employee buyout in a bargaining game with asymmetric...

American Economic Association

Employee Buyout in a Bargaining Game with Asymmetric InformationAuthor(s): Avner Ben-Ner and Byoung JunSource: The American Economic Review, Vol. 86, No. 3 (Jun., 1996), pp. 502-523Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/2118209Accessed: 09-06-2017 13:59 UTC

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Employee Buyout in a Bargaining Game with Asymmetric Information

By AVNER BEN-NER AND BYOUNG JUN*

Why are somefirms purchased by their employees? The paper explores this question theoretically, suggesting that employees may attempt to overcome their informational handicap regarding firm profitability by making simultaneous offers on wages and a purchase price for the firm. Owners of relatively unprofitable firms will tend to sell out for low prices instead of paying high wages, whereas owners of profitable firms will prefer to pay high wages over receiving low firm prices; the buyout serves as a screening mechanism. The probability of an employee buyout decreases with the employees' outside options and increases with owners' outside options. (JEL C78, D23, J54, L22)

An employee-owned firm is a firm in which the majority of employees own a majority of the stock.1 Employee-owned firms have a small but visible presence in most industrialized economies. In the United States, the better-known cases include United Airlines (with 84,000 employees), Avis (12,500 employees), and Weirton Steel Corporation in West Virginia (6,100 employees) (see National Center for Em- ployee Ownership (NCEO) [1994] for a list of employee-owned firms). The list of firms that' nearly became employee owned is long, and includes much of the airline and steel industries. In the European Economic Community, there were about 15,000 employee-owned firms em- ploying more than half a million employees in the early 1980's, and many have been added since then.2 In addition, there are numerous part-

nerships in the accounting, law, and medical pro- fessions. An employee-owned firm may come into existence through formation de novo, or via the sale of an existing firm to its employees. Most employee-owned firms with more than a few dozen employees appear to have been formed through employee buyouts.

Various reasons are commonly cited for employee buyouts. In several countries, most no- tably the United States and England, laws give beneficial tax treatment to the allocation of stock to employees via Employee Stock Own- ership Plans (ESOPs). This may make the sale of firms to employees more rewarding than sale to other parties.3 The difficulty of finding buyers for small businesses in small localities, and the desire of some retiring owners to have their business remain in the locality in which they operated for many years, may also lead to sellouts to employees. Finally, a buyout may be initiated to exploit a productivity advantage of employee ownership. However, some change must occur which increases the productivity advantage in order to precipitate a buyout, yet no reasons are adduced by pro-

* Ben-Ner: Industrial Relations Center, University of Minnesota, Twin Cities, Minneapolis, MN 55455; Jun: Department of Economics, Korea University, Seoul 136-701, Korea. We acknowledge helpful comments made by anonymous referees, Sam Bowles, Greg Dow, Preston McAfee, Paul Milgrom, Louis Putterman, Ariel Rubinstein, Theresa Van Hoomissen, participants at several conference presentations, and at seminars at the Carl- son School of Management at the University of Minnesota and the Departments of Economics at Tel Aviv, Ben- Gurion, and Ewha Universities.

' This working definition is stricter than theoretically necessary, because dominant control may be secured with ownership of less than a majority of a firm's equity.

2 See Ben-Ner (1988a). These are conservative esti- mates, because the data concemn only producer coopera-

tives, a subset of employee-owned firms, hence excluding well-known cases such as the British National Freight Consortium (see Keith Bradley and Aaron Nejad, 1989).

' However, experts doubt that there is a true tax incentive to ESOPs relative to other means of corporate finance. See, for example, Michael Conte and Jan Svejnar (1990) and Myron S. Scholes and Mark A. Wolfson (1990).

502


VOL 86 NO. 3 BEN-NER AND JUN: EMPLOYEE BUYOUT 503

ponents of this explanation as to why the productivity differential between conventional and employee-owned firms might change. Al- ternatively, a permanent difference might exist but some obstacles to the formation of employee-owned firms-such as lack of awareness of the feasibility of this type of organization-could prevent the formation of employee-owned firms, but when these obstacles are lowered, employee buyouts will be observed.4

The economics literature that deals with the existence of employee-owned firms has paid little attention to employee buyouts; see the surveys by John P. Bonin and Louis Putterman (1987) and by Bonin et al. (1993). The few careful attempts to explain the phenomenon of employee buyouts adduce different reasons than those surveyed above. These attempts concentrate on employees who risk losing their jobs or are being asked by their employers for large wage concessions in circumstances when alternative employment is scarce and alternative wages are low. Such employees may prefer to buy the firm in which they work, because in firms they own employees can insure against layoffs in bad times by instituting more flexible compensation schemes than those attainable in conventional firms. Employee-owners may do so by paying them- selves below the minimum wage, or by accepting returns on capital that would be deemed to be too low by other investors. This prevents loss of employees' investments in communities that may be decimated by the loss of a major employer (Bradley and Alan Gelb, 1983 pp. 35-36; Hajime Miyazaki, 1984; and Martin Browning, 1987).

In this paper we propose a different explanation for employee buyouts in the framework

of strategic bargaining 'a la Ariel Rubinstein (1982, 1985). We assume that management has superior information about the firm's profitability than the employees. Traditionally, it has been assumed that the parties exchange offers consisting of a single element such as wage or price. We allow offers with multiple elements. In particular, we assume that the bargaining parties can make the following type of offers: pay us (accept) w as wages or sell us (we buy) the firm at price p. We find that the employee buyout serves as a screening (or signaling) mechanism. If a firm is unprofitable, then its owners prefer to accept a low price for the firm than pay high wages, whereas if the firm is profitable, the owners prefer to pay high wages rather than sell the firm for a low price. Employees can use "wage-and- price-for-the-firm" double offers to screen different types of firm with which they bargain at a lower cost than through delays of the agreement or other costly screening mecha- nisms.' This schematic representation of the interaction between employees and owners captures the principal common features of many buyouts, as analyzed by Bradley and Gelb (1983, 1985) and other observers.

The organization of the paper is as follows. Section I examines the problem of information in firms in order to motivate the main assumption of the model (asymmetric information), offers a stylized scenario that describes many buyouts, and introduces the intuition behind the model. The formal model is presented and investigated, and the main results are stated, in Section II. Section III extends the discussion to more complex situations and assumptions. Conclusions are presented in Section IV.

I. Preambles

The scenario of an employee buyout presented later in this section, and which lies at the core of the model examined in the paper, rests critically on the existence of asymmetric information between owners and employees. It is therefore useful to explore first the nature of information within firms, the sources of

4'Some buyouts seem to have been initiated by management without any involvement by employees, apparently in order to fend off hostile takeovers or as part of management's leveraged buyout (see NCEO, 1994; Scholes and Wolfson, 1990; and Joseph Blasi 1988). Other buyouts may involve fraud, when those who act as trustees on behalf of employees, acting in concert with selling owners, choose to buy a company on their behalf at an overstated price (see Blasi, 1988; and NCEO, 1994). For additional theories of employee-owned firm formation, see Conte and Jones (1985) and Ben-Ner (1988b).

'We are implicitly assuming that both sides can com- mit to negotiate on both wage and price.


504 THE AMERICAN ECONOMIC REVIEW JUNE 1996

asymmetric information, and some of the responses it engenders.

A. The Problem of Information in Firms

Information concerns numerous dimensions of firm activity, and it may differ in the extent of its accuracy, usefulness, and credibility.6 Lewin ( 1984) suggests that information about costs and the workforce is largely available to labor unions, but detailed information regarding profits and plans that may affect future profitability is considered proprietary and is not ordinarily available to unions. Even in publicly-traded firms the information available to employees is incomplete.7

Management has incentives to claim that profits are low even when they are high because this favors a lower-wage settlement. Un- derstanding this, employees seek information about firms' operations. However, unions' demands to open company books have almost universally been met with resistance by employers.8 Sharing strategic and financial in-

formation with employees is rare even among relatively "information-sharing minded" companies (Lewin, 1984). Employees may

attempt to learn about firm profitability by test- ing owners' willingness to delay the conclu- sion of the bargaining process, and by forcing them to respond with counteroffers that reveal information about profitability. The diverse

screening tactics used by unions, such as work-to-rule and strikes, inflict costs on employees as well as on owners (Karl Moene,

1988; Oliver Hart, 1989). The management of a veritably unprofitable

firm would like to signal actual profitability to convince unions of the need for concessions.9 But often there are no means for credible one- time transfer of information on profitability, or information cannot be interpreted without sus- tained experience with a company's books.'0 In addition, sharing information only during bad times supplies a signal about profitability when information is blocked. Hence information sharing cannot be implemented ad hoc but must represent a long-term commitment. An "open-books" strategy will be evaluated by management for its long-term benefits rather than short-term expediency, because "once the spigot of confidential information is turned on, it cannot easily be turned off .... An open policy on information may encourage union

6 Important dimensions include (a) strategic business plans regarding capital investment and marketing, (b)

comparative costs of production in different facilities within the firm and competing firms, (c) accounting in-

formation regarding profitability (aggregated, by strategic

business unit, and by product line) and the depreciation method, (d) acquisition and divestiture plans, and (e)

workforce composition changes, and skill and hiring re-

quirements (David Lewin, 1984). 'John Kennan and Robert Wilson (1993 p. 49) explain

these points as follows. "A firm may open its books along

with publicly accessible accounting and financial statements (such as 10k reports filed with the SEC) to the un-

ion, but even so there are substantial limitations on the

relevance of this kind of information. Partly this is because the past only partly reveals the future: firm's predictions of production, demand, and prices of factors and output

can be manipulated. Further, actual costs may be less im-

portant than opportunity costs: the union may be unable to assess the opportunities the firm has to redeploy its capital in other locations, product lines, or industries, or to

substitute capital for labor. And partly this is because mea- surement of labor's product is manipulable or even intrin-

sically ambiguous, especially for a single craft union within a larger enterprise: and in any case, standard ac-

counting and financial statements usually exclude such information."

8 The confidential treatment of business information is legally protected. Only in rare cases, is some usually-

confidential information revealed to unions, for firms

claim that they will be bankrupted by meeting union

demand, only after the intervention of a labor court is the information provided (Betty Justice, 1983; and Morris Kleiner, 1984).

9 For example, the director of industrial relations of a manufacturing firm stated the problem as follows: "In the

late 1970s and early 1980s, the business became much

more competitive, both internationally and domestically

.... Union leaders indicated that they knew of our financial difficulties as well as those of other firms in the same and related business that had recently sought bargaining con-

cessions from their unionized employees. However, they

felt they would have to have more detailed information on the operating and business plans of the company if they were even to raise this issue with their members .... It was

agreed that detailed plant-by-plant production-cost data as well as local area competitors' production-cost data (to the

extent available) should be provided to the union officials in advance of negotiations" (quoted by Lewin, 1984

p. 7). 10 See, for example, Alan Manning (1989). Firms can

credibly but inefficiently signal their profitability by setting inefficient employment levels (Sanford Grossman and Oliver Hart, 1983).


VOL. 86 NO. 3 BEN-NER AND JUN: EMPLOYEE BUYOUT 505

moderation in hard times, but it may also work against the company in collective bargaining when profits rise." " Because of such long- term strategic considerations, crucial information about profits that can be used in bargaining by individual employees and par- ticularly by unions is generally unavailable to employees."2

B. A Stylized Scenario of Employee Buyouts

Studies of employee buyouts focus on individual cases, and there have been no econometric analyses of employee buyouts.'3 The stylized scenario offered below represents an abstraction of case studies, and relies partic- ularly on the aforementioned analysis by Bradley and Gelb (1983, 1985).14 This sce-

nario provides the motivation and intuitive background for the model examined in the re- mainder of this paper. The scenario and the model capture the chief elements that may precipitate a buyout decision, and ignore the numerous factors that may also weigh in and even determine the feasibility of a buyout. (We comment on these factors in the last section.)

Consider a situation in which management is better informed about the firm's profitability than employees, and suppose that management has determined that it does not want to share information with employees. Employees may seek to become better informed through tactics discussed above, and they may substitute or complement such tactics with offers to buy the firm.

Such seems to have been the case in the negotiations that took place in 1992 and 1993 between the management of the privately- held Northwest Airlines and its unions. When management (which includes key stockhold- ers) asked for wage concessions, its unions claimed that the financial difficulties were in- tentionally exaggerated. In what was per- ceived by some observers as an attempt to signal the true and dire situation of the company, management had canceled a large order of new aircraft. Some union leaders regarded this move as a ruse.'5 Only when the unions asked for an 80 percent ownership stake, and when large lenders to the heavily leveraged company became involved in negotiations over the fate of the company, did financial information became available to people outside management. But even then crucial information regarding future plans (for example, regarding the construction of maintenance bases for planes that for the most part were not yet

" The president of Organization Resource Counselors, Incorporated, quoted by Lewin (1984 p. 16). Crucial information may be shared by allowing employee representatives to sit on the board of directors of a company. This has been the case, for example, when in the early 1980's a union representative was added to the board of the Chrysler car manufacturing company, which was facing extreme financial difficulties.

12 Access to information by nonunionized employees is even more restricted both because they do not have contractual rights to receive certain information that unions do, and because they do not have the resources for col- lecting information that many unions do. In much of this paper we use the terms employees, employee representatives, and unions as synonyms, and do the same with the terms owners and management. This ignores the agency problems that might arise in the relationship between employees and their representatives and owners and management; more importantly, this disregards the considerable differences between the structure of negotiations between employees and owners in unionized and nonunionized set- tings. Although the model developed in this paper applies most clearly to unionized firms, we believe that there are circumstances in which it can represent relations in nonunionized firms, too, and can be used to interpret buyouts in the case of such firms.

'3 The reason is the absence of data. There have been several studies of the formation of employee-owned firms, but these studies cannot distinguish between formation from scratch and buyouts, and have no information about the circumstances of the formation of individual firms (see Conte and Jones, 1985; Conte, 1986; Ben-Ner, 1988a; Jan Podovinsky and Geoff Stewart, 1991; Raymond Russell and Robert Hanneman, 1992; and the survey by Bonin et al., 1993).

"4 Most case studies concentrate on the factors that facilitate buyouts, often in order to provide lessons for future buyouts, and ignore factors that may trigger them. For

example, Jack Quarter and Judith Brown (1992) are inter- ested in the role of umbrella organizations and consulting firms in facilitating buyouts, William Foote Whyte and Charles Kraypo (1988) focus on the financing of buyouts, and Arthur Hochner et al. (1988) emphasize the relations among groups participating in the buyout. For additional case studies, see Corey Rosen et al. (1986), Job Ownership Ltd. (1991), and Robert Stern et al. (1979).

'5 In February 1996 the order was reactivated, and the deposits forfeited in 1992 will probably be applied against the purchase price.



purchased) remained closely guarded; information about the company's future profitability was therefore incomplete. The unions continued to negotiate over a wage agreement while simultaneously discussing a buyout. In late 1993, one third of Northwest Airlines stock was purchased by employees."6

In this and other instances, instead of bargaining over wages only, employees and management exchange offers that contain two elements: a wage proposal, and a price for the firm. For employees, the role of the buyout offer in conjunction with a wage offer is to evince information about firm profitability. Employees will seek to structure their offers so as to induce management to behave more truthfully than if the negotiations were restricted to wages only.

The idea behind a "wage-and-price-for-thefirm" double offer is simple: if a firm is unprofitable, its owners prefer to accept a low price for the firm rather than pay high wages, whereas if the firm is profitable, they prefer to pay high wages rather than sell the firm for a low price. To understand how this may work and to anticipate our main results, it will be useful to examine informally some aspects of the bargaining process between management and a union.

Assume that there exist only two types of firms ("profitable" and "unprofitable"), employees and owners are risk neutral, accepted offers cannot be withdrawn, and ownership transfer is costless. If the union makes the initial offer the bargaining process unfolds as follows. The union offers a wage settlement and

a price for the firm, and management responds by accepting either the wage or the price or by rejecting both elements and making a wage- price counteroffer.

Consider first the case of complete information. If the parties negotiated only over wages, they would settle on some wage rate Wh if the firm were profitable and we if it were unprofitable, whereas if they bargained only over the transfer of ownership, they would agree to a price Vh(ve) for a profitable (unprofitable) firm. Wages and prices negotiated under perfect information reflect accurately the financial condition of the firm, and both parties would be indifferent between a wage settlement and an ownership transfer. Regard- less which type of agreement is adopted, the parties will receive the same share in the firm's surplus. 17

Under asymmetric information, the union negotiates without knowing whether the firm is profitable or not. Therefore, it will seek to elicit from management responses that reveal information truthfully, by structuring offers so as to prevent the management of a profitable firm to behave (make and reject offers) as if it were the management of an unprofitable firm, and vice versa. When it faces only two possible types of firm, the union can make four wage-price offers: (Wh, Vh), (Wh, ve), (we, Vh), and (we, ve). The first offer consists of a high wage and a high buyout price, both reflecting a profitable firm. When it receives such an offer, the management of a profitable firm would accept either component at random, whereas the management of an unprofitable firm would represent that the firm is profitable and accept the high price component of the offer (thus rejecting the high wage settlement), making a gain at the expense of employees. Alterna- tively, if the union offered (we, Vh), the management of a profitable firm would accept the low wage and that of an unprofitable firm

6 This account is based on newspaper reports in the Twin Cities, where Northwest Airlines is based. For a detailed account of the first employee-buyout attempt of United Airlines in 1987 and 1988 that echoes similar themes, see Alan Hyde and Craig Harnett Livingston (1989). While that attempt failed, the company was eventually purchased by employees in 1994. On the basis of several case studies, Bradley and Gelb (1983 p. 26) conclude that the circumstances that are most conducive to employee buyouts are those in which employees feel that management "has access to superior information on the current situation and future prospects of the firm." The authors suggest that the low-trust relationship generated by the informational asymmetry induces employees to reject wage concessions and to view a buyout as the only alternative.

" The sources of profitability which gives rise to the bargaining situation include the organizational rent that results from firm-specific or idiosyncratic human and physical capital, market power derived from patents, and so on (see, for example, Masahiko Aoki 1984; and Felix FitzRoy and Dennis Mueller, 1984). The bargaining problem does not arise in a competitive environment.



would sell the firm for the high price. Em- ployees are losing in either event: in the first case they get paid as if the firm were unprofitable when in fact it is profitable, and in the second case they purchase an unprofitable firm for the price of a profitable one. If the union offered a low wage-low price combination (we, vi), then the management of an unprofitable firm would accept either component of the offer at random, whereas the management of a profitable firm would take the low wage. Hence the three wage-price combination offers examined above do not screen between the two firm types.

Consider now the high-wage-low-price offer (Wh, vi). The management of a profitable firm would not want to imitate an unprofitable firm by accepting a low price for ownership transfer because such a price does not incor- porate the full value of the firm; instead, it will settle on the high wage, which it can afford. Likewise, the management of an unprofitable firm will not want to pay the high wage but will prefer instead the low price which reflects the (low) value of the firm."8 The foregoing discussion thus implies that unprofitable firms will be sold to their employees while profitable ones will not be sold but instead will pay wages which reflect their economic circumstances.

II. Employee Buyout as a Screening Device

This section formalizes the simple scenario discussed above, modeling the interaction between employees and owners as an infinite sequential bargaining game with asymmetric information. In this Rubinstein-type model, employees and owners alternate in making offers consisting of wages and prices for transfer of the ownership of the firm. The analysis of the model identifies the circumstances in which ownership transfer may occur as a unique sequential equilibrium, focusing on the financial condition of the firm and the identity

of those who make the initial offer in the bargaining process.

A. The Simple Model

The situation described above can be con- veniently cast in a noncooperative sequential bargaining game in the spirit of Rubinstein's work ( 1982, 1985). 9 While in these and most other models the parties bargain over one element only, in our model the union and management bargain simultaneously over two elements, a wage settlement and ownership transfer.20

There are two factors of production, labor and capital, owned by employees and owners, respectively. Members of each group are ho- mogeneous and are represented by single representative players: player 1, the union, and player 2, the management. Capital in this model is synonymous with the firm. Both players derive utility only from monetary income, are risk neutral, have a common time discount factor 6 < 1, and maximize the discounted value of their payoffs. If employees purchase the firm, the union assumes the role of the management, and the firm continues to employ the same production function and produce with the same efficiency as before the buyout.

Output produced by labor and capital gen- erates revenue (r), which can be high (h) or low (f), representing high or low profitability.21 A firm with high (low) revenue is termed a firm of type h (e) and is denoted by 2h (2e). Asymmetric information exists in that the management knows the true level of revenue before the bargaining begins, whereas the union knows only the a priori probability associated with h: 7ro.

18 Since an unprofitable firm's management has no incentive to refuse to sell the firm, refusal of both elements of the offer reveals that revenue is high, and therefore the management of a profitable firm will accept the high-wage offer.

'9 Grossman and Motty Perry (1986) and Anat Admati and Perry (1987) also worked out sequential bargaining solutions under asymmetric information.

20 We focus on screening by the uninformed party, but our model also contains signaling by the informed party. Conceptually, our model resembles multidimensional signaling (for example, Paul Milgrom and John Roberts, 1986) and multidimensional screening (for example, Steven Matthews and John Moore, 1987).

21 What is relevant for wage bargaining and is reflected by r is the revenue net of nonlabor costs during the period of employment.



The union and management bargain over a wage settlement or an ownership transfer.22 Bargaining takes place in discrete periods of equal duration (the time discount 6 reflects the length of a bargaining period). In each period one offer is made, with the players alternating in making offers. Offers can be made indefi- nitely into the future. An offer consists of the pair (w, v) selected from [0, h] x [0, h]; that is, each offer consists of a wage (w) to be paid by management to the union, and a price (v) to be paid by the union to management if the firm's ownership is to be transferred. The re- sponder may accept either the wage or ownership transfer offer, or reject both. In addition to these pure strategies (denoted by Y1, Y2, and N, respectively), the players may also make random choices in accepting an offer.

A player's strategy is a list of proposals and responses for every bargaining period, representing a complete plan of what to do at each contingency. The union's strategy is denoted by al, whereas that of the management is denoted by a> when the true profitability level is r (r = e, h). A strategy profile is a list of all players' strategies: (al, a>, aC). Each strategy profile determines two bargaining outcomes, one for r = 1 and the other for r = h. Let s' denote a sequence of offers up to and including period t, and let S' be the set of all such sequences. Then the proposer's strategy in period t is a function a':S' ' -- [0, h] x [0, h].

A bargaining outcome (w, v, p, t) means that wage offer w and buyout offer at price v are made and are accepted in period t with probabilities p and (1 - p), respectively. The payoffs are as follows. If a wage settlement is reached, the employees get w and the owners (r - w), whereas in the case of ownership transfer employees get (r - v) and the firm's (former) owners receive v.23

A player's strategy depends on the oppo- nent's previous actions and the player's inter- pretation of these actions. In the case of the uninformed player (the union), this interpre- tation amounts to beliefs about the profitability

of the firm. The initial belief is the a priori probability associated with h, 7ro, and it is up- dated on the basis of information infered from the actions of the informed player in a way consistent with Bayes rule. The union's re- vised belief is denoted by ir(s').

A sequential equilibrium is a strategy profile with a system of beliefs such that every player's strategy is optimal with respect to the other's strategy, given the uninformed player's beliefs. In the absence of asymmetric information a player's belief is knowledge of the actual situation. In this case the sequential equilibrium requires that each player's strategy be optimal with respect to the other's at each point where decisions are made. A strategy profile which satisfies this requirement is called a subgame perfect equilibrium.

B. Results

The negotiations between the management and the union may start with an offer from either party. Consider first the case when the union makes the initial offer. It is useful to start first with a situation of complete information, whereby both parties know with cer- tainty the level of the revenue, then move on to the asymmetric-information case in which the parties are restricted to single-element offers. The first two theorems which summa- rize results based on these situations are well known (and therefore labeled here as "facts""). They are offered in order to establish bench- marks for the asymmetric-information case with two-element offers.

Fact 1: (Rubinstein, 1982). With complete information, the unique subgame perfect equilibrium for bargaining games with single element offers (for example, only wage or only ownership transfer) is such that the union offers a settlement for a wage or price for the firm r/(1 + 6), and the management accepts this proposal immediately.

Fact 2: (Rubinstein, 1985). In the asymmetric- information bargaining game between an uninformed union and an informed management, where the union makes the initial offer and offers are restricted to a single element, there exists a unique bargaining sequential-equilibrium

22 This statement refers to the bargaining process; in fact, the parties bargain over the division of r.

23 As remarked earlier, in the case of perfect information, w = r - v.



outcome if 7ro * e/h.24 If 7ro > e/h the union demands h[l - (1 - _ro)62]/(I + 6), which will be accepted when r = h and rejected when r = e (in which case 67roh/( 1 + 6) will be counteroffered and accepted next period). If 7ro < 4/h the union demands l/( 1 + 6), which will be accepted immediately.25

In the circumstances described above the union and management are identical in every respect with the exception of initial ownership of the firm. Indeed, in these cases it does not matter who owns the firm, hence the indeterminacy between a wage settlement and ownership transfer.26 We now turn to state our main result.

THEOREM 1: In the asymmetric-information bargaining game between an uninformed union and an informed management where the union makes the initial offer and offers may consist of two elements, wage and price for ownership transfer, there exists a unique sequential equilibrium outcome. In this equilibrium, the union makes a wage-and-price offer (h/(l + 6), bel(1 + 6)). The management accepts the wage demand h/( 1 + 6) if the firm is profitable, and accepts the buyout price b6/ (1 + 6) if thefirm is not profitable. The agreement is reached in the first period.

The proof is placed in Appendix A. Theorem 1 implies that the equilibrium payoff of the

bargaining game between the union and management under asymmetric information is identical to the one under complete information, although the choice between wage settlement and ownership transfer is no longer indeterminate. The employees receive r/( 1 + 6), either in wages or as the residual if they purchase the firm. The double offer thus serves as a perfect screening device. This is a very strong result compared with the single-element offer bargaining (see Fact 2).

The intuitive reason for this result is as follows. For the profitable firm a wage offer of w is equivalent to a buyout offer of h - w whereas for the unprofitable firm it is equivalent to a buyout offer of e - w. Hence the union can effectively make two offers with a difference of h - e. With this difference the union can arrange the offer in such a way that the high-revenue type prefers the wage offer and the low-revenue type prefers the buyout offer. This makes it possible for the union to bargain with (potentially) two different types at the same time.

Notice the specific way in which screening takes place: in effect, the union demands a high wage from a profitable firm and offers a low price for an unprofitable one, but it never demands a low wage from an unprofitable firm and offers a high price for a profitable firm. As a consequence of this screening strategy buyouts occur only in unprofitable firms.

Consider now the case when the management makes the initial offer. Again, we state first the benchmark cases of complete information and asymmetric information with single element offers.

Fact 3: (Rubinstein, 1982) With complete information, the unique subgame perfect equilibrium for bargaining games with single element offers is such that the management offers a settlement for a wage br/( 1 + 6), and the union accepts this proposal immediately.

Fact 4: (Rubinstein, 1985) In the asymmetric- information bargaining game between an uninformed union and an informed management where the management makes the initial offer and offers are restricted to a single element, there exists a unique sequential equilibrium outcome if 7ro < U/h, in which the management

24 A bargaining sequential equilibrium is a sequential equilibrium with some restrictions on how the uninformed player revises beliefs. See Rubinstein (1985) for details.

2S The offer and counteroffer when 7ro > (/h are x and y, respectively, where x and y simultaneously solve the following two equations:

(FI) y = 6x-(1-7ro)b(1-6)h

(F2) b(h - y) = h - x.

(Fl) and (F2) respectively correspond to dW and ds, in Rubinstein (1985).

26 Indeterminacy means that the players' shares in the revenue are the same whether they bargain over wages or over an employee buyout. This indeterminacy will be re- solved in favor of wage settlement if any of a number of commonly assumed factors are present, such as that employees are more risk averse than owners, employees face higher financing costs, employees have to bear costs of organization in order to execute a buyout, or if there are other costs associated with the transfer of ownership.



offers b/( 1 + 6) for wage and the union accepts it immediately. If 7ro > U/h, then there are two bargaining sequential-equilibrium outcomes: in one equilibrium the management offers 67roh/(l + 6) for wage and the union accepts it immediately; in the other equilibrium the management offers 6e/( 1 + 6) which the union rejects and counteroffers h [1 - (1 - 7ro)62]/( 1 + 6), which in turn will be accepted by the profitable firm, but rejected by the unprofitable firm which counteroffers 67roh/( 1 + 6), which is then accepted by the union.

In an asymmetric-information bargaining game with two-element offers we obtain the following result.

THEOREM 2: In the asymmetric-information bargaining game between an uninformed union and an informed management where the management makes the initial offer, an agreement is reached in the first period. In equilibrium, the management gets r/( 1 + 6) for its share when the revenue is r, r = h, e. (i) When the firm is profitable, the management offers a wage bh/(l + 6) which is accepted by the union with probability one except when a buyout price h/( 1 + 6) is offered at the same time. In the latter case, the union is indifferent between the two offers and may choose between them randomly. However, the probability with which the buyout offer is accepted is not greater than 6/( 1 + 6). (ii) When the firm is unprofitable, the management demands a price e /( 1 + 6) for the firm which is accepted by the union with probability one except when a wage l/( 1 + 6) is offered at the same time. In the latter case, the union is indifferent between the two offers and may choose between them randomly. However, the probability with which the buyout offer is accepted is at least 6/( 1 + 6).

This follows from the fact that the equilibrium constructed in the proof of Theorem 1 is also a sequential equilibrium for the new bargaining game if "t odd" is replaced by "t even" and vice versa. The inequalities which put bounds on the acceptance probability follow from the incentive compatibility of the equilibrium. Theorem 2 implies that even if the management makes the initial offer the employees get the same share they would get

under complete information, because perfect screening occurs. This is again quite different from the single-offer case (see Fact 4). As before the option to make double offers is a very strong screening device. There is a multiplicity of sequential equilibria because we allow random acceptance of offers. However, in this case we can put some bounds on the probability with which the offers are accepted. While the specific bounds are of no interest, they imply that the wage offer is more likely to be accepted when the firm is profitable, whereas the buyout offer is more likely to be accepted when the firm is unprofitable.

Theorems 1 and 2 show that when double offers can be used complete screening is possible, and the union gets a bargaining share equal to that it would obtain under complete information. This outcome is independent of the specific initial belief the union holds about firm profitability. Most importantly, the theorems indicate that buyouts are more likely to occur in unprofitable firms.

III. Extensions

The results stated above were derived under the assumptions made at the beginning of the previous section. The results will remain es- sentially unchanged if several assumptions were altered, for example, allowing for the management to have incomplete information about the profitability of the firm,27 or if the response time between rounds of negotiations was chosen by the parties instead of being fixed exogenously.28

27 Suppose that the management can only observe some signal which conveys information regarding the firm's profitability. Assume that both the probability that the high

signal Sh is observed when r = h and the probability that

the low signal se is observed when r = ( are higher than 1/2. Suppose also that this signal is observed only by the management. In this situation our argument will still be valid if we replace h and ( by the management's evalua- tions when it observed Sh and se, respectively.

28 Even when the timing of responses to offers can be chosen by the responders, as in Admati and Perry (1987), the proof given in Appendix A is still valid. The union can force the management to choose between two alternatives, and hence complete screening occurs. As a consequence, the management has no reason to delay its response, and the results obtained in the previous section remain intact.


VOL. 86 NO. 3 BEN-NER AND JUN. EMPLOYEE BUYOUT 511

In this section we explore two extensions. First, we relax the assumption of only two levels of revenue. Second, we examine the possibility that the union and management have nonzero outside options if their negotiations fail.

A. More than Two Levels of Revenue

The results we have obtained thus far are fairly clear-cut thanks mainly to the assumption that there are only two possible levels of revenue. Proposition 1 below extends these results to the continuous (as well as the discrete) revenue case.

PROPOSITION 1: Suppose that firm revenue, r, is a random variable distributed on the closed interval [e, h] with a cumulative probability distribution F(r). In the asymmetric- information bargaining game between an uninformed union (that knows only F(*)) and an informed management (that knows the actual r) where the union makes the initial offer and offers may consist of two elements, wage and price for ownership transfer, the following is a sequential-equilibrium outcome: the union offers (h'/(1 + 6), b6'/(1 + 6)) in the first period; the management offirms with revenue r 2 h' accepts the wage offer and the management offirms with revenue r c e' accepts the buyout offer; the management offirms with revenue r, e' < r < h', counteroffers (br/(1 + 6), r/(1 + 6)) next period, and the union accepts the wage offer with probability 1/(1 + 6) and the buyout offer with probability 6/(1 + 6).

The definitions of h' and e' and the proof can be found in Appendix B. We provide a sufficient condition for uniqueness later in this subsection.

In order to understand better the implications of Proposition 1, consider the example of a discrete distribution (covered by the Propo- sition) with three levels of revenue, r = e, m, h, where e < m < h. Denote by p(r) the probability that revenue is r. Then, h' = h and e' = e if p(h)(h - m) 2 p(m)m(l - 62) and p(fe)6(m - e) 2 p(m)m(1 - 62). That is, unless m is close to h or e, complete screening takes place and the union gets the share of revenue it would get in the complete-information bargaining game, with a buyout outcome if

revenue is e and a wage settlement if it is h. However, if the revenue is m then delay occurs, unlike in the case of two levels of revenue. If m is close to either h or e, then it is not worth it to the union to delay a settlement. The union offers (m/(1 + 6), 6e/(1 + 6)) or (h/ (1 + 6), bm/( 1 + 6)) depending on whether m is closer to h or 1, and agreement is reached in the first period. Thus in this case pooling between 2h and 2m or between 2m and 2e occurs. With m quite different from the other two revenue levels, agreement will be delayed; a wage settlement or ownership transfer will occur with a certain probability. For example, if e = h/2, m = (e + h)/2, 6 = 0.9, and p(r)

= '3 for r = , m, h, then when the actual revenue is m, agreement will be delayed by one period and an employee buyout will occur with probability 0.4737 and a wage settlement with probability 0.5263. If m is closer to e, for example, m = (3e + h)/4, then the probability of a buyout increases to 1. 2m and 2e are pooled together. There will be no delay in this case.

Compared to the bargaining outcome under complete information in which the union gets r/( 1 + 6) for all r with no delay, the union gets less (and the owners get the same or more) in this equilibrium: if r > h' the union gets less wage; if r < e' the union pays a higher price for the ownership; if e' < r < h' the union gets br/(l + 6) with one period delay. It is also interesting to compare our equilibrium outcome with the asymmetric information bargaining outcome with single element offers studied by Grossman and Perry (1986). They show that in the (unique) perfect sequential equilibrium agreement is reached consecutively from the most profitable firm and delay could be longer than one period. The comparison suggests that the buyout option enhances efficiency by providing the parties with a screening device other than delay in agreement.29

29 This result cannot be interpreted as an argument in favor of granting subsidies to employee buyouts, because the efficiency result hinges on a voluntary buyout. How- ever, if buyouts are hindered, for example, by imperfect capital markets or similar obstacles (see below), then gov- emnment loans and other forms of support for employee buyouts would represent a good policy.



The equilibrium outcome described in Prop- osition 1 is the only equilibrium outcome under the following conditions:

1. The management uses a stationary strategy. 2. In any subgame in which the management

is indifferent between two outcomes obtained from two different strategies, it chooses the strategy which results in an earlier settlement.

3. Suppose that the management proposes an offer (w, v) which would yield the union at least the equilibrium payoff against any type of management if the union accepts (w, v) with probability (p, 1 - p) for some p E [0, 1]. Then the union accepts the offer.

Condition 1 requires that the management's strategy be independent of time and previous actions but allows that its acceptance decision depend on the current wage and buyout price. Condition 2 encourages early resolution of the bargaining process, and represents a tie-breaking assumption similar to the one made by Rubinstein (1985). Condition 3 describes the union's response to a particular type of offer which is motivated by the following consideration. Suppose there exists an offer which would yield the union at least the equilibrium payoff against any type of management if accepted with a certain probability combination. Accepting the offer with the right probability poses no risk for the union. Under condition 3 those types of management which would benefit from an earlier agreement will actually make the offer. With- out condition 3, however, the offer might not be made because the union might in fact reject the offer in anticipation of an even higher payoff. Condition 3 guarantees that there re- mains no more mutually beneficial opportunity to improve the equilibrium outcome within the given information structure.

PROPOSITION 2: Under conditions I to 3 the equilibrium outcome described in Propo- sition I is the only possible equilibrium outcome.

See Appendix C for the proof. The next corollary follows from this proposition.

COROLLARY: Suppose that conditions I to 3 hold. In the situation described in Proposi- tion I if the management makes the initial offer, then the following is the unique equilibrium outcome: the management of firms with revenue r offers (brl(1 + 6), r/(1 + 6)); the union accepts the wage offer with probability 1 / (1 + 6) and the buyout offer with probability 6/(1 + 6).

The sharp results obtained with two revenue levels are weakened. In particular, we need additional conditions in order to obtain uniqueness. But the flavor of the previous results is preserved: the less profitable firm is more likely to be purchased by its employees. These results have an added touch of reality in that not all unprofitable firms are bought by their employees, and some profitable firms are purchased by employees.

B. Nonzero Outside Option

The model developed in Section 2 was based on the assumption that if negotiations break down completely, the parties have noth- ing to fall back on. Typically, however, the parties have some options outside their relationship: employees may eventually find alternative employment and owners may move their capital elsewhere or hire substitute workers. The analysis can be easily extended to include such nonzero outside options.

Suppose that the employees have an outside option w0. If w0 eI/( 1 + 6), then Theorems 1 and 2 will not be affected, because the outside option is never binding.3" If w0 2 h/( 1 +

3 Well-known refinement criteria based on equilibrium domination tests such as the intuitive criterion of In-Koo Cho and David M. Kreps (1987) and the divinity of Jeffrey S. Banks and Joel Sobel (1987) do not guarantee this be-

cause they do not help eliminate the union's anticipation of a higher payoff.

"' This follows from the principle that the presence of an outside option has no effect if it is lower than the payoff the player in question could obtain in the absence of that option; however, if the value of the outside option exceeds the aforementioned payoff, then the payoff of the player



6), then the union will receive wo regardless of the actual revenue of the firm, or else it will take the outside option. An offer (wo, ( - wo) can be used by the union to guarantee the equilibrium payoff. There is no need to screen in this case, because the payoffs are the same regardless of the actual revenue. The management of the low-revenue firm is indifferent between the two offers, and a buyout may not occur. However, a buyout will never occur if the revenue is high, whereas a buyout may oc-

cur if the revenue is low. If wo falls between h/( 1 + 6) and t /( 1 + 6), then the employees will get wo if the firm is unprofitable and h/( 1 + 6) if the firm is profitable. An offer (h/( 1 + 6), f - wo) can be used by the union to do the screening, and buyout occurs only when the firm is unprofitable. (If wo > e, then an agreement is reached only when the firm is profitable, and the situation is the same as where there is no uncertainty.) Thus, as wo increases a buyout becomes less likely. The reason is that employees with high outside options will not be employed in unprofitable firms, hence they will not need to screen as much as other employees.

Consider now the outside options of the owners. Let vr be the outside option of owners of a firm with revenue r, r = h, (. Let Xr = max{ Vr, 6r/(1 + 6) }. If O < xh - xe < h - X, then our previous analysis holds. The union can screen by offering (h - Xh, xe), and a buyout occurs when the firm is unprofitable. How- ever, if xh - xe > h - e, then the same offer cannot screen the two types. In this case, depending on which is larger between h - xh and (1 - 7ro)(I - xe), the union will settle with the low wage h - xh with both types of firm, or else it will reach an agreement only with the unprofitable firm either at the high wage f -

Xe or at the buyout price xe. In order to consider the effect of changes in the firm owners' outside option, assume that there are three possible levels of revenue, and all types of firm share the same outside option vo. When vo s be(1( + 6), the previous result will not change, because the outside option is not binding. If be(1( + 6) < vo s 6m/(1 + 6), then the situation is the same as if ( = (1 + 6)vo/

6. As vo gets close to bm/( 1 + 6), the union offers (h/(1 + 6), bm/(1 + 6)) and a buyout will occur when the revenue is m as well as e. Thus in this case an increase in the firm's outside option increases the probability of a buy-

out. If 6m/(1 + 6) < vo - bh/(l + 6), then the union offers (h/( 1 + 6), vo) and a buyout will occur when the revenue is m or e. If vo > 6h/( 1 + 6), then the union offers (h - vo, vo) and again a buyout occurs when the revenue is m or E. Hence, when all types of firms have the same outside option, the increase in the outside option increases the probability of a buyout. The reason is that as the firm's outside option increases the number of types for which the outside option is binding increases. All the types for which the outside option is binding look the same to the union and are screened from more profitable firms through buyouts.

IV. Some Implications and Conclusions

When employees are at an informational disadvantage, they suspect that the management represents profits as lower than they actually are. In this paper we have shown that the phenomenon of employees buying out firms in which they work may result from an attempt by employees to reduce their informational handicap. By appropriately structuring wage and purchase-price offers, employees can elicit responses that help them determine the type of firm (its profitability) with which they bargain. The expansion of the bargaining do- main from wages only to include also the possibility of ownership transfer increases efficiency by providing the parties with a screening device other than delay in agreement.

The key finding of this paper is that firns facing financial difficulties are more likely to be purchased by their employees than profitable firms.32 The reason for this is that employees structure their offers so that more profitable finns will tend to accept high-wage demands, whereas less-profitable firms will tend to accept low-price

is simply the value of the outside option. See Avner Shaked and John Sutton (1984).

32 These findings suggest that, because they are drawn predominantly from the unprofitable end of the distribution, in the absence of any compensatory factors (such as greater productivity), firms purchased by employees will be in more peril of failure than other firms.



offers for their finns. This finding is quite robust, and it survives various changes in the assumptions underlying the model.

Industry and economy-wide recessions, when difficulties are experienced simultaneously by many firms within an industry or the entire economy, are therefore likely to increase the incidence of employee buyouts. Al- though the existence of a widely-acknowledged recession may buttress the claim of difficulties in individual firms, it by no means provides information about the specific profitability of individual firms. Hence the main effect of recessions is to increase the proportion of unprofitable firms rather than eliminate asymmetric information, thus leading to a greater incidence of employee buyouts.33

Asymmetric information and firm profitability may precipitate an employee buyout. There are several factors that also affect the likelihood of buyouts. We concluded that de- clines in employees' options outside the firms in which they work (due, for example, to an economy-wide recession) will make them more likely to conclude a buyout deal. Im- provements in owners' outside options (for example, as a result of lower impediments to the movement of capital to Mexico) increase the likelihood that they will sellout to employees.

Will employee buyouts occur whenever and wherever the circumstances shown in this paper to favor buyouts do arise? Certainly not. First, there might be insufficient awareness

and acceptance of employee ownership among employees and owners to even attempt it.34 Second, because employees may face higher borrowing costs than others, the cost of ownership transfer may stifle employee buyouts.35 Third, the purchase of a firm by employees entails problems of collective action, which amount to an additional cost that reduces the probability of an employee buyout. Differ- ences in the productivity of employee-owned firms relative to conventional firms or in the tax treatment they enjoy will also affect the potential for buyouts in an obvious direction.36

Various observers have identified unfavor- able economic circumstances at the level of individual firms, industries, and the entire economy as being conducive to employee buyouts. For example, in the late nineteenth and early twentieth centuries, many employee buyouts occured during recessions in the shin- gle, weaving, fish-canning, shoe-manufacturing, cigar-making and other industries, at the initiative of either employees, their unions, or employers (Arie Shirom, 1972). Most plywood cooperatives in the Pacific Northwest were formed through employee buyouts during periods of financial distress in the first half of the twentieth century (Ben Craig and John Pencavel, 1992). During the 1980's, hundreds of successful and failed attempts at employee buyouts of medium-sized and large companies, many of which were experiencing financial difficulties, were documented in the United States 37 and in other developed market economies.38

33 The permanent decline of an industry may have an ambiguous effect on employee buyouts. In addition to a similar effect to the one discussed in the text, an expected

decline of an industry may convince management that the long-run profitability associated with complete information is greater than that associated with maintenance of asymmetric information, hence inducing it to open the "spigot of information," for example by adding employees representatives to the board of directors, or establish- ing joint labor-management committees.

3 For example, the idea of a possible employee buyout of United Airlines was first raised (in 1985) by outsiders, Louis Kelso, the creator of the ESOP idea, and F. Lee

Bailey, an attorney married to a United employee (Hyde and Livingston, 1989 p. 1157). Awareness of employee ownership has apparently grown in recent decades, per- haps due to the promulgation of ideologies stressing self- reliance and sometimes even employee ownership (as in

the case of Margaret Thatcher in Great Britain), and the

prominence of some employee-owned firms.

3 See Herbert Gintis (1989). With improvements in financial markets, these costs may have been lowered in recent times.

36 Lowering of the various obstacles to employee ownership will, as noted in the introduction, lead to buyouts if employee-owned firms are more productive than conventional firms.

3 See Joseph Blasi and Douglas Lynn Kruse (1991), especially Appendix F, and Hyde and Livingston (1989), especially the Appendix. The first authors concentrate solely on employee-owned firms with shares traded on stock ex- changes, and the latter authors focus on union-lead buyouts that were financed through employee stock ownership plans. Thus both studies exclude many employee-owned firms, including well-known cases such as Avis.

38 See Bradley and Gelb (1983, 1985), and Rob Paton (1989). In a recent paper, Susan Chaplinsky et al. (1994)



These observations conform generally with our theoretical prediction that the incidence of employee buyouts is inversely related to the business cycle. Unfortunately, there is no econometric evidence to bear directly on our hypotheses. If a panel data set containing information on firms that were bought out by employees as well as on firms that settled on wage agreements could be constructed, these hypotheses could be tested by estimating the effect of profitability on the probability of a buyout, and the effects of labor-market conditions (employees' outside options) on this probability.39 A weaker test requiring only industry-level panel data would be to relate the incidence of employee buyouts in individual industries to industry-level productivity. These tests can discriminate between our hypotheses and the hypothesis that employee buyouts come into existence because they can reap some productivity advantages (this hypothesis does not link buyouts to product or labor- market conditions) .40

The factors that affect the cost of ownership transfer to employees are not fixed over time and across place, hence the estimated relationship between employee buyouts and profitability will vary. If this cost has dropped in recent decades, as we conjecture, then the strength of the relationship will be most strongly manifested in more recent data. This would also explain what

seems to be a more pronounced increase in the incidence of buyouts in response to recessions in the 1970's and 1980's than has been the case in the more distant past.

The model developed in this paper may be extended to explore related phenomena. For example, employee buyouts can be viewed as instances of vertical integration by employees into the firms in which they work. Firms often suffer from incomplete information about their trade partners. The attempt to improve their information through screening may be investigated as an additional reason why some firms buy out the producers of their inputs to become verti- cally integrated corporations, while other firms choose to purchase their inputs on the market.

APPENDIX A

We provide the proof of Theorem 1 below. First, we need some preliminary results which we provide as lemmas. For simplicity we denote a = 1/(1 + 6).

LEMMA 1: In a sequential equilibrium, (i) the (undiscounted) share of the union never exceeds ah, and (ii) the (undiscounted) share of the management is at least 6ae.

PROOF: For conventional single-offer bargaining

games, (i) has already been proved in the literature (for example, Lemma 3.1 of Grossman and Perry, 1986). Since the proof does not rely on the single-offer aspect, it is still valid for our model. (ii) can be proved in a similar way.

Define ur to be the infimum of the set of the sequential equilibrium payoff of the management when the revenue is r. Then, Lemma 1 implies the following.

LEMMA 2:

(i) Uh 2_ 6ah. (ii) ue 2 6ah.

Define Zh to be the infimum of the sequential equilibrium share of the management

analyzed in detail seventeen employee buyouts that took place during the 1980's in the United States. The authors conclude: "Our evidence suggests that EBOs [employee buyouts] typically occur in firms with financial difficulties and in industries that experience a high growth in employee earning. These findings are consistent with the hypothesis that employee participation in buyouts is motivated in many cases by a need to restructure labor contracts. Straight wage reductions may be infeasible because employees, being asymmetrically informed, do not trust managers when the latter claim concessions are needed" (Chaplinsky et al., p. 25).

'9 Profitability represents a current and expected variable. At the firm level, it could be measured around the time of negotiations, correcting for the possibility that, for various reasons, a buyout may affect productivity and therefore post-buyout profitability.

4 To discriminate between our explanation and that of Miyazaki (1984) and Browning (1987) much more detailed data would be needed, including specific information about the circumstances of individual firms before and after buyouts.



when the revenue is high in a subgame which begins after the initial offer by the union is rejected. Then, Lemma 2 implies the following.

LEMMA 3: Zh 2 ah.

Define - to be the supremum of the sequential equilibrium share of the management when the revenue is low in a subgame which begins after the initial offer by the union is rejected. Lemma 4 follows.

LEMMA 4: Z-e a? .

PROOF:

Suppose Ze > ae. Define? = - ae, >0. Then, for 1 < ( 1- 62) ?, there is z such that

Ze z Z > Ze - s1 and 2e receives z in equilibrium. Either the offer is made by the management and accepted by the union, or vice versa.

Case 1: The offer is made by the management and is accepted by the union.

The share cannot be larger than ae if the union is certain that r = e. Hence, the union must be uncertain about the firm's revenue when the offer is made. This implies that no agreement would have been reached with 2h either so far. Then, by Lemma 3 when the union accepts the offer, the union's expected share is

(Al) x < 7r6ah + (1-7r)(e-z).

Consider the following strategy for the union: follow the equilibrium strategy up to period (t - 1), reject the offer in period t, and offer (ah - 82, 6Z4e + 82) in period (t + 1), where 82 is an arbitrary small positive number. 2e will accept the buyout offer. Thus, if the offer is rejected, then the union would believe that r = h, and consequently the management's share will be 6ah. Hence, 2h will accept the wage offer in period (t + 1). This strategy guarantees the union the following share:

(A2) x' = irah + (1 - ir)( - 6e) -2

By subtracting (Al) from (A2) discounted by 6, we obtain

6x' - x

2: (I - )7r{ (6 I )f + Z _ 62 Ze }-682

>( -7r) {(6- l)e

+ (1 - 62)Z- _6 } - 662

= (1 - r) { (1- 62)? - 61 } - 682.

Since (1- 62)6 > si and 62 is arbitrary, we can get 6x' > x, a contradiction.

Case 2: The offer is made by the union and

is accepted by 2e.

In this case, too, the union must be uncertain about the firm's profit. Hence, no agreement would have been reached with 2h either so far. The equilibrium share of the union is

x < Irah + (1 -7r)(e - z).

By offering (ah - 82, 6Te + 62) instead, the union can secure

x' = 6[7rah + (1 - 7r)(e - Ze)- 82],

which is larger than x as we have already seen.

Now define ue to be the supremum of the set of the sequential equilibrium payoffs of the management when the revenue is e. Then we have Lemma 5.

LEMMA 5: U-e ' 6ae.

PROOF: Similar to Lemma 4. (One can use the fact

that the union can always offer (ah - s, 6ae + 6) to screen the two types.)

Lemmas 2 and 5 imply that the equilibrium payoff for 2e is exactly 6ae and that for 2h is at least 6ah. Hence, the maximum equilibrium payoff for the union is ae when r = e and ah when r = h. Define Wr(1ir) to be the infimum (supremum) of the union's equilibrium payoff in the original game when the revenue is r,



v J i

ah

al

II X \I>

0 6al6 ah I h w

FIGURE 1. UNION'S STRATEGY: REGION I, ACCEPT W; REGION II, ACCEPT v; REGION III, RANDOMLY

ACCEPT W OR v; REGION IV, REJECT BOTH.

r = h, e. Then, We -< ae and -h < ah. In the following lemma, we will show that we 2 ae and Wh 2 ah.

LEMMA 6: we 2 ae and Wh 2 ah.

PROOF: Suppose either one is false. Then for some

equilibrium the union's payoff is less than 7roah + (1 - ir0)ae. Consider the union's strategy of offering (ah - s, 6ae + s) in the first period for small s > 0. 2e will accept the buyout offer, because acceptance of the wage demand yields e - ah + s which is less than 6ae + s and rejection yields 6ae. 2h will accept the wage offer in equilibrium for the following reason. Suppose that 2h rejected the offer. 2h'S payoff must be at least 6ah + s in the subsequent game. This is only possible when the union is uncertain about 2's type, which, in turn, is only possible if 2e also rejects the offer, which is not the case as we saw. Hence, 2h will accept the wage offer. This strategy yields to the union 7roah + (1 - Iro)ae - s which is greater than the equilibrium payoff for s small enough, a contradiction.

PROOF OF THEOREM 1: Since the payoff to the management is at

least 6ar and the payoff to the union is at least

ar, the agreement must be reached in the first period. The offer that is accepted by 2h must be a wage offer, since otherwise 2e's payoff would be 6ah. The offer that is accepted by 2e must be a buyout offer, since otherwise 2h'S payoff would be larger than 6ah, leaving to the union less than ah. Hence, the offer made by the union must be (ah, 6at). The following strategy actually constitutes a sequential equilibrium.

Union's strategy: At t = 0, 2, 4,..., offer (ah, 6at). At t = 1, 3, 5, ..., respond as follows (see Figure 1.):

(i) accept w if the offer belongs to region I,

where w 2 6ah and w + v 2 h; (ii) accept v if the offer belongs to region II,

where v < ae and w + v < e; (iii) accept w with probability a and accept v

with probability (1 - a), if the offer belongs to region III, where e < w + v < h, and w 2 6v;

(iv) reject both if the offer belongs to region IV, where w < 6ah, v > aC, and w < 6v.

Management's strategy: At t = 0, 2, 4, ..., respond as follows:

(i) acceptw,ifw < arandv ?r-w; (ii) accept v, if v 2 6ar and v > r -w; (iii) reject both, if w > ar and v < 6ar.

At t = 1, 3, 5, ... , offer (6ar, ar).

Union's belief: If 7r(s') = 1(0), then 7r(St+ 2)= 1(0). If O < 7r(s') < 1, then ir(s', (w, v)) = 1, if the offer belongs to region I; 0, if the offer belongs to region II; (w + v - -t)/(h - 4), if the offer belongs to region III; 7r0, if w < 6aro, and v > aro; (w - 6aC)/ (6a(h -43)), if 6aro - w < 6ah and w < 6v; (v - a43)/(a(h - 43)), if a4 < v - aro and w < 6v; where ro = -7roh + (1 - i7ro)f (see Figure 2).4'

To check the sequential rationality of the union's strategy, notice that:

4" For the offers off the equilibrium path, beliefs are assigned to justify union's behavior and keep the union's strategy stationary. Of course, one can construct different beliefs.



h

II III

0 I h W

FIGURE 2. UNION'S BELIEF: REGION I, 7r = 1; REGION II,

7r = 0; REGION III, 7r = (w + v - )/(h- 1).

(i) accepting w is optimal if w 2 7rh + (1 - 7r)f - v and w 2 6a[7rh + (1 - 7r)f

(ii) accepting v is optimal if w < 7rh + (1 7r) - v and 7rh + (1 - 7r)e - v 6a[7rh + (1 - ir)f];

(iii) rejecting both is optimal if w < 6a[irh + (1 - ir)f ] and v > a[irh + (1 - ir)f].

APPENDIX B

PROOF OF PROPOSITION 1: In order to prove the proposition we need to

construct an equilibrium-strategy profile together with the union's belief. First, we need to introduce some notation. The union's belief

after a history s' is denoted by F(rI s'). By con- vention F(rIs0) = F(r). If F(rls') has a point mass at r, we write the probability measure at r as ir(rIs'). Let h' and e' be defined as

(et', h') E argmax(a,,, (r - 6aa)dF(r Is')

tb- th

+ 62aridF(rIs') + fhabdF(rIs').

If the management of a firm with revenue r could make an offer in the next period that assures it a share of the revenue equal to what it could get in a complete-information bar-

gaining game, then the union would maximize its expected payoff by offering (ah', 6ae '). The management of a firm with revenue of at least h' will accept the wage offer, whereas the management of a firm with revenue of at most e' will accept the buyout offer. We denote the probability measure concentrated on

h'(e') by 7rh'(7re'). Also define ro(s') = fef rdF(r Is'), and

uo(s')= f (r - 6ae')dF(r Is')

+ 6J2ardF(rls') + f ah'dF(rls'). I P+ h'I ro(s') is the expected revenue according to the distribution F(rls'), and uo(s') is the expected payoff to the union when making the offer (ah', 6at') in the situation mentioned above. We define h * = sup [support of F(r st - '2)I, e * = inf[support of F(rl s' - 2)] . Given a distribution F and an interval [a, b], F - [a, b] represents the distribution obtained from F conditional on the fact that r t [a, b ]. Finally define h = max{h', (1 - (1 - 62),

6)h*} ande = min{I',e*/62}.Wecannow extend our analysis to the continuum case by focusing on an equilibrium analogous to the previous one. The following is a sequential equilibrium.

Union's strategy: At t = 0, 2, ..., offer (ah', 6ae' ). At t = 1, 3, ... , respond as follows:

(i) accept w if the offer belongs to region I, where w 2 6ah' and w + v -h;

(ii) accept v if the offer belongs to region II, where v s aC' and w + v s e;

(iii) accept (w, v) with probability (a, 1 - a) if the offer belongs to region III, where w - 6v and C' < w + v < h';

(iv) reject both otherwise.

Management's strategy: At t = 1, 3,..., offer (6ar, ar). At t = 0, 2,..., respond as follows:

(i) accept wifw s arand w r-v; (ii) accept v if v s bar and v > r-w; (iii) reject both otherwise.


VOL 86 NO. 3 BEN-NER AND JUN: EMPLOYEE BUYOUT 519

Union's belief:

(i) if the management's last offer belongs to region I, then ir(h' js') = 1;

(ii) if the management's last offer belongs to

region I, then ir(e'Is') = 1; (iii) if the management's last offer belongs to

region III, then 7r(w + v I s') = 1; (iv) if w < 6uo, and v > ro - 6uo, then

F(rls') = F(rls' 2)I - h]; (v) otherwise, F(rls') = aF(rls'-2) +

b7re, + c7rh - I , AhI, for a,b,c-O such that a + b + c = 1 and rejection is optimal.42

It is trivial to check that the management's strategy is a best response to the union's strategy. It is also clear that the union's strategy is a best response to the management's strategy given its belief. The union's belief satisfies Bayes' rule on the equilibrium path.

APPENDIX C

We provide the proof of Proposition 2, the uniqueness result. First, we introduce a lemma.

LEMMA 1': In any sequential equilibrium 2r's payoff is at least 6ar.

PROOF: Let GEbe the set of sequential equilibria with

the support of union's initial belief contained in [f, h]. For e GE and t= 1, 3, 5, ... , define

A(e, t) = {(w, v)Ipw - (1- p)v 2 pw' - (1 - p)v', where (w', v') is accepted by the union with probability (p, 1 - p) in period t in e}, where A(e, t) = [0, h] X [0, h] if the game ends before t according to e. Define

U = [0, h] x [0, h]

- neeE[nSf=l A(e, 2s -1)].

The boundary of A (e, t) traces the points most favorable to the management among the points attainable at t according to the union's acceptance strategy in equilibrium e. U represents the points unattainable in some period in some equilibrium. Define

c = sup{dI thereis(w,v)in U

such that w - 6v = d }.

We claim that c < 0. Suppose that c > 0. Let

(wo, vo) be a point at which the straight line w - 6v = c is tangent to the closure of U. By the definition of c the offer (wo - s, vo + s) is rejected by the union in some period in some equilibrium. After rejection the management's payoff is not less than a(r - wo) + (1 - a )vo two periods later. Hence, the maximum payoff the union can get after rejection is

6[r - 6 a(r- wo) + (1- a)vo}]

= 6ar + 62a(wo - 6vo)

= 6ar + 62ac.

On the other hand, by accepting the offer (wo - s, vo + s) with probability (a, 1 - a) the union gets

aw0 + (1 - a)(r - vo) - s

= bar + a(wO - 3vo) - 6

= bar + ac - s > bar + 62ac

for small s,

a contradiction which proves our claim. Then {(w, v)Iw - 3v > 0} is contained inA(e, t) for t = 1, 3, 5, ..., for any equilibrium. Hence, 2r can get no less than ar in period 1 in particular. This completes the proof.

PROOF OF PROPOSITION 2: In order to prove the proposition we need

some preliminary concepts. Consider a line w + v = r. Each point in this line represents a wage and a buyout offer between which the management of type r is indifferent. The management of type r prefers a point in the offer

42 The weights a, b, c after an offer (w, v) is made can be chosen for example as the weights given to the three

points (buo, ro - buo), (6bat', at'), and (6ah', ah') when (w, v) can be expressed as a convex combination of the three points. If (w, v) is not a convex combination, it is still a linear combination, and the weights can be chosen from the linear coefficients by setting the negative coef- ficient to 0 and rescaling the remaining two.



space [0, h] x [0, h] to any other point which lies to the southeast of it. The payoff the management of type r derives from an outcome (wo, vo, p, t) is the same as the payoff it derives from wage offer ws(r) 1 - 3'-sp)r + t-s{w I - (1 - p)vo} and buyout offer vs(r) bt-{p(r - wo) + (1 - p)vo} in period s. If we trace the points (ws(r), vs(r)) for all r, we obtain a line segment which satisfies

(I - ''-p ) 1 = (1 L'P wo

/1 -p\ + ( ) vO, vs(e) < vs < vs(h).

Fix an equilibrium. Consider a subgame starting after the union offers (h, 0) in period 0. This offer will be rejected by all types according to Lemma 1'.

Step 1. The subgame ends in period 1.

Denote by (Wr, Vr, Pr, tr) the equilibrium outcome in the subgame when the revenue is r. Define

+ Wr + (1 ; r }) Pr

Hr = (w, v) I w > I tr- IPr )

+ Wr + 1 -Pr) Vr} Pr

and

A* = UrIr - UrHr-

A * is a union of line segments and convex toward southeast. Line w + v = r intersects A * exactly at one point, and the intersection represents 2r's equilibrium payoff. Pick a point (w*, v*) in A* and let k E [0, oo] be

the slope (dwldv) of a line tangent to A * at (w*, v*). The intersection of the line tangent to A * at (w *, v*), which we denote by L* and the line w + v = r represents 2r'S payoff when the union accepts the wage offer w * and the buyout offer v * with probability 1/(1 + k) and kl( 1 + k), respectively. Since L* lies below A *, accepting the offer (w *, v *) with probability 1/( 1 + k) and kl ( 1 + k) guarantees the union a payoff no less than the equilibrium payoff against any type. Hence, according to condition (3) offers in A * will be accepted. Then, by condition (2) agreement will be reached in period 1. Let (w*, v*) be the intersection of A* and the line w + v = r. Denote by Pr the probability with which w* is accepted.

Step 2. Either W* h bah (hence vh ? ah) or Ph = 1, and either v e at (hence we* 2 ?af orpe = 0.

If Ph < 1, then wh c E(r) - vh . This implies E(r) 2 w* + v* = h, which means that the union believes that the revenue is h with probability 1. Then the union would not accept w* < bah or v* > ah. If pe > 0, then w* 2 E(r) -4v*. This implies E(r) < w* +v = 1, which means that the union believes that the revenue is f with probability 1. Then the union would not accept v > at or we < baft. Define r- = inf{ rIw = wN } and r = sup I rI w * = we }. Then, according to Step 1 the management of type r > r- makes a wage offer wh* and the management of type r < r makes a buyout offer 4*43

Step 3. w * = barforr <r<r-.

By Lemma 1' wh barF. If r- = h, then h is the only type offering (wh*, vh) and wh* must be bah. If r-< h and wh* < bar-, then the union would rather reject wh* and counteroffer (1 - ) r-+ bwh - s for small s. This is because, if 2r makes a wage offer w, then stationarity and

4 A wage offer w (buyout offer v, respectively) means an offer (w, v) where w (v, respectively) is accepted with probability 1.



subgame perfection require that it accept any wage w' < (1 - 6)r + bw. Hence, w* = barF. Similarly, v = ar. The fact that A * is convex toward southeast together with Lemma 1 ' implies that w* = bar for r < r < r.

Step 4. r= h and r = f.

Suppose 7 < h. Consider a subgame starting after (ar' + s', bar' - s') is offered in period 0, where r-< r' < r-+ sfors, s' > 0. Subgame perfection implies that the management of type r t [(r' + br-)1(1 + 6) - S'W6, (r' - 62r)1(1 - 62) + s'I(l - 6)] would accept either the wage or the buyout offer. Hence if the management rejects the offer the union would infer that r E [(r' + br-)1(1 + 6) - s'6, (r' - 62)1(I - 62) + 'I(1 - 6 )]. If r' rejects the offer and propose w* = 6ar-, the union will reject as long as s' < (1 - 6)62a(r' - 7), because the union gets more than b6aby rejecting and offering w' = (1 - 6){(r' + br-)/(I + 6) - ? '16} + 62a7. After the rejection the management gets at most r' - w' in the following period. Since 62(r' - w') < bar' for small s and s', the payoff of the management of type r' is less than bar'. However, according to the proof of Lemma 1 ' the management can get a payoff arbitrarily close to bar'. Hence, the strategy of making a wage offer of bar is not optimal for the management of type r'. This proves that 7 = h.

Suppose r > e. Consider a subgame starting after a wage offer of ar - s, where 0 < s < (1 - 6)r. If the offer is rejected the union would infer that r < r - s. Choose r' E (62r, r - (1 + 6) s). If the management of type r' rejects the wage offer and proposes ve = ae, then the union will reject the offer and the management gets at most bar in the following period. The management's payoff is r' - (ar - s) < bar' if it accepts the wage offer, and at most 63ar < bar' if it rejects the wage offer. Hence, the strategy of making the buyout offer of ar is not optimal for the management of type r'. This proves that r = e. According to the previous result this means that w * = bar for all r.

Hence, it must be the case that the management makes an offer (6ar, ar) for some r, and all such offers must be accepted with proba-

bility (a, 1 - a). In fact we can conclude that the management of the firms with revenue r offer (6ar, ar), because otherwise one can always find s > 0 such that 2r'S strategy is not optimal in a subgame starting after the union offers (ar + s, bar - s). For the union offering (ah', 6ae') is the only optimal strategy in such a situation.

REFERENCES

Admati, Anat and Perry, Motty. "Strategic Delay in Bargaining." Review of Eco- nomic Studies, July 1987, 54 (3), pp. 345 - 64.

Aoki, Masahiko. The co-operative game theory of the firm. Oxford: Oxford University Press, 1984.

Banks, Jeffrey S. and Sobel, Joel. "Equilibrium Selection in Signaling Games." Economet- rica, May 1987, 55(3), pp. 647-61.

Ben-Ner, Avner. "Comparative Empirical Ob- servations on Worker-Owned and Capitalist Firms." International Journal of Industrial Organization, March 1988a, 6(1), pp. 7- 31.

' "The Life Cycle of Worker-Owned Finns in Market Economies: A Theoretical Analysis." Journal of Economic Behavior and Organization, October 1988b, 10(3), pp. 287-313.

Blasi, Joseph. Employee ownership: Revolution or ripoff Cambridge, MA: Ballinger Pub- lishing Company, 1988.

Blasi, Joseph and Kruse, Douglas Lynn. The new owners: The mass emergence of employee ownership in public companies and what it means to American business. New York: Harper Business, 1991.

Bonin, John P.; Jones, Derek C. and Putterman, Louis. "Theoretical and Empirical Studies of Producer Cooperatives: Will Ever the Twain Meet?" Journal of Economic Liter- ature, September 1993, 31(3), pp. 1290- 320.

Bonin, John P. and Putterman, Louis. Economics of cooperation and the labor-managed economy. Harwood Academic Publishers, 1987.

Bradley, Keith and Gelb, Alan. Worker capital- ism: The new industrial relations. London: Heinemann, 1983.



. "Employee Buyouts of Troubled Companies." Harvard Business Review, September-October 1985, pp. 121-30.

Bradley, Keith and Nejad, Aaron. Managing owners: The National Freight Consortium in perspective. Cambridge: Cambridge Uni- versity Press, 1989.

Browning, Martin. "Co-operatives, Closures, or Wage Cuts: The Choices Facing Workers in an Ailing Firm." Canadian Journal of Eco- nomics, February 1987, 20(1), pp. 114-22.

Chaplinsky, Susan; Niehaus, Greg and Van de

Gucht, Linda. "Employee Buyouts: Causes and Consequences." Working Paper No. DSWP-94-32, Darden Graduate School of Business Administration, University of Vir- ginia, 1994.

Cho, In-Koo and Kreps, David M. "Signaling Games and Stable Equilibria." Quarterly Journal of Economics, May 1987, 102(2), pp. 179-221.

Conte, Michael. "Entry of Worker Coopera- tives in Capitalist Economies." Journal of Comparative Economics, March 1986, 10(1), pp. 41-47.

Conte, Michael and Jones, Derek C. "In Search of a Theory of Formation for U.S. Producer Cooperatives: Tests of Alternative Hypoth- eses." Proceedings of the 37th Annual Meeting of the Industrial Relations Re- search Association, 1985.

Conte, Michael and Svejnar, Jan. "The Perfor- mance Effects of Employee Ownership Plans," in Alan Blinder, ed., Paying for productivity. Washington, DC: Brookings Institution Press, 1990, pp. 143-81.

Craig, Ben and Pencavel, John. "The Behavior of Worker Cooperatives: The Plywood Companies of the Pacific Northwest." American Economic Review, December 1992, 82(5), pp. 1083-105.

FitzRoy, Felix R. and Mueller, Dennis C.

"Cooperation and Conflict in Contractual Organizations." Quarterly Review of Eco- nomics and Business, Winter 1984, 24(4), pp. 24-49.

Gintis, Herbert. "Financial Markets and the Po- litical Structure of the Enterprise." Journal of Economic Behavior and Organization, May 1989, 11(3), pp. 311-22.

Grossman, Sanford and Hart, Oliver. "Implicit Contracts under Asymmetric Information."

Quarterly Journal of Economics, Supple- ment 1983, 98, pp. 123-56.

Grossman, Sanford and Perry, Motty. "Sequen- tial Bargaining under Asymmetric Infor- mation." Journal of Economic Theory, June 1986, 39(1), pp. 120-54.

Grout, Paul A. and Jewitt, Ian. "Employee Buy- outs: Some Theoretical Issues." Interna- tional Journal of Industrial Organization, March 1988, 6(1), pp. 33-45.

Hart, Oliver. "Bargaining and Strikes." Quar- terly Journal of Economics, February 1989, 104(1), pp. 25-43.

Hochner, Arthur; Granrose, Cherlyn; Goode,

Judith; Simon, Elaine and Appelbaum, Eileen.

Job saving strategies: Worker buyouts and QWL. Kalamazoo, MI: W. E. Upjohn Insti- tute for Employment Research, 1988.

Hyde, Alan and Livingston, Craig Harnett. "Em- ployee Takeovers." Rutgers Law Review, Summer 1989, 41(4), pp. 1134-95.

Job Ownership Ltd. Struggling to get onto the same side: The experience of America's re- public engineered steels after a union led employee buy-out. A Research Report Pre- pared by Job Ownership Ltd. for Partnership Research Ltd., London, July 1991.

Justice, Betty. Unions, workers, and the law. Washington DC: Bureau of the National Af- fairs, 1983.

Kennan, John and Wilson, Robert. "Bargaining with Private Information." Journal of Eco- nomic Literature, March 1993, 31(1), pp. 45-104.

Kleiner, Morris. "Public Policy Implications of Financial Information Requirements of Na- tional Labor Relations Act." Journal of Ac- counting and Public Policy, Winter 1984, 3(4), pp. 253-57.

Lewin, David. "Opening the Books: Corporate Information-Sharing with Employees." The Conference Board, Research Bulletin No. 167, New York, 1984.

Manning, Alan. "An Asymmetric Information Approach to the Comparative Analysis of Par- ticipatory and Capitalist Finns." Oxford Eco- nomic Papers, April 1989,41(2), pp. 312-26.

Matthews, Steven and Moore, John. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimen- sional Screening." Econometrica, March 1987, 55(2), pp. 441-67.



Milgrom, Paul and Roberts, John. "Price and Advertising Signals of Product Quality." Journal of Political Economy, August 1986, 94(4), pp. 796-821.

Miyazaki, Hajime. "On Success and Dissolu- tion of the Labor-Managed Firm in the Capitalist Economy." Joumal of Political Economy, October 1984, 92(5), pp. 909- 31.

Moene, Karl Ove. "Unions' Threats and Wage Determination." Economic Journal, June 1988, 98(391), pp. 471-83.

National Center for Employee Ownership. Em- ployee ownership report. A Publication of the National Center for Employee Owner- ship, Inc., 14(4), July/August 1994.

Paton, Rob. Reluctant entrepreneurs: The extent, achievements and significance of worker takeovers in Europe. Milton Keynes, England and Philadelphia: Open University Press, 1989.

Podovinsky, Jan and Stewart, Geoff. "The De- terminants of Labour-Managed Entry: Poi- sson Regression Models of U.K. Count Data." Working Paper, Department of Eco- nomics, University of Southampton, South- ampton, U.K., 1991.

Quarter, Jack and Brown, Judith. "Worker Buyouts in Canada: A Social Networking Analysis." Economics and Industrial De- mocracy, February 1992, 13(1), pp. 95- 117.

Rosen, Corey; Klein, Katherine and Young, Karen M. Employee ownership in America. Lex- ington, MA, Lexington Books, D. C. Heath and Co., 1986.

Rubinstein, Ariel. "Perfect Equilibrium in a Bargaining Model." Econometrica, January 1982, 50(1), pp. 97-109.

. ("A Bargaining Model with Incom- plete Information about Time Preferences." Econometrica, September 1985, 53(5), pp. 1151-72.

Russell, Raymond and Hanneman, Robert. "Co- operatives and the Business Cycle: The Israeli Case." Journal of Comparative Eco- nomics, December 1992, 16(4), pp. 701- 15.

Scholes, Myron S. and Wolfson, Mark A. "Em- ployee Stock Ownership Plans and Corpo- rate Restructuring: Myths and Realities." Financial Management, Spring 1990,19(1), pp. 12-28.

Shaked, Avner and Sutton, John. "The Semi- Walrasian Economy." ST/ICERD Work- ing Paper No. 98, London School of Economics, 1984.

Shirom, Arieh. "The Industrial Relations Sys- tem of Industrial Cooperatives in the United States, 1889-1935." Labor History, Fall 1972, 13(4), pp. 533-51.

Stern, Robert; Wood, K. Haydn and Hammer, Tove Helland. Employee ownership in plant shutdowns: Prospects for employment stability. Kalamazoo, MI: W. E. Up- john Institute for Employment Research, 1979.

Whyte, William Foote and Craypo, Charles. Evaluation research on federally assisted employee buyouts. RED-816-G-84-13, Eco- nomic Development Administration, U.S. Department of Commerce, 1988.


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