? At least$30 million.

It is important to observe that the focus hereis entirely on the quantity of economic value aparticular agent captures in return for the part itplays in the aggregate creation of value within theindustry. Thus, there is no discussion of prices ormargins or even a description of the products thatgenerate revenue or induce costs. Specifying prices,quantities, and costs is not the goal of this sort ofanalysis.4 Rather, this method places the productivepowers of agents, the competition between them totransact with one another, and the implications forvalue capture front-and-center.

Notice that competition operates symmetrically.To induce the other agents in Network A to forgoalternative deals in favor of transacting with it, Fmust offer them a sufficient share of the value cre-ated by their joint economic activities. However,those very same transaction partners must, simul-taneously, offer F a sufficient quantity of value toensure that it does not act upon the alternative trans-actions that it has available. Here we see a flip side toadded value: when the added value being computedis with respect to a status quo value network thatdoes not include the agent, that added value repre-sents a lower bound on the value the agent must cap-ture. Thus, competition need not hurt an agent—itmay play out in its favor. Value capture theory sortsout both sides of competition.

Thus, without imposing too many restrictions(and computing only four numbers), we expectthat the quantity of value captured by F will bebetween $30 and $50 million. The former is a floorimposed by competition for F, and the latter is aceiling imposed by competition for F’s transactionpartners. The analytic work in the literature wereview follows this thrust. In general, there aremany configurations to consider, many ways to addinteresting structure, and many insights available byso doing. Let us consider some now.

4 A feature of cooperative game theory is consistent with the callby Wernerfelt (1984) and noted by Lippman and Rumelt (2003).



SOME BLIND SPOTS IN PREVAILINGTHEORY

The modern era of strategy scholarship dates tothe famous collection of papers appearing in the1980s, all of which offer explanations for the phe-nomenon of persistent performance heterogeneityamong firms. These include Porter (1979, 1980),which initiated the “industry positioning” stream(IP); Wernerfelt (1984), the paper that sparked the“resource-based view” line of work (RBV); andWilliamson (1981), an early paper advocating his“transactions cost” approach to organizational anal-ysis (TCE).5 In the years following, strategy schol-ars expanded these original ideas in a number offruitful directions, thereby forming a commonlyaccepted collection of explanations for persistentdifferences in firm performance. Our goal in thissection is to identify several substantive oversights,or “blind spots,” shared by these mainstream expla-nations. Blind spots are eliminated by turningattention toward them. By so doing, we see theissues surrounding our extant body of theory morecompletely which, in turn, opens the door to greatergeneralization and unification.

Of more immediate relevance for our purposes isthat the blind spots discussed below were revealedby the methods reviewed by this article. Thus,our presentation reverses the historical processof analysis-reflection-insight by which these blindspots were revealed. Instead, we begin with theblind spots, explained in plain language. Our hope isthat, upon reflection, these explanations will triggerinsights into both the existence and potential impor-tance of the identified oversights. Then, once we doelaborate the technical details of the method, ourfurther hope is that these insights will carry over,allowing readers to grasp how the mathematics ofvalue capture reveal the identified blind spots in anexplicit fashion.

Before proceeding, we warn that any generaliza-tion of large, complex streams of scholarly workwill, by its nature, blur their finer and more subtlepoints. Our intent is not to gloss over these sub-tleties. Rather, we wish to provide a persuasive illus-tration of the way in which different approaches (in

5 The rapid coalescence of these ideas into a separate field,business strategy, was surely facilitated by the disinterest towardthis phenomenon apparent in economics at that time. Economicshas since come around; see, e.g., Syverson (2011) and Bloom et al.(2013).

this case, mathematical) can expand our explana-tory horizons. Many scholars have weighed in onboth sides of the argument regarding the efficacyof mathematical theory in management research.Again, our purpose here is not to engage those argu-ments. Rather, we simply point out that, for betteror worse (depending upon one’s philosophical sen-sibilities), a unique feature distinguishing the valuecapture stream from others in strategy is that itsclaims are formulated using a single, overarchingmathematical framework. The result is a collectionof rigorously derived findings that build upon oneanother to create a coherent whole, one with thepotential to unify and refine prevailing theory.6

The free-entry blind spot

Because strategy is about the performance of firmsin free markets, competition is always a cen-tral concern. In proposing their explanations forfirm performance heterogeneity, traditional theo-ries share the premise (often implicit) that wher-ever positive profits are to be found, competitorsare attracted like a swarm of locusts to a lus-cious crop of wheat. Thus, “competition” is typ-ically conceived of as an ever-present, corrosiveforce directed toward those enjoying positive eco-nomic profits.7 The entrants-as-a-swarm-of-locustsconception is one inherited from neoclassical eco-nomics. As Makowski and Ostroy (2001) explain(p. 484): “Neoclassical economists borrowed fromtheir classical predecessors the view that, in a pro-duction economy, perfect competition is the simple,inescapable conclusion of free entry. And with freeentry comes zero profits.” This notion of how com-petition works continues to run deep, both in strat-egy and beyond.8

The founders of modern strategy were inter-ested in explaining what seemed obvious by casualempiricism—that persistent performance differ-ences within industries was more the rule thanthe exception. Indeed, strategy presently sports aremarkable body of empirical work directly at oddswith the claim that competition inexorably drives

6 In this sense, the work surveyed here answers the challengeposed by Oxley et al. (2010).7 See, for example, the comments by Porter (1980: 5 and else-where).8 See, e.g., any strategy textbook for first-year MBAs or, ineconomics, historic work such as Schumpeter (1934) to moremodern pieces like Hopenhayn (1992).



industry profits to zero.9 However, to supervene thisclaim, one must find a way to escape the neoclassi-cal logic. One reasonable escape path is to propose aclass of barriers thought to interrupt the progressioninduced by free entry toward zero profits. This isprecisely the approach adopted by each of the majorschools: IP proposes barriers to industry mobility,the RBV proposes barriers to resource mobility,and TCE proposes barriers to perfect information.It is important to note that, even though it avoidsthe essential conclusion of the standard neoclassi-cal model, this “barrier view” retains its essentialpremise—that entry is an ever-present threat when-ever positive profits are present.10

The challenge we now pose is: Why not discardthe neoclassical premise altogether? Suppose theworld’s stock of economically productive resources(raw materials, capital, human beings, time, etc.) isfinite. Of all the assumptions one might entertain,the finitude of resources strikes us as supremelyreasonable—an immediate, universal feature of ourshared economic experience. Yet, this axiomaticpremise has serious implications. In such a world,logic does not dictate that the moment someresource becomes a source positive value capturefor its owner, other agents will reallocate their ownresources against it in a tsunami of competition.Rather, economic logic implies that agents allo-cate away from less profitable to more profitablesettings, and resource finitude implies that suchsettings need not be exhausted— in a finite world,economic profit may well be the rule rather thanthe exception.

The importance of this point cannot be overem-phasized in the context of strategy: global resourcefinitude implies that special barriers to competitionare neither necessary nor sufficient for the existenceof persistent economic profit. To be sure, there maybe settings in which such barriers are a proximatecause of profit persistence.11 That said, a body oftheory focused only upon this aspect of competitionmust, in itself, be incomplete. This carries with it the

9 To cite several compelling instances: Cubbin and Geroski(1987), Dosi (2007), Jacobsen (1988), Knott (2003), Madsen andLeiblein (2015), McGahan and Porter (1999), Mueller (1977,1986), Roberts (2001), and Villalonga (2004).10 Gans, MacDonald, and Ryall (2008) elaborate on this idea. Asan anonymous reviewer pointed out, the free-entry, “swarm oflocusts” idea appears most prominently and explicitly in RBVscholarship.11 By “special” we mean explicit barriers to the allocation orreallocation of economic resources.

empirical implication that variation in the strengthof special barriers is unlikely to be a robust predictorof variation in firm performance. As we show below,the finite agent/resource assumption is explicitlyembedded in the value capture model, even whenscaling up to global-economy-level scope.

The competitive-determinism blind spot

Theorists have an aversion to models prone toambiguous conclusions. For example, the two mar-ket models with which most strategy scholars arefamiliar are Cournot and Bertrand, the workhorsetools of industrial organization economics. Nosmall part of the popularity of these models arisesfrom their tractability, in particular, their ability toprovide exact, point-estimate solutions for profitsonce their parameters are fixed. In what follows,we show that the value capture model suggests thatcompetition is properly construed as placing boundson the amount of value an agent may capture with-out fully determining it. Taking the premises ofthe model seriously, this is a “feature not a bug”(in the parlance of our time). It says that, in gen-eral, competition defines a precise interval withinwhich an agent’s value capture lies; where withinthat interval actual capture lands is due to factorsother than competition.12 As we discuss in greaterdetail below, the theory points toward a new con-ception of “competitive intensity,” as well as theexistence and possible importance of “persuasive”resources, the express purpose of which is the cap-ture of more value within the range permitted bycompetition.13

The product-price blind spot

Harkening back to modern strategy’s foundingcorpus, Wernerfelt (1984) argues that, in order

12 On the issue of generality, it is worth reminding readers of Krepsand Scheinkman (1983), who illustrate the sense in which theCournot results are consistent with a Bertrand game with capacitycommitments. Similarly, Stuart (2005) shows that Cournot canalso be thought of as a special case of a cooperative game withcapacity precommitments. In other words, both Cournot andBertrand can be thought of as special cases of a cooperative game.A related line of research is pursued in Byford (2010).13 Here, it is useful to note that empirical research in strategy indi-cates that the firm effect is significant in explaining performanceheterogeneity (see Dosi, 2007, for a review). The possible impor-tance of a “persuasive” category of resources opens up a new areaof exploration for empirical scholars interested in explaining theseeffects (e.g., in the spirit of Roberts and Dowling, 2002; Villa-longa, 2004).



Figure 2. A balanced, but tangled, view of the one “force” of competition

to develop a deeper understanding of persistentperformance heterogeneity, analysis must shift fromthe pervasive price-product orientation of industrialorganization economics to a more strategy-usefulagent-profit perspective. The massive, resource-based view literature, which arose from thisobservation, extends the issue by positing thatpersistent performance heterogeneity is due to theexistence of unpriced resources (a result of “marketfailure”). The blind spot here is not in arguing thatthe product-price unit of analysis is problematicbut, instead, in not taking the agent-appropriationperspective sufficiently seriously. When the agentis the unit of analysis, the quantity of value itcaptures is, in essence, a price. It is the price ofengaging that agent—including its resources andcapabilities, themselves priced or not—in theactivities required to produce value. Market failureat one level does not imply failure at the other. Thevalue capture model shifts away from products andprices toward agents, the myriad value creationopportunities available to them, the value actuallyproduced, and what it takes in terms of valuecapture to engage them in the associated productiveactivities.

The web-of-transactions blind spot

The central insight of Porter (1979, 1980) is thatunderstanding competition requires a broad view ofwho counts as a competitor. In his famous “FiveForces” model, Porter (1979) argues that the setof active market participants—those agents whosedecisions are aimed at appropriating a share of thevalue produced within an industry—must includebuyers, suppliers, rivals, even potential rivals andthe producers of substitute goods outside the indus-try. Extending this insight to its logical conclu-sion, Porter’s (1979) model itself is incomplete: afirm’s appropriation ultimately depends upon theFive Forces groups, as well as suppliers of sup-pliers, substitute buyers in other markets, potentialentrants into distribution channels, and so on andso on. One gets a sense of the larger picture fromFigure 2, though this too falls short. In any givenindustry, value is created and appropriated throughcomplex webs of transactions pursued by multiplelayers of active, intelligent agents. Returning atten-tion to market models like Cournot and Bertrand,the problem is that the only active agents (i.e., theonly agents whose decisions are taken into account)



are typically the firm and its direct rivals. Theytoo are incomplete, often making implicit, ad hocassumptions that leave price-setting power in thehands of the firms, with all other market participantsplaying a passive role.

THE BIFORM MODEL

The biform model of Brandenburger and Stu-art (2007) is presently the state-of-the-art modelfor analytical work in strategy on value captureunder competition. The “biform” model is so-calledbecause it synthesizes two distinct areas of gametheory—noncooperative (NGT) and cooperative(CGT) —into a single model. The great strengthof NGT is its ability to capture strategic behav-ior; i.e., situations in which agent actions interactin the generation of outcomes and, therefore, inwhich assessing the behavior of others is impor-tant. The power of CGT is in its ability to ana-lyze value creation and capture in markets, espe-cially in settings where agents’ dealings do not fol-low some predefined process. In a biform model,each type of theory plays a role consistent withits strengths, thereby creating a complementarywhole.

Biform models consist of two stages. The firststage, NGT, includes all the agents whose actionshave a significant impact upon the outcomes for afocal firm. In an industry, this typically includesdirect rivals as well as, e.g., the agents in theother categories of Porter’s Five Forces frame-work (buyers, suppliers, etc.). In the NGT stage,agents take actions designed to “prepare the com-petitive battlefield” to their advantage—that is, tostructure their competitive environments in a waythat permits them to capture the most value possi-ble. Such actions include initiatives like marketingprojects, capacity decisions, new product or tech-nology introductions, mergers, recruiting policies,market entry, and so on. The joint actions takenby the agents in the first stage induce a particu-lar market environment in the second stage, CGT.Here, agents engage in organizing and executingthe “free-form” deals that result in the productionand capture of value. Essentially, the value cap-tured in second-stage competition serves as the thepayoff to the strategic action taken in the first. Webegin by elaborating the second (cooperative game)stage.

COOPERATIVE GAME STAGE

A cooperative game consists of a pair (N, v) whereN ≡ {1, … , n} indexes the n<∞ agents participat-ing in the market, and v, referred to as the char-acteristic function, is a map from each subset ofagents to the quantity of economic value producibleby the agents within it. The scope of this setup isbroad: it can be used for small interactions (e.g., nequal two to a few, such as firms competing for anacquisition or contemplating a strategic alliance fortechnology development), all the way up to thoseinvolving large numbers of agents (e.g., the globaleconomy). Given a group of agents G⊆N, v(G)denotes the amount of value the agents in G cancreate on their own (i.e., when the members of Glimit their transactions to one another only). Thus,the starting point for the CGT stage is an elaborationof how much value each of the various groups ofagents could create in this way were they to decideto do so. Out of all the possibilities so elaborated,some deals do occur, some value is produced, andsome share of it (possibly zero) is captured by eachof the agents in N. A distribution of value, denoted𝜋 ≡ (𝜋1, … ,𝜋n), is a list indicating how much eachagent captures in return for its productive activities(i.e., agent i captures 𝜋i).

Again, the central idea behind this setup is toshow how the feasible productive opportunities in amarket shape a firm’s ability to capture value. Thisrequires some linkage between v, which describesthe former, and 𝜋, which describes the latter. Thefirst step is to determine how much aggregate valueis actually produced within the market. The answeris straightforward: v(N) is, by definition, the aggre-gate value generated by the agents in N. In strat-egy applications, v(N) represents the actual, aggre-gate quantity of economic value that will be created(in the case of a theoretical prediction) or was cre-ated (in the case of an empirical analysis). It is akey “observable” associated with the model. Thestrategy literature commonly uses the special labelV ≡ v(N) to emphasize this distinction. The majorityof of the v(G)s for groups other than N never actu-ally materialize. These unrealized possibilities areconstitutive of competition and, as such, shape thedistribution of value.14

14 When the value created within a market arises as the aggregateof productive activities by distinct groups, then the economicvalue created by each of those particular groups is, in fact,realized.



Note that V and the v(G)s are real numbers. Theusual interpretation is that v(G) is the economicvalue created by the transactions that would actuallyarise were transactions restricted to the agents inG. However, depending upon the application, theycan also represent cash, expected value, net presentvalue, etc. Frequently, authors assume that v issuperadditive: the union of two disjoint groupsproduces at least as much as the sum of whatthe groups produce independently. The rationalefor this is that the transactions associated with theindependent group values are still feasible eventhough new, cross-group transactions may ariseunder the union of the two groups.15

How do the value creation opportunities shapevalue capture? Typically, two assumptions aremade. The first is a feasibility assumption:∑

i∈N

𝜋i = V , (1)

i.e., the amount of value captured equals the amountproduced. The second is a competitive consistencyassumption: for every group G⊂N,∑

i∈G

𝜋i ≥ v (G) , (2)

i.e., the aggregate value captured by the agentsin G must be at least as large as the value theycould produce on their own. Suppose, in returnfor their contributions to the production of V , theagents in G face deals such that

∑i∈G 𝜋i < v (G).

Then, the agents in G could eschew those deals and,instead, undertake to produce v(G) under terms thatwould make each and every one of them strictlybetter off.16 In the strategy literature, a distributionof value that meets the feasibility and consistencyconditions is said to be competitive. The set of allsuch distributions is referred to as the core.17

15 In most strategy applications, this assumption isinnocuous—although it does rule out cases in which somesubset of agents creates negative externalities with others (and,additionally, in which economic activities cannot be organized insuch a way as to neutralize them).16 Some authors refer to this as the “stability” condition; theidea being that aggregate production of V is assured only if thiscondition is, by necessity, met.17 This term is imported from economics, which, like most eco-nomics terminology associated with CGT, is not especially helpfulor clarifying. There are many other approaches to analyzing thesolutions to cooperative games in strategy settings. For example,de Fontenay and Gans (2008) use the Shapley value, which has the

In what sense are distributions that meetEquations (1) and (2) “competitive”? The answerlies in thinking of V as the aggregate value arisingfrom a specific set of actual transactions. Think ofthese transactions, the value they create, and theshares of value captured by the agents involved asobservables (i.e., as data or potential data). Thev(G)s, then, are the feasible values produceablethrough alternative transactions and groupings. Inthis context, v(G) should reflect the actual eco-nomic value that would be produced via some otherspecific set of transactions, including any costsassociated with organizing them (e.g., switchingcosts). Then, the alternative transactions competewith those anticipated in the production of V . Or, asviewed from the agent perspective, the members ofG provide competition for one another and againsttheir respective transaction partners in the creationof V .

To interpret competitive distributions in a strat-egy context, bring Figure 2 to mind. The firmengages in specific transactions with a specific net-work of suppliers and buyers resulting in the cre-ation of actual economic value. At the same time,rivals, potential entrants, and producers of substi-tute products offer the firm’s customers and suppli-ers productive alternatives. These agents competeagainst the firm and for its partners. Simultaneously,rivals, potential entrants, and substitutes operate atevery level of the value chain, thereby providingcompetition for the firm and against its partners.The characteristic function v provides a summaryof all these competitive alternatives. This leads tothe following insight.

Insight 1

There is only one force of competition, not five orsome other number. Competition is implied by atension between having to neutralize all the com-peting alternatives in Equation (2) using the lim-ited value produced in Equation (1). These condi-tions impose value capture consequences on everyagent in the market. That is, while its value captureimplications may vary from agent to agent, the setof competitive consistency conditions from whichthose implications arise is the same for every agent.All agents face a tension between Equations (2) and

feature of providing point-estimates in place of core intervals. Aswe explain below, however, the identification of intervals is a use-ful feature with respect to understanding one’s strategic situation.



(1). From the firm’s point of view, the effects ofthis tension run in two directions: one in its favor(providing it more options), the other against it (pro-viding others more options). Thus, the CGT concep-tualization treats competition as a single force, withsymmetric structure and two effects, one good andone bad, on each agent.

Insight 2

Competition bounds an agent’s value capture pos-sibilities. Mathematically, Equations (1) and (2)imply an interval of value capture possibilities foran agent. That is, for every agent i, competitiondetermines an interval, with bounds 𝜋min

i ≤ 𝜋maxi ,

such that 𝜋i is part of a competitive distribution ofvalue if and only if it is contained in

[𝜋min

i , 𝜋maxi

].

This is contrary to the point-estimate intuitioninherited from familiar models like Cournot andBertrand. Competition for an agent pushes up 𝜋min

i ,while competition against it drives down 𝜋max

i .By way of analogy to bilateral trade, 𝜋max

i is themarket’s “willingness-to-pay” for agent i’s involve-ment in the creation of V . Similarly, 𝜋min

i is,loosely, i’s “willingness-to-sell” that involvementto the market. Both values are pinned down bycompetition—implicit in the feasible alternatives toproducing V available to market participants.

Insight 3

Competitive intensity with respect to agent i shouldbe conceptualized with respect to the length of[𝜋min

i , 𝜋maxi

]. At its most intense, 𝜋min

i = 𝜋maxi .

While the usual conception of extreme competi-tive intensity (i.e., “perfect competition”) may hold(𝜋min

i = 𝜋maxi = 0), so may competitive intensity at

the other end of the spectrum (𝜋mini = 𝜋max

i = V),and everything in between (Montez, Ruiz-Aliseda,and Ryall, 2015). Thus, extreme competitive inten-sity is neither good nor bad per se. At the same time,the model admits situations in which 𝜋min

i = 0 and𝜋max

i = V; i.e., competition plays no role in deter-mining what the agent captures. If these distinctionsare features of real-world industries, they have sub-stantial implications for strategy scholars and prac-titioners alike.

Insight 4

Value capture depends upon two classes ofresources—competitive and persuasive. Which is

class is most important varies with competitiveintensity. The value captured by firm i is the sum ofits competitively guaranteed minimum plus someportion of its feasible interval, the latter obtainedvia extra-competitive means. Formally,

𝜋i = 𝜋mini + 𝛼i

(𝜋

maxi − 𝜋

mini

), (3)

where 𝛼i ∈ [0, 1] is called i’s appropriation factor.The 𝛼i parameter summarizes the effect of allsuper-competitive determinants of firm i’s abilityto capture value—i.e., factors that induce othersto part with value beyond the implications of Con-dition (2).18 When competitive intensity is slack,the control of superior “persuasive resources” isthe key to value capture (Ryall, 2013). From apositive perspective, the prediction here is thathigh-performing firms in low-intensity industrieseither control superior persuasive resources orenjoy institutional advantages (e.g., bidding norms)vis-à-vis the other agents. At the other end of thespectrum, when intensity is at its most extreme,persuasive resources play no role. Accordingly,empirical analyses that fail to account for vari-ation in intensity/control of superior persuasiveresources are unlikely to provide consistently goodexplanations of firm performance heterogeneity.19

NONCOOPERATIVE GAME STAGE

Ultimately, strategy scholars and practitioners alikeare interested in understanding how firm strategiesaffect value capture. To investigate this issue, Bran-denburger and Stuart (2007) propose linking thecompetitive (CGT) stage to a preceding strategic(NGT) stage by way of a “biform game.” The goalis to admit a model in which the agents vie with oneanother to alter the competitive landscape (i.e., thesecond-stage cooperative game) to their advantages.For example, firm strategies may involve invest-ments in cost-reducing process technologies, capac-ity expansion, new market development, person-nel practices, attempts to adjust corporate culture

18 When used prospectively, the appropriation factor can bethought of as a subjective estimate of an agent’s own ability topersuade its transaction partners to part with value, by all meansother than pointing out the implications of v.19 We are presently unaware of any explicit investigations into thecompetition/persuasion resource dichotomy. However, the theoryis consistent with phenomena such as the investments in theacquisition of partner information prior to price negotiations, asdescribed by Madsen and Leiblein (2015).



and so on. Simultaneously, distributors may adoptnew technologies, end users may hire negotiationexperts, suppliers may implement new informationsystems, etc. All of these activities, presumably theresult of each agent’s business strategy, interact todetermine the actual value creation opportunitiesavailable in the marketplace.

Formally, each agent i∈N begins with a setof feasible actions, Ai, with typical element ai,an action. Action sets can be finite or infinite,scaler or multidimensional, depending upon theapplication. Since the first stage is a noncooperativegame, it can take strategic or extensive form. Thelatter is appropriate for investigating situations inwhich move timing and information issues areimportant. To keep it simple, we will describe thegeneral strategic form: each agent chooses its actionwithout knowledge of the other agents’ choices (i.e.,simultaneous-moves). The result is a list containingeach agent’s action, referred to as an action profileand denoted a≡ (a1, … , an). The set of all suchprofiles is denoted A.

The idea is that the joint actions of the marketparticipants interact to influence both the charac-teristic function, v, as well as each agent’s appro-priation factor, 𝛼i ∈ [0, 1], ultimately determiningeach agent’s appropriation, Equation (3). Thus, theparameters describing value capture in the secondstage can be identified by action profile superscripts.For example, two different action profiles a anda’ induce cooperative games (N, va) and (N, va’)as well as appropriation factors 𝛼a

i and 𝛼a′

i foragent i, etc. Then, each agent’s payoff in the sec-ond stage is assessed according to Equation (3).Thus, the value captured in the market stage is thepayoff to an agent’s action in the strategic stage,given the effects of everyone’s actions. Formally,agent i’s value capture given action profile a can bewritten

𝜋i (a) = 𝜋mini (a) + 𝛼

ai

(𝜋

maxi (a) − 𝜋

mini (a)

), (4)

where 𝜋maxi (a) and 𝜋min

i (a) are the bounds impliedby va and 𝛼a

i is the net effect on i’s persuasiveeffectiveness implied by the actions in a.

In closing this section, it is worth pointing outthat the biform setup opens strategy analysis tothe entire toolbox of NGT. For example, moststrategy applications to date have used Nash, orBayesian Nash, as a solution concept in making the-oretical claims in specific settings. However, those

interested in strategic settings of bounded rational-ity might employ subjective equilibrium (Kalai andLehrer, 1995; Ryall, 2003, for a strategy applica-tion) or ambiguity-averse Nash equilibrium (Ells-berg, 1961; Ryall, 2009, for a strategy application).On issues of persistent performance heterogeneity,the model can be expanded into a repeated game.In addition, methods used in studies of cheap talk,information asymmetry, and behavioral economicscan all be adapted to this framework. All of thesepowerful modeling techniques can be brought tobear to examine how firms in a wide variety of set-tings behave and how those behaviors affect valuecapture under competition.

For example, consider application of subjec-tive equilibrium in a simple setting. A subjectiveequilibrium arises when (1) each agent chooses astrategy optimizing its expected payoffs given itssubjective beliefs and (2) actual expected payoffsinduced by these strategy choices are consistentwith subjective expectations. In other words, theconsequences of agent actions are consistent withtheir subjective beliefs along the path of play—butmay be wrong in critically important ways off theequilibrium path.

To see this, suppose there are n symmetric firmsfacing n buyers. Each firm can produce one unit ofproduct at cost c. Buyers value one unit of productat u= x+ c where x> 0. Here, each firm is essen-tially in a pure bargaining contest with its buyer:any split of x between the buyer and seller is possi-ble. Assume the firms begin with 𝛼i = 0. However,in the NGT stage, each firm chooses either to investin bargaining training or not. The cost of the train-ing is 0< z< x, the consequence of which is to shiftthe firm’ 𝛼i from 0 to 1. The unique Nash equi-librium for this game is for every firm to invest inthe persuasive resource and receive a CGT-stagepayoff of (x− z)> 0. Suppose, however, that thefirms believe (incorrectly) that they are in a tradi-tional “perfectly competitive” market—that is, inwhich 𝜋max

i = 𝜋mini = 0. In such a situation, persua-

sive resources are useless. Based upon this belief,the subjectively optimal choice is not to invest inbargaining. Then, in the CGT stage, 𝛼i = 0 for allfirms and, as a result, actual value captured is 𝜋i = 0.Of course, this is exactly as expected. This is a sub-jective equilibrium: poor performance is attributedto tough competition when, in fact, it is due to zeroinvestment in persuasive resources—and no invest-ment will occur as long as markets are believed tobe tough.



COMPARISON TO OTHER MODELINGAPPROACHES

Many readers for whom the preceding formalismis novel will already be quite familiar with thestandard models of NGT (e.g., Cournot, Bertrand,Stackelberg, and variations). These models areworkhorse theoretical tools in industrial organi-zation economics. Thus, a perfectly legitimatequestion is: Why should strategy go in the directionof biform games rather than follow the standardadopted by economics? Essentially, this articletaken as a whole is intended to provide a compellinganswer to that question. Even so, this is a goodpoint at which to provide a couple of more specificanswers to it.

First, optimal model selection is highlycontext-dependent—which approach is “best”depends upon the questions being asked. That said,our hope is that the preceding discussion illustrateswhy the biform model is ideal when the questionsbeing asked are general ones about value creationand capture in market settings. In the standardmarket models of NGT, a raft of assumptions mustbe made, including whether managers set prices orquantities, the precise order of moves, what man-agers know when they move, specific functionalforms for costs and demand, etc. If these detailsare available to the investigator, great. Most of thetime, however, economic activities in real marketsoften involve messy, arm’s-length wheelings anddealings that are incompatible with this minutelevel of specificity. The CGT framework, in con-trast, invokes relatively weak premises. These grantthe analyst considerable freedom of interpretationwith respect to the details of value creation beingrepresented by the formalism. As a result, thefindings derived via CGT tend to be applicable toa broad spectrum of settings of interest to strategyscholars.

Second, there are instances of papers that provideformal translations between the various standardmodels used to analyze competition. The mostfamous of these is Kreps and Scheinkman (1983).In their model, firms choose capacities ahead ofa Bertrand price-setting game. The main result isthat, under certain rationing rules, the equilibriumof the game gives rise to the same equilibriumresult in prices and quantities as would arise under asuitably-chosen Cournot game. In other words, theyshow the sense in which Cournot can be thought ofas a special case of a Bertrand model with capacity

choices. Stuart (2005) demonstrates that Cournotcan also be thought of as a special case of a biformgame with capacity choices. The mapping fromsimultaneous-move Bertrand games to CGT gamesthat result in equivalent value-capture outcomes isrelatively trivial. Hence, Cournot and Bertrand areoften special cases of a more general cooperativegame.20

Choice of solution concept is another issue. CGTsports a number of different solution concepts—thecore, stable set, strong epsilon-core, Shapley value,kernel, nucleolus, and Nash bargaining. In strategy,the core is typically the solution concept of choice.Why the core? Because, as already noted, it imposesa weak set of competitive consistency conditionsthat seem reasonable in market settings. Moreover,we argue throughout, the identification for eachagent of an interval of appropriation consistent withthese conditions (i.e., rather than a point-estimate)is actually a desirable feature—one that generatesseveral important insights about the effects of com-petition on value capture.

There are examples of biform game applicationsoutside of strategy that use other solution concepts.For example, the property rights theory of the firmby Hart and Moore (1990) uses the Shapley value.The Shapley value is sensible in this setting becausethere are no competitive externalities requiring res-olution outside of the game. This is not the casein many strategy contexts (de Fontenay and Gans,2005, 2014). Also, some recent industrial organiza-tion papers doing structural estimation of verticalrelations use the Nash bargaining solution for theCGT stage (Collard-Wexler, Gowrisankaran, andLee, 2014). This also poses difficulties for dealingwith competitive externalities (that arise when com-peting firms are prevented, say by antitrust laws,from negotiating directly with one another), but ithas proven to be tractable for the study of verticalrelations when downstream firms operate in distinctmarkets.

The primary issue raised against the core is thatthe primitives of value creation may be such suchthat there are no 𝜋is satisfying conditions (1) and(2). This is of sufficient concern to Lippman andRumelt (2003) that, at the same time they argueeloquently in favor of using CGT as a foundationfor strategy theory, they also express reservations

20 Byford (2010) provides a variant on the biform model in whichthe second stage is a CGT, but with linear prices as assumed byKreps and Scheinkman.



about using the core as a solution concept. Thesource of the problem in such situations is alwaysthe same: V is too meager to be shared in a waythat prevents every group G from acting on its alter-native, v(G).21 The frequency of such situationsin the real world is an open empirical question.22

Moreover, Stuart (1997) demonstrates that the coredoes, in fact, exist for a wide range of situationsrelevant to strategy research. In our judgment, theoverall benefits of using the core to develop strat-egy theory, particularly in terms of the insightsit provides into value capture under competition,presently outweigh these concerns.

GENERAL PRINCIPLES

The extant theoretical literature using cooperativeor biform games to investigate issues in businessstrategy can be categorized into two substreams.The first takes characteristic functions as given,operating at the general, abstract level to developgeneral principles with respect to value creation,competition, “persuasive” resources, and firm per-formance. The second builds up the characteristicfunction from primitives that are relevant to a partic-ular issue. For example, the analysis may be specificto two-sided markets, productive networks, or dif-ferentiated products. These studies begin with spe-cific assumptions about agents and their roles, buyerpreferences, production technologies, costs, capac-ities, etc. The primitive assumptions are then usedto construct the implied characteristic functions thatarise from the agents’ various strategic choices (i.e.,in a biform game). In this section, we focus upon thehistorical development of the former and highlightits most significant findings.

The first paper to use CGT to examine value cap-ture in strategy is Brandenburger and Stuart (1996).This paper introduces the strategy audience to theformal notion of agent added value.23 Informally,an agent’s added value is the difference between

21 Put another way, for any collection of nontrivial v(G)s, thereis a minimum V below which there are no distributions of valuesatisfying core conditions (1) and (2).22 In the real world, there are many ways competition may besoftened to admit existence. For example, if antitrust law prohibitsthe agents in G from transacting, then v(G)= 0. Alternatively, ifthe agents in G are unaware of their productive possibility then,again, v(G)= 0.23 This idea arises in economics at least as early as Edgeworth(1881). More recently, economists Makowski and Ostroy, in asubstantial line of joint work, demonstrate the importance of

the aggregate value created in a market in whichthe agent participates and the amount of value thatcould be created were that agent to be removed fromthe market (alternatively, were all the other agentsto shun transactions with that agent). Formally, theadded value of agent i is:

avi ≡ V − v(N−i

), (5)

where N−i denotes the set of agents other than i.

Principle of the added value (GP1)

From Equation (5), it follows that added valueplaces an upper bound on what an agent can appro-priate (Brandenburger and Stuart, 1996): If 𝜋i > avi,then satisfaction of Equation (1) implies

∑j∈N−i

<

v(N−i

), which violates Equation (2). In words: pos-

itive added value is a necessary condition for valuecapture. Here, competition works against i in thesense that, the agents on the other side of the trans-actions with i that contribute to V must be inducedto freely accept these and not some other set oftransactions from which i is excluded—in this case,the ones involved in the production of v(N−i). Theadded value of i is an upper bound on the otheragents’ “willingness-to-pay” for i’s involvement inthe production of V . When 𝜋i = avi, agent i is saidto be a full appropriator.

Principle of adding up (GP2)

Brandenburger and Stuart (1996) clearly state thatadded value is a necessary but insufficient condi-tion for value capture (p. 14). Nevertheless, theiranalysis proceeds (from p. 15) under the premisethat achieving positive added value “is the pathto value appropriation” (i.e., rather than being onestep on that path). They then illustrate severalexamples in which every agent captures exactly itsadded value—no more, no less. These examplesare built on an interesting condition known as the“adding-up” property: if the agent added valuesthemselves sum to V, then every agent captures

understanding that, in a general equilibrium model, agents andthe value they capture are the mathematical dual to solutionsbased upon products and prices (see, e.g., Makowski and Ostroy,1995). They refer to added value as “agent marginal product.”Brandenburger and Stuart (1996) cite this work as having hadin important influence on their paper (p. 23). See Makowski andOstroy (2001) for a wide-ranging, highly accessible review.



precisely its added value. Formally, if∑

i∈N avi = Vthen, for all i, 𝜋min

i = 𝜋maxi = avi.

The preceding result corresponds to what gen-eral equilibrium theorists Makowski and Ostroy(1995, 2001) define as “perfect competition.” Strat-egy scholars who are used to identifying “perfectcompetition” with the zero profit world induced byfree entry may find this definition jarring: here, per-fect competition implies everyone is a full appropri-ator. Note that this definition includes the traditionalmeaning of perfect competition as a special case:under free entry, added values are driven to zero and,hence, so is value capture (agents are, trivially, fullappropriators). Now, competition is “perfect” in thesense that it squeezes everyone’s core interval to asingle point (equal to the added value).

Principle of the minimum residual (GP3)

A grasp of the preceding, counterintuitive con-ceptualization of perfect competition invites schol-ars to stop thinking of competitive intensity as aforce of pure badness. GP2 shows that, under theright circumstances, competitive intensity actuallyguarantees full appropriation. This finding natu-rally leads one to wonder about cases in whichcompetition is not so intense as to induce trivialintervals. MacDonald and Ryall (2004) note theabsence of attention in strategy research on the goodside of competition—namely, its potential effectof guaranteeing positive value capture (𝜋min > 0).They define agent i’s minimum residual: mri = V −∑

j∈N−iavj. It follows that every agent must capture

an amount of value at least as great as its minimumresidual. Formally, 𝜋i ≥mri. This is implied by thestraightforward logic of GP1: since added value isan upper bound to value capture, if the sum of every-one else’s added values (i.e., besides i’s) is less thanV , then i must receive (at least) the difference. WhileGP3 is simple to derive, its interpretation is subtle.Agent i’s minimum residual is an indirect conse-quence of the n− 1 alternatives to exclude preciselyone of the other market participants from the trans-actions that produce V . When other participants addmeager value compared to i, implicit competitionfor i is high, guaranteeing i positive value capture.

Principle of the essential tension (GP4)

The preceding are all based upon added value,an intuitive and technically simple idea. However,added value ignores the lion’s share of the feasible

opportunities to create value elaborated in compet-itive consistency condition (2). The agent addedvalues depend upon the n groups of the form N−i.More generally, however, there are 2n − 1 possiblegroups that can be formed from the n agents in N.If the number of agents in a market is even moder-ate, added value is unlikely to account for much ofcompetition’s overall impact on value capture. Hav-ing established GP3, MacDonald and Ryall (2004)go on to examine the effect of all the alternativeson an agent’s competitive minimum. Specifically,they seek to characterize the conditions under whichcompetition alone guarantees that an agent mustcapture a positive share of value. In service of thisgoal, they define an agent’s minimum value and useit in their main proposition.

Agent i’s minimum value, denoted mvi, is thesolution to the following optimization problem:minimize the aggregate amount of value requiredto make sufficient payments to agents other than isuch that i receives zero and, yet, cannot induce anygroup to deviate from the production of V . Formally,mvi is the solution to the following linear program:

mvi ≡ min𝜋∈ℝn

+

{∑j∈N

𝜋j|𝜋i = 0 and∑k∈G

𝜋k ≥ v(G+i

)for all G ⊂ N−i

}, (6)

where G+i is the group G with i added. The impor-tant thing to note is that, the more productive i iswith the various groups, the more the aggregatevalue required to pay off the other agents such thati—facing zero value capture—cannot organize adeal with the members of some that makes every-one in it (including i) strictly better off than whatthey would get by participating in the productionof V . Put differently, if “the market” proposes thathighly productive agent i receive a “price” of zeroeconomic value in return for its participation in cre-ating V , the other agents will need to receive largequantities of value if i is to be prevented from induc-ing them to deviate to some other activities.

Once the concept of minimum value is grasped,it is easy to see that V <mvi if and only if 𝜋i > 0;i.e., competition guarantees strictly positive valuecapture when a particular tension arises between anagent’s potential to create value versus the actualquantity of value it creates. Note that mvi dependsonly upon the groups in which i is a member. Thus,



cf

u1

u2=cr

Transaction

f and b1 r and b2

Total value created> Value captured by b1

Value captured by f

No value created or captured byr and b2—parties just indifferentto the transaction

Figure 3. Perfect competition

mvi is an important measure of competition fori. MacDonald and Ryall (2006) explore whetherthe entry of any new agent (direct competitor,supplier, employee, buyer, etc.) affects the firm’scompetitively guaranteed value capture—‘underwhat conditions is this guarantee created, destroyed,or maintained? In particular, they identify whichcategories of value-creating groups—those thatinclude the entrant, exclude it, include only the firmand the entrant, and so on—matter for the creation,destruction, or maintenance of the guarantee.

A new example ending in a paradox

Before moving on to the last general principle inthis section, it may be instructive to illustrate thesevarious results with a series of related examples inthe simplest context possible—a small, two-sidedmarket. To start, assume there are two firms, fand r (for “rival”). Each firm has one unit ofcapacity with which to make a product at constantmarginal cost cf and cr, respectively, with cf < cr.

There are two buyers, 1 and 2, who each wishto consume exactly one unit of product. Supposeeach buyer views the firms as indistinguishable:ui denotes the utility enjoyed by buyer i fromconsuming one unit of either firm’s product. Atthe same time, assume the buyers are heterogenousin their utilities such that u1 > u2 = cr. Since thebuyers view the firms’ products as identical, whichbuyer buys from which firm is not a critical issue:the overall value created in this market should beV = u1 + u2 − cf − cr or, since u2 = cr, V = u1 − cf .Assume the agents’ outside options are normalizedto zero.24 See Figure 3.

The first step is to compute added values. Itshould be easy to see that removing r or buyer2 from the market has no effect on the aggregatevalue produced. Therefore, avr = av2 = 0. In theabsence of f , r and buyer 1 transact to producev({r, 1})= u1 − cr > 0. Therefore, f ’s added value isavf = cr − cf (the incremental effect of its superior

24 Setting v({i})= 0 is without loss of generality.



Table 1. Implications of added values

Firm f Firm r Buyer 1 Buyer 2

Added value cr − cf 0 u1 − u2 0Implication for 𝜋max

i 𝜋maxf ≤ cr − cf 𝜋max

r = 0 𝜋max1 ≤ u1 − u2 𝜋max

2 = 0Implication for 𝜋min

i None 𝜋minr = 0 None 𝜋min

2 = 0

Table 2. Implications of adding up

Firm f Firm r Buyer 1 Buyer 2

Added value cr − cf 0 u1 − u2 0Implication for 𝜋max

i 𝜋maxf = cr − cf 𝜋max

r = 0 𝜋max1 = u1 − u2 𝜋max

2 = 0Implication for 𝜋min

i 𝜋minf = cr − cf 𝜋min

r = 0 𝜋min1 = u1 − u2 𝜋min

2 = 0

cost position). Similarly, removing buyer 1 resultsin a transaction between f and buyer 2, whichimplies av1 = u1 − u2 (the incremental effect ofthe greater value it places on these products). Theimplications of GP1 are summarized in Table 1.

As it turns out, there is much more we can say. Amoment of reflection indicates that GP2 applies:∑

i∈N

avi = cr − cf + 0 + u1 − u2 + 0

= u1 − cf .

Since u1 − cf =V , we know that each agent mustreceive exactly its added value. Competition is fullydeterminative; there is no room for extracompetitivevalue appropriation.

When adding-up is satisfied, all minimum residu-als equal their corresponding added values. Since anagent can get no less than its minimum residual andno more than its added value, it must get exactly thisamount. Here, competition for each agent (as mea-sured by minimum residual) is perfectly balancedwith competition for their transaction partners (asmeasured by added value), thereby guaranteeingthat every agent is a full appropriator (see Table 2).

GP3 also holds. To see this, begin by impos-ing 𝜋f = 0 and ask how much value is required toensure that f cannot offer the buyers a profitableside deal. The answer is straightforward. If 𝜋f = 0,buyer 1 must capture at least 𝜋1 = u1 − cf . Other-wise, competitive consistency fails since it would bethe case that 𝜋f +𝜋1 < v({f , 1})= u1 − cf . Similarly,buyer 2 must capture at least 𝜋2 = u2 − cf > 0. Hap-pily for f , V = u1 − cf is not sufficient to make bothpayments, which is what is required to neutralize

f ’s ability to upset the production of V in theevent that 𝜋f = 0: if the buyer transacting with finsists on 𝜋f = 0, f can always make a deal withthe other buyer that makes both it and the otherbuyer strictly better off. Therefore, we know that𝜋min

f > 0—competition for f is too intense for it tocapture no value (which we already knew, but nowsee as a result of the essential tension). The samereasoning applies to buyer 1. Finally, it is not hardto see that mvr =mv2 =V . There is exactly enoughvalue available to assure that r and buyer 2 receiveno economic value.

The paradox

Assume everything is as before, with the exceptionthat now the buyers are identical—each values oneunit of consumption from either firm at u> cr. Now,V = 2u− cf − cr, arising from two transactions, oneeach between a buyer and a firm. Focus attention off . The competitive distribution in which f capturesits maximum is the one in which the firms arefull appropriators. That is, 𝜋max

f = avf = u − cf . The

worst f can do is to capture 𝜋minf = cr − cf . The

reason is that r’s buyer competes with f ’s buyer todo a deal with f because it is the efficient producer.Thus, if f ’s buyer insists on leaving it with less thancr − cf , r’s buyer can agree to a deal that makes bothstrictly better off.

Now, suppose f is not happy with 50 percentmarket share and, being the efficient producer,decides to “own” the market by expanding capacityto two units. How much better off is f followingsuch a move? Both buyers transact with f to produceV

′ = 2(u− cf ). If f is removed from the market,



one buyer will still be able to transact with r.Therefore, its added value is av′f = 2

(u − cf

)−(

u − cr

)= u − cf + cr. Note well that av′f > avf .

In this situation, there is nothing preventing thebuyers from being full appropriators: feasibilityand competitive consistency conditions are allsatisfied in such a scenario. Therefore, 𝜋min′

f = 0.Moreover, the buyers must each appropriate u− cr.Any amount less than this allows the buyer to cut adeal with r that makes both better off. Therefore,𝜋max′

f = 2(u − cf

)− 2

(u − cr

)= 2

(cr − cf

).25

Suppose f ’s efficiency advantage is small relativeto the quality of its product—specifically, that2(cf − cr)< (u− cf ) – then, 𝜋max′

f < 𝜋maxf .

In other words, reasonable parameters can befound for this example such that f unambiguously(1) increases its added value through the capac-ity expansion and (2) worsens its situation withdecreases in both its minimum and maximum. Thisoutcome is so counterintuitive that it has been usedby some in economics to argue against the use ofthe core as a solution concept.26 As we now show,the result is actually quite sensible once the shiftingeffects of competition in this example are properlyunderstood.

Principle of competitive intensity (GP5)

Montez et al. (2015) are motivated by Insights 1–3of the earlier section. In particular, they investigateincreasingly complex notions of “competitive inten-sity,” each of which is consistent with the thrust ofthese insights. As it turns out, the simplest of thesefully explains why the preceding result, thoughcounterintuitive, is economically intelligible.

To see this, begin by defining a focal valuepartition, denoted 𝒫 ∗, for a cooperative game.Mathematically, 𝒫 ∗ is a collection of subsets ofagents with the following properties: (1) 𝒫 ∗ is apartition of N and (2)

∑G∗∈𝒫 ∗ v (G∗) = V .27 The

groups in 𝒫 ∗ are called value networks.28 This

25 Firm r is still in the market. Obviously, the persistent lack ofrevenue must induce exit. However, it is sufficient that r’s capacityutilization drops to less than 100% (i.e., and possibly greater than0%).26 See, e.g., Postlewaite and Rosenthal (1974).27 A partition of N is a collection of disjoint groups, the union ofwhich equals N.28 The asterisks on the groups indicate their status as valuenetworks.

structure is meant to represent industries containingdistinct value chains—each value network is aset of agents linked to one another through theirtransactions, with the value created by the industrybeing equal to the aggregate of the value created byeach network. For any particular game, there maybe many candidates for 𝒫 ∗ (i.e., many ways toallocate the agents into groups such that the groupvalues add up to V). The label “focal” is intendedto convey the idea that 𝒫 ∗ corresponds to a realsituation; e.g., the actual transactions an empiricistwould identify upon observation of the industry.

To understand the simplest notion of competitiveintensity and grasp its implications for value cap-ture, assume an industry is decomposable into twoor more value networks. The notion of competitiveintensity is based upon added value. Symbolically,if G* is a value network in which firm f is not amember, then f ’s added value to G* is given by

avf (G∗) = v(

G∗+f

)− v (G∗). If avf (G

*)> 0, then

the value network G* competes for f —the membersof that network would like f to join because, in thatway, more value will be produced. Competition ofthis kind raises f ’s minimum. Indeed, 𝜋f ≥ avf (G

*).The reason is that the agents in a value networkmust, in aggregate, capture exactly the value pro-duced by that network; i.e.,

∑i∈G∗ 𝜋i = v (G∗). If,

in addition, 𝜋f < avf (G*), then the group comprised

of G* and f violates the competitive consistencycondition.

An agent’s “first-order competitive intensity”(FOCI) is defined as the maximum value added toa value network outside its own. The general prin-ciple is that every agent must capture value at leastas large as its first-order competitive intensity. Theeconomic intuition is immediate from the precedinglogic. Consistent with Insight 1, the logic appliessymmetrically to all the other agents in f ’s ownvalue network. The greater the competitive inten-sity for f ’s transaction partners in that network, theless value is left over for f —its maximum is drivendown. This is consistent with Insight 2. As com-petitive intensity for f and its transaction partnersincreases, f ’s competitive interval narrows, consis-tent with Insight 3.

Our earlier, “paradoxical,” example is fullyexplained by this simple notion of competitiveintensity. Let us see how, by assuming the param-eters are such that the nonintuitive outcome arises;i.e., 2(cf − cr)< (u− cf ). Consider the focal valuepartition prior to the capacity expansion. Suppose



f sells to buyer 1 and r to buyer 2. Then, thevalue networks can be denoted F* = {f , b1} andR* = {r, b2}. These represent simple transactions,with v(F*)= u− cf and v(R*)= u− cr. This impliesV = v(F*)+ v(R*). Therefore, 𝒫 ∗ = {F∗,R∗}fulfills the requirements for a value network. Weloosely conceive of buyer 2 creating competitionfor f because it provides an opportunity to createmore value than does transacting with r. FOCIquantifies this: the added value of f to R* is cr − cf(in the group containing f , r, and b2, b2 simply dealswith f rather than r). Therefore, 𝜋f ≥ cr − cf . Atthe same time, buyers 1 and 2 are interchangeable.As a result, there is no FOCI for b1: inserting b1to R* does not create any additional value. Thus,𝜋f ≤ u− cf .

How do the economics change when fexpands capacity? First, both buyers trans-act with f . We have F*′ = {f , b1, b2} andR*′ = {r} with v(F*′

)= 2(u− cf ), v(R*′)= 0 and

V = v(F*′)+ v(R*′

). Now, having enticed b2 intoits own transaction network, competition for fdisappears. Simultaneously, the empty capacity inR*′

creates competition for both of f ’s buyers.29

The loss of competition for f drops its minimumand the appearance of competition for f ’s buyersdrops its maximum. The FOCI for the post-capacityexpansion of f is zero, while the FOCI for eachbuyer is u− cr.

Beyond the economic insights provided, there area couple of additional points worth mentioning withrespect to this novel conceptualization of competi-tive intensity. First, the definition of FOCI presentsan alternative solution concept to the core. Second,unlike the core, it always exists. Third, the con-cept is simple—it relies on a very small number ofgroups, as compared to the core. Moreover, it is setup to facilitate reference to actual transactions (i.e.,as embodied in the focal value networks). Thesefeatures make it much friendlier to empirical anal-ysis than findings that rely on the entire set of coreconstraints. Finally, it provides a basis for relatedextensions, several of which are investigated (e.g.,a notion of indirect competition called second-ordercompetitive intensity).

29 Note that the effect would have been the same had the examplebeen such that several other buyers preferred r’s product andremained with it. The key to the outcome is that b2’s switch leavesr with one unit of slack capacity.

APPLICATIONS TO SPECIAL SETTINGS

In this section, we turn our attention to papersthat approach their analysis from the bottom up.That is, whereas the work cited in the previoussection begins with an arbitrary characteristic func-tion (and, hence, provides abstract but general find-ings about the nature of value creation and capturein markets), the following work starts with specificassumptions that are relevant to a specific setting ofinterest, and then analyzes performance in light ofthe resulting characteristic function.30

The application papers reviewed below are a sig-nificant complement to those focused on the devel-opment of general principles—from them, a deeperunderstanding emerges of the theoretical links fromvariation in agent resources, skills, strategies, andcontexts to variation in the force of competitionand effectiveness of persuasive abilities (and, hence,in performance itself). In the following discussion,the connections made from the specific findings ofthese papers to the general principles elaboratedabove are our own, with the intention of illustrat-ing how the latter illuminate the former and, thus,of conveying a sense of the overall coherence of thisline of work.

A demand-based perspective

One of the important messages in the value captureliterature, that arises implicitly from the formalism,is that end-users are integral to the value creationand capture story: without them, there is no valuecreation. While it is possible to construct a biformgame that shunts buyers into the background (à lathe demand curve in a Cournot model), there isnothing in the formalism that requires it. Indeed,the modeler is encouraged to treat buyers on anequal footing, in terms of model inclusion, asany other kind of agent. Thus, the approach is anatural choice for Adner and Zemsky (2006), whoare motivated to study demand-side influences onsustained competitive advantage.

Adner and Zemsky (2006) set up a model inwhich consumers vary in terms of their preferencefor quality as well as the extent to which theyhave decreasing marginal utility (DMU) for per-formance. Firm heterogeneity is captured on four

30 In some papers, the characteristic function is explicitly derivedfrom the more primitive assumptions. In others, it is left implicitto operate behind the scenes.



dimensions: (1) rate of technology acquisition, (2)technology lead (or lag), (3) a fixed quality com-ponent, and (4) marginal cost of production. Valuecapture is assumed to be proportional to valueadded.

The analysis goes on to relate competitive advan-tage to the interaction between firm strategies andthe degree of DMU inherent in consumer prefer-ences for product performance. For example, theyshow that the ability of a challenger to unseat anincumbent through innovation depends subtly upona firm’s cost position and the degree of DMU. Ifthe new technology comes with a cost advantage,higher DMU speeds adoption. However, if the chal-lenger has a cost disadvantage, higher DMU retardsadoption.

The paper also explores GP1 under the effects ofdifferent types of resources (process, product, inno-vation), the effects of imitation, multisegment com-petition, and strategic diversity. Throughout, thefocal issue is on the interaction between firm strate-gies and the features of consumer preferences (pri-marily DMU). Because the model assumes valuecapture is proportional to added value, competitiveintensity and the distinctions between competitiveversus persuasive sources of performance advan-tage are not a feature of the analysis.

Value capture in productive social networks

A persistent empirical finding with respectto productive social networks is that networkbrokers—agents who intermediate transactionsbetween two or more parties—tend to enjoy higherlevels of value capture than agents with similarcharacteristics but less central network positions(see Burt, 2000, for a review of empirical findings).A question that naturally arises is whether thesuperior performance is due to a broker’s networkposition, or whether the agent’s position is due toits superior productive characteristics. In the lattercase, network centrality and superior performanceare due to the common cause of the agent’s abilityto create superior value.

Ryall and Sorenson (2007) build a biform gamein which second-stage value creation possibilitiesdepend upon a collection of possible projects which,themselves, require subsets of connected agents forcompletion. For example, an action movie requiresa set of agents—director, actors, producers, specialeffects artists, and so on—with complementaryabilities to come together for its completion. The

key feature of the model is that agents must beconnected within a productive network in orderto work on a project. The formation of networkrelationships occurs in the first stage of the biformgame, in which agents make and accept (or reject)offers to work with one another.

The paper demonstrates that brokers can, in fact,enjoy guaranteed value capture purely by virtueof the competition for them generated by theirnetwork position, viz. the Principle of the EssentialTension. However, it also illustrates the insightthat attaining such a position is problematic: If anindividual really has no effect on value creation perse, the agents who are required for value creationhave no interest in accepting relationships that havethe end-effect of installing that individual into avalue-soaking position of network scarcity.

Vertical integration

De Fontenay and Gans (2008) examine firms’decisions to outsource functions and transactunder separate ownership. In their analysis, theNGT part of the biform game is a market wherereal assets are traded while the CGT part of thegame is based on the Shapley value. While it iswell known that consolidation of ownership canallow those owners to capture more value, thismust be traded off against any value creation thatmight arise form outsourcing (that is, verticaldisintegration or separation of ownership). What deFontenay and Gans (2008) show is that, consistentwith our earlier blind spot regarding the harmgenerated by competition, it matters who yououtsource to.

For instance, if you outsource and use that to cre-ate competition, that improves value capture in theCGT part of the game relative to outsourcing to anexisting firm that keeps competition (at least struc-turally) the same. But, precisely because of this, theNGT part of the game that involves a transactionwith the outsourcing firm (which acquires assets toprovide services), involves several parties that careabout the degree of competition that results. Thepaper shows that the NGT incentives dominate theCGT outcomes and, in equilibrium, a firm will endup outsourcing to an established firm (keeping com-petition structurally the same) rather than an inde-pendent firm that creates more competition. Thus,the biform structure of value capture theory—byforcing us to understand the full consequences ofan outsourcing relationship—can turn traditional



intuition about the competition-creating effects ofoutsourcing on its head.

Strategic factor markets

The RBV claims that sustained performance advan-tage arises from control of resources and capabili-ties that are rare, valuable, and inimitable. Barney(1986) and Makadok and Barney (2001) furtherassert that a source of inimitability is a superiorunderstanding of resource value. To frame the ideain the logic of this paper: Competition for the trans-action partners of a superior performer may fail toappear because the agents required to provide suchcompetition simply do not understand the value cre-ation possibilities of their resources in that context.Heterogeneous expectations, then, become the basisfor “strategic factor markets” (SFM) —markets inwhich value-creating resources are demanded andsupplied as a result of heterogeneous expectationsregarding their value.

In elaborating the free-entry blind spot, weexplained why material finitude implies thatresource mobility barriers are neither necessary norsufficient for sustained performance advantage.31

Adegbesan (2008) explores the substance of thisimplication explicitly in the context of strategicfactor markets. The setup is an assignment model:a cooperative game representation of a two-sidedmarket in which sellers offer units of an undif-ferentiated product to buyers. While the sellers’products are identical, buyers do not value themidentically.32 The interpretation here is that theproducts are resources that offer heterogeneouscomplementarities to the firms on the buy-side ofthe market. Thus, performance heterogeneity doesnot arise as a result of heterogeneous expectationsbut, rather, of heterogeneous resource comple-mentarities. Note well the implicit premise thatthe features of the buy-side firms that create thecomplementarities are, themselves, in finite supply.

Adegbesan (2008) demonstrates a number ofinteresting findings. First, the analysis shows thatthe resource acquirers with greater complementar-ities are guaranteed greater value capture (via the

31 See also Pacheco-de Almeida and Zemsky (2007: 651–652) fora discussion of other issues that have been raised with respect tothe theoretical underpinnings of the RBV.32 The canonical example is a housing market in which all thesellers offer houses that, for all relevant purposes, are identical.However, buyers may have a different willingness-to-pay due totheir individual preferences for house features.

Principle of the Essential Tension). Second, thepaper highlights the traditionally overlooked factthat a portion—potentially significant—of superiorperformance may be due to persuasive capabilities(relating to Insight 4 and to the Principal of Com-petitive Intensity). This latter issue is in the con-text of SFMs themselves. At the top end, of course,the importance of persuasive capabilities is cappedaccording to the Principle of the Added Value. Here,added value is also computed in context of the SFMand arises as a consequence of complementarities.

Value chain frictions

Chatain and Zemsky (2011) study what happenswith respect to value creation and capture when fric-tions arise in industry value chains. The issue arisesas a natural consequence of conditions (1) and (2)for a competitive distribution of value. The num-ber of possible value-creating groups that one must,theoretically, consider is exponentially increasingin the number of agents, n. In most real-world sit-uations, search and switching costs may preventagents from being aware of or, equivalently, beingunable to act on a large portion of these possibilities.

The model examines two firms competing fora single buyer, in which each firm fails to meetthe buyer with some probability. This quantifies thefirm-specific “friction” inherent in the market. Theanalysis proceeds to examine the effects of frictionin the context of each of the five “forces” in Porter(1979). An important, cumulative insight arisingfrom these findings is that Porter’s Five Forces can-not be considered in isolation. For example, changesin persuasive capabilities affect threshold frictionlevels that induce entry. This message is consistentwith our earlier Insight 1: there is only one, highlyinteractive force of competition. Changing any oneof the values actually created, relative persuasiveadvantage or the value of productive alternatives,has the potential to alter the balance of competitionthroughout the system in subtle and counterintu-itive ways.

Obloj and Zemsky (2015) examine competitiveadvantage in the context of buyer–supplier relation-ships in which the integrity of the supplier plays arole in determining which deals are consummated,how much value is created, and how that value isdistributed. The novel aspect of this setup is that itembeds a contracting problem in the first stage: con-tracts are offered in the first (NGT) stage, and valuecreation and capture are determined in the second



(CGT) stage. Value creation in stage two dependsupon the relative efficiencies of supplier produc-tion technologies, the contracts offered, the actualdeals struck (implied by the characteristic function),and the gaming proclivities of the suppliers. Actualvalue created depends only upon supplier effortsdevoted to productive actions. Buyers would like tocontract on these actions, but cannot. Instead, theycan only contract on an observable that, while cor-related with productive effort, can be gamed whensuppliers engage in certain unproductive tasks. Sup-pliers are of two types—gamers and honest—withthe former more inclined to divert effort to unpro-ductive activities. This sets the stage for an interest-ing moral hazard problem integrated into a biformgame.33

This paper has a number of interesting results.For example, dishonest suppliers who yet have asufficient efficiency advantage may have greateradded value than honest suppliers and, hence, beselected by buyers. By implication, it is possible forinefficiency rears its head in stage two whenevera deal is consummated with a dishonest supplier.More significantly, they show that an increase inintegrity on the part of either type of supplier resultsin: (1) greater value creation regardless of whichsupplier is ultimately chosen for the deal, (2) greatervalue capture for the buyer, (3) greater value capturefor the supplier with greater integrity, when used,and (4) less value captured by the supplier with nochange in integrity, when used.

Apart from these specific results (and more), thisanalysis is significant for at least two additionalreasons. First, it demonstrates the idea that thecharacteristic function represents the actual valueproducible by agents in various combinations,“implicitly accounting for limitations implied byinformation and agency considerations, transac-tions costs, configuration of productive resources,barriers to technology transfer, institutional struc-ture, regulation, and so on” (MacDonald and Ryall,2004: 1324). Second, the model identifies a novelcategory persuasive resource—reputation forhonesty—and examines its effect on value creationand capture. In so doing, it also reminds us to castour nets wide regarding the possible sources ofvalue capture above and beyond the competitiveminimum.

33 There is no adverse selection here—buyers know the suppliertype (e.g., due to unmodeled reputation effects).

EMPIRICAL PROGRESS

Value capture theory has recently led to empiri-cal work that utilizes both the theory’s insights andits methodological innovations. Here, we reviewthese papers, highlighting how value capture the-ory has given researchers a way of endogeniz-ing elements—particularly regarding multiagentinteractions—that were previously held exogenouswhen formulating hypotheses. This has led both tocleaner hypothesis specification and new ways oflooking at the identification of causal relationshipsin explanations of firm performance.

Consider, first, the papers that use value capturetheory for hypothesis formulation. One exampleis Marx, Gans, and Hsu (2014), who examine thecommercialization choices of startup firms in thespeech recognition industry. In their model, star-tups face a choice between competing with estab-lished firms or cooperating with them. However,what makes this a complex interaction is that thechoice is exercised over time and startups canpivot between different commercialization strate-gies. Their model uses value capture theory byexplicitly modeling the amount of value createdthrough a cooperative choice relative to a compet-itive choice, taking into account the fact that thosechoices may impact on future value creation andalso the value that each party can guarantee toappropriate. This allows them to hypothesize howtechnological characteristics impact the sequenceof observed commercialization choices of startups.For instance, for disruptive technologies that are ini-tially of low value to incumbents and are difficultto integrate, competition will be preferred. How-ever, following the resolution of uncertainty overthe future trajectory of the technology, a switch tocooperation may be observed. As that uncertaintyis actually resolved to the empirical observer, Marxet al. (2014) can actually test whether those pivotsoccurred—and whether they related to the technol-ogy being commercialized in the fashion anticipatedby the theory. They found that the data were, indeed,consistent with the theory.

Chatain (2011) uses value capture theory toinvestigate an important new area regarding theresource-based view of the firm: namely, howdoes competition itself impact on the relationshipbetween capabilities and performance? This is asubtle issue. As noted earlier, while improved capa-bilities improve value creation (in general), theymay not improve a firm’s ability to appropriate



that value precisely because the terms of competi-tion change. Chatain (2011) distinguishes betweencertain actions that improve total value creationbetween a firm (in his application law firms) andits clients but in a way that is specific to a client(for instance, knowledge of a law firm of third-partycontract specifics or the details of manufacturingoperations) and those that are more generic. For theformer, the very action reduces the set of agents thatcan compete effectively for the client’s business.He finds that if a client requires new services, thenthose are more likely to be provided by the client’sexisting law firm when client-specific knowledgeis an important component of those new services.By contrast, the aggregate level of expertise inthe firm does not spur a similar bias in a client’schoices for new services. Finally, the agglomerationof services is related positively to the client-specificrelationships of a firm and also negatively to theclient-specific relationships of rivals. Using data onU.S. law firms, Chatain (2011) confirms the pre-dicted hypotheses from value capture theory in thiscontext.

One of the primary empirical challenges posedby the theory—especially since it represents oneof the theory’s essential features—is how to workwith the inequality constraints posed by competitiveconsistency conditions (2). Chatain (2013) breaksnew methodological ground in this stream by imple-menting value capture estimates based upon an esti-mation approach that admits the use of inequalityconstraints. This approach was introduced to eco-nomics by Fox (2008) and first applied in strat-egy by Mindruta (2013) in her study of the driversof researcher–firm matching. Applying this newmethodology to the two-sided market between lawfirms and their corporate clients, Chatain (2013)uses law firm quality rankings to construct implicitwillingness-to-pay on the part of firms that, in turn,implies inequalities, Equation (2). He finds that lawfirms with broader client scope appropriate less and,moreover, at an equal cost per lawyer as those withnarrrower scope—results that run counter to theprevailing wisdom of practitioners in this industry.

Also ambitious is Grennan (2014). His paperexamines negotiations between suppliers and buy-ers (usually hospitals) of medical devices. Grennan(2014) is able to observe total value created com-puted from observed prices and market shares forcoronary stents. Importantly, the prices are nego-tiated prior to quantity being chosen, with doc-tors doing that depending on demand and relative

costs. This allows Grennan (2014) to identify keyelasticities that drive willingness to pay for thesestents because some of the later variation in demandare not observed or anticipated when prices arenegotiated (e.g., a large study taking place in ahospital). Grennan (2014) also observes the sup-plier costs of stents based on their type. He thenuses the Nash bargaining solution, simultaneouslysolved and applied across the market, to generate astructural equation for the determinants of supplierappropriation. As he shows, this is equivalent to thevalue capture model based on the core in the contextof his setting. Critically, this allows him to decom-pose the determinants of value capture by suppliersinto their competitive options (namely, computedadded value) and also bargaining ability. He findsthat 79 percent of the variation in appropriationacross suppliers is explained by bargaining abil-ity. Moreover, this ability is itself correlated withfirm identity. It differs across hospitals, improv-ing over time as hospitals learn how to negotiatewith suppliers.34 This suggests the long-anticipatedefficacy of trying to consider firm organizationand performance as embedded in their competitiveenvironments.

Bennett (2013) explores the sources and effectsof persuasive resources in an analysis rich withinstitutional detail. He exploits variation in the orga-nizational design of car dealerships to examine theimpact of this on subsequent bargaining outcomesin a biform game. In some car sales negotiations,a salesperson owns the entire deal (a parallel pro-cess), while in others deals are closed by a, pre-sumably, more expert salesperson (a serial process).Recall that the price eventually negotiated will be,under value capture theory, a function of compet-itive options for the seller and the seller’s rela-tive bargaining ability. Because bargaining abilityis likely to be higher when an expert salesperson isbrought in, then it is also the case that the impactof competitive options on the final price is lower inthis organizational form. Bennett shows, consistentwith the theory, that as the inventory of cars dimin-ishes (a proxy for competition or scarcity), pricesincrease under the serial sales process by relativelyless. In addition, using the college education of buy-ers as a proxy for Internet search saaviness, Bennett

34 Adegbesan and Higgins (2011) also find a similar impacton bargaining ability in their study of biotech–pharmaceuticalcompany alliances, although their analysis is not structural innature, nor is it causally identified in the way Grennan (2014) isable to do in his setting.



finds that in this situation the serial process per-forms worse than the parallel one; i.e., the costs ofthat more drawn-out process are not translated intopricing benefits.

In summary, the empirical work based on valuecapture theory is young but already yielding valu-able insights. In particular, the broad predictionsof the theory do appear in the data in a variety ofapplications. Moreover, some empirical work hasdemonstrated that competition alone cannot explainall of the variation in firm performance and thatsome idiosyncratic factors that drive relative bar-gaining power can be very significant. It will beinteresting to see how that assists in focusing outattention on the drivers of those factors, as well ashow far the theory can be pushed to assist in quan-tifiable structural modeling.

FUTURE DIRECTIONS

While the cooperative game theory has a long his-tory in economics, it is relatively recently thatthis methodology began being applied to the cen-tral questions in strategic management. That theoryreviewed here grounds the issue of firm perfor-mance in both a market setting and in a settingwhere resource constraints are endogenous to over-all economic activity. This allows the researcherto fully characterize how the force of competitionprovides bounds on a firm’s appropriability andhow these bounds relate to value capture by otherfirms, customers, and suppliers. This approach notonly provides insights into the robustness of predic-tions stemming from more conventional models ofmarket competition but also provides entirely newinsights that are not available from those models.Here, we have highlighted areas where the theoryprovides both nuance and challenge to existing pre-conceptions.

At the same time, we must stress that theseinsights have just begun to be broadly tested byour empirically motivated colleagues. Indeed, asexcited as we are by the promise posed by therecent flurry of empirical work, the surface has onlybeen scratched. In our view, one of the most impor-tant issues is further effort designed to identifyand measure the impact of “persuasive” resources.That is, how do firm strategies affect the value cap-ture Equation (3)? What, exactly, are “persuasive”resources? Do they operate as predicted? Are theymore or less likely to convey durable advantages to

their owners? Of course, these questions are closelyrelated to competitive intensity. The theory pre-dicts that persuasive resources are important whencompetitive intensity is low, competitive resourcesmore so when intensity is high. Initial empiricalwork (e.g., Bennett, 2013) is promising. However,the extent to which competitive intensity variesacross markets and firms is an open question. Ifthe typical firm faces strong intensity (and, hence, anarrow competitive interval), then claims about per-suasive resources are a theoretical curiosity with-out real-world relevance. In either event, the answerwill provide a deeper understanding of persistentperformance heterogeneity among related firms.

Another important opportunity, as highlighted byGrennan (2014), is the ability to use value capturetheory to bring structural modeling to strategy—ina fashion distinct from the present approaches usedin the empirical industrial organization (based ondynamic, NGT). Combined with a refined under-standing of how firms’ actions affect their valuecapture equations, structural models along the lineof Grennan (2014) permit researchers to explorethe drivers of firm performance in a market set-ting. Moreover, they permit “what-if” assessmentof business policy counterfactuals. The formalapproach requires precision, but with that precisioncomes a more subtle set of hypotheses that can betested and examined.

Finally, the theory is far from settled. The empiri-cist’s ability to classify resources to capabilitiesinto persuasive versus competitive categories willbe greatly facilitated by further theoretical work onthis issue. This suggests a need for more theory thatavails itself of the full biform formalism (in con-trast to much of the theoretical work to date, whichfocuses primarily upon the second-stage, CGT partof the model). While the early focus on understand-ing this less familiar side of the theory is justifi-able, the pressing questions for strategy transcend it.Critically, we must understand how the implicationsof value capture drive actual firm behavior—howdo managers formulate strategies to capture valuegiven their competitive environments? What shouldthey do? In thinking seriously about managerialaction in the real world, issues of bounded ratio-nality inevitably arise. Many tools have been devel-oped for the study of bounded rationality usingNGT. Here we have in mind evolutionary game the-ory, subjective rationality, game theoretical learn-ing, and behavioral economics. All of these areavailable to biform game analysis. Hence, we are



optimistic that future strands of this work will takesuch issues seriously and explore their implicationsfor strategy. In summation, there is much, muchmore to be done.

ACKNOWLEDGEMENTS

Thanks to Adam Brandenburger, Martin Byford,Olivier Chatain, Catherine de Fontenay, Glen Mac-Donald, and Gus Stuart for detailed discussionsover the years. We also wish to express our grati-tude to the editorial team of the special issue andthe excellent comments and suggestions providedby three anonymous referees. Responsibility for allviews expressed remains our own.

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