Dynamic Oligopoly

Jonathan Williams

February 17, 2010

1

1 Evans and Kessides (1994, QJE)

1.1 Introduction

� paper empirically examines the e¤ects of multi-market contact on pricing in the U.S.

airline industry

� looks at the 1000 largest domestic city pairs (very small portion of all markets, but

most important)

� �nd that there is statistically signi�cant evidence of multi-market contact facilitating

collusion that results in higher fares.

� These �ndings are consistent with the claims by industry experts that carriers are

restrained from pricing aggressively out of fear of being punished on other jointly

contested routes.

� there is a nice little quote from a Northwest executive at the beginning of the paper

about how Northwest decided to "live by the golden rule" after they cut prices on one

over-night route to raise load factors and were met by continental cutting fares in a

number of northwest�s most pro�table routes. Wall Street Journal

1.2 Econometric Model

� Theory suggests that the conduct of �rms ought to be di¤erent from that of signle-

product �rms competiting in only one market.

� As Bernheim andWinston (1990) show, mutli-market contact can potentially strengthen

oligopolistic coordination within speci�c markets.

� This paper tests whether the degree of multi-market in the airline industry is enough

to weaken price competition.

� The airline industry is perfect for studying this topic

2

�markets can be clearly and accurately de�ned, travel between an airport pair

in a market is de�ned as a market. if we are going to construct measures of

multi-market contact this is very important.

� airlines compete against one another in a variety of markets and there is a large

number of �rms that have varying degrees of contact with one another in these

market.

� The econometric methodology Evans and Kessides use to test the Bernheim and Win-

ston hypothesis is a very simple linear regression model.

ln(priceijt) = Xijt� + Zjt + �i + �t + �j + �ijt

where priceijt is the average fare charged by airline i on route j in time period t,

Xijt are variables that vary by the �rm�s identity within the route, and Zjt are route

characteristics that vary over time. The remaining terms are airline, time and route

speci�c �xed e¤ects.

� The �xed e¤ects approach is important for controlling for market, carrier, and time

speci�c factors that are invariant across time or routes.

� The X vector includes: RouteMarketShareijt (route market share of each carrier),

AirportMarketShareijt (the average of airlines i�s market share at the two endpoints),

Directijt (the fraction of tickets that are direct �ights), Roundijt (the fraction of tickets

that are roundtrip), the simple average of airline i�s market share at the two endpoints

of route j;

� Does anyone see any problems with any of these right hand side variables if we are

not going to instrument for anything? Roundtrip, Direct, Price, Route Share, are all

simultaneously determined.

� The Z vector includes: RouteHer�ndahljt (the her�ndahl index for route j in year t)

and their measure of multi-market contact.

3

� The measure of contact they use is constructed as follows

�First they construct the matrix A where elements are

akl =nXj=1

DkjDlj

and Dkj is an indicator for whether carrier k is in market j, and n is the number of

markets. Therefore, akl is the number of markets where both k and l are active.

� from this matrix, they then construct a measure of average route contact as

1

(fj(fj � 1)=2)

mXk=1

mXl=k+1

aklDkjDlj

where fj is the number of �rms serving the market.

� Any drawbacks to this measure of multi-market contact? What if one carrier has no

contact with the other two, who have a lot of contact? Does not appear that the mean

is a su¢ cient statistic to capture the e¤ect of multi-market contact on pricing.

� They also construct another rmeasure that weights contact in particular routes more

in the average, by weighting the contact points by the relative revenues in each route.

1.3 Data and Results

� Data comes from the 4th quarter of the DOT�s Origin and Destination Survey for the

years 1984 through 1988. This is a 10% random sample of the population of all tickets

sold by domestic carriers.

� This data is publicly available and I know it well, so if you are ever interested just let

me know.

4

� Table 1

5

� Table 2

6

� Table 3

7

� Table 4

� The statistical signi�cance of the route contact variable is clear, it has a t-value over

12. The question is whether this e¤ect is economically signi�cant. If you move from

the 25th percentile of contact to the 75th (a very large change, way more than one

standard deviation), you get a 5.1 percent increase in fares. On the median ticket that

would increase a round trip fare by about $13 or a one-way fare by $7.50.

� These are actually very small e¤ects compared to other important determinants of

market power, Ciliberto and Williams (2010, JLE) �nd that exclusive leasing practices

of airport boarding gates raise fares by over 10% with this percentage increasing the

more congested an airport is.

8

2 Borenstein and Shepard (Rand, 1996)

2.1 Introduction

� Borenstein and Shepard want to test the Rotemberg and Saloner (1986, AER) and

Haltiwanger and Harrington (1991, Rand) models in the context of the gasoline market.

� The Rotemberg and Saloner (1986, AER) supergame model of tacit collusion shows

that supportable price cost margins increase with expected future collusive pro�ts,

ceteris paribus.

� Otherwise said, the more there is to lose in the future by cheating now, the more

collusive arrangement you can support now.

� This implies that collusive margins will be larger when demand is expected to increase

or marginal costs are expected to decline.

� Borenstein and Shepard use panel data on sales volume and gasoline prices in 43 cities

over 72 months and they observe behavior consistent with this type of collusive pricing.

Controlling for current demand and costs, current margins increase with expected next

month demand and decrease with expected next-month cost.

� There study is a bit di¤erent than the Evans and Kessides work, because the industry

is much di¤erent. Airlines have common set of airlines that compete in many markets

with one another. Here we have retailers that compete with a very large number of

�rms in only one geographically isolated market (market here is well de�ned due to

transport costs). However, it is often the case that one manager sets the price at a

number of stations and also the �rms are somewhat di¤erentiated as we saw with the

Shepard paper on price discrimination (full service, store, car-wash, and di¤erent fuel

addatives).

� The nice part about gasoline markets, is that there are predictable changes both in

retail demand for gasoline and marginal cost.

9

� As far as demand, there is a big seasonal cycle in the demand for gasoline, so some of

the movement in demand can be anticipated. Therefore, retailers can largely predict

demand �uctuations over a calender year.

� A great proxy for marginal cost in this industry is wholesale gasoline prices. The

nice part about this is that changes in wholesale gasoline prices are largely driven by

variation in oil prices. However, the variation in oil prices a¤ects wholesale gasoline

prices with a lag. Therefore, an oil price at a given time allows retailers to form a

solid expectation about the future path of wholesale gasoline prices which largely drive

marginal cost.

� They will measure margins as the price at the pump minus the wholesale price.

2.2 Data

� The data they will use to estimate their model will use data on retail prices, wholesale

prices, crude oil prices and gasoline demand.

� The data comes from the U.S. Federal Highway Administration.

� again, the margin is measured as retail price minus the whole sale price.

10

� Table 1

� Table 2

11

� Table 3

2.3 Econometric Model

� Borenstein and Shepard do a bit of what i would classify as "dirty" econometrics to

start the paper just to look at correlations.

� They form estimates of �rms expectations regarding future volume and whole-sale

prices by regressing these variables on lags of themselves, an autoregressive process.

They then take the �tted values from these regressions and use them as proxies for

retailers expectations of these variables.

� They run OLS regressions of margins on current volume, next period volume, current

12

terminal price, next-period terminal price and a set of time and city �xed e¤ects.

So they �nd that current margins are increasing in future demand (not expected) and

falling in expected future marginal cost (not expected).

� From their, Borenstein and Shepard go on to do some fancier econometrics where they

try to take autocorrelation a bit more seriously. However, none of the results really

change all that much.

13

3 Porter (1983, Rand)

3.1 Introduction

� Price series: two regimes of pricing. Can periods of low pricing be explained as "price

wars"?

� repeated games theory: view observed price series as realization of some equilibrium

price process.

� Standard repeated games (ex. Cournot) with unchanging economic environment: equi-

librium path is constant. Need to speci�cy punishment strategies which support col-

lusive equilibrium, but punishment is never observed on the equilibrium path. Or the

punishment is su¢ cient to maintain collusion.

� We need a model with nonconstant equilibrium price process.

� Two famous models that generate periods of low and high pricing on the equilibrium

path. However, low prices are not caused by cheating, rather they are a manifestation

of collusive behavior:

1. Rotemberg and Saloner (1986): with iid demand �uctuations, �xed discount rate,

and constant marginal production costs, collusive prices will be lower in periods

of above-average demand (price wars during booms). You cheat when current

gains exceed future losses. Current gains highest during boom periods reudce

incentives to cheat by lowering collusive price. Demand shocks are observed by

�rms.

2. Green and Porter (1983): same framework as R-S, but imperfect information,

�rms cannot observe the output choices of their competitors, only observe realized

market price. Prices can be lower during periods of low demand (price wars during

recessions). The market price can be low due to either cheating or adverse demand

shocks. Firms cannot distinguish. Intuitively, the equilibrium trigger strategies

involve low price regime when prices are low. Noncooperativ

14

� The empirical problem is that the noncooperative regime arises due to low demand not

cheating. Therefore, we don�t observe when a "price war" is occuring. How can we

estimate the model?

� Prices should be lower in price war periods, holding the demand function constant.

Price change re�ects change in �rm behavior.

� They decide to estimate a simultaneous-equation switching regression model with un-

observed regimes.

3.2 Data

� observed data are market level output (Qt) and price (pt) for weekly grain shipments

between 1880 and 1886.

� N �rms (railroads), each producing a homogenous product (grain shipments). Firm i

chooses qit in period t.

� Market demand is given by:

log(Qt) = �0 + �1 log(pt) + �2Lt + U1t

Qt =Xi

qit

where Lt is a demand shifter which equals 1 if the Great Lakes are open to navigation

(substitute to rail transport).

� Firm i�s cost function is given by

Ci(qit) = aiq�it + Fi

� Firm i�s pricing equation is then:

pt(1 +�it�1) = mc(qit)

15

where�it = 0 (bertrand)

�it = 1 (monopoly)

�it = sit (cournot)

� After some algebra, aggregate supply can be written as

log(pt) = log(D)� (� � 1)log(Qt)� log(1 +�t�1)

with the empirical version

log(pt) = �0 + �1 log(Qt) + �2St + �3It + U2t

where St are supply shifters (dummies for additional railroads entering the industry)

� Porter assumes thatU1t

U2t~N(0;�)

with this assumption and knowledge of the regime at each point in time (It = 0 or

It = 1)

� Rewriting the structural model as

Y � = BX +�I + U

where

Y � =

0@ log(Qt)

log(pt)

1A0@ 1 ��1��1 1

1A

BX =

0@ �0 �2 0

�0 0 �2

1A0BBB@

1

Lt

St

1CCCA�It =

0@ 0

�3

1A Itwe can then write the FIML function as

L(YtjIt) = j�j�12 jBj exp

��12(Y ��BX +�I)0��1(Y ��BX +�I)

�

16

� However, we do not observe It and so we can�t condition on it. If we want the

unconditional likelihood function, we can treat it as an unobservable and integrate out

across its distribution (bernoulli since it is a dummy variable):

L(Yt) = �L(YtjIt = 1) + (1� �)L(YtjIt = 0)

3.3 Results

� Porter �nds and estimate for �3 = 0:545 which tells us the prices are higher when �rms

are in the "cooperative" regime.

� This estimate implies a � = 0:336 which is between the range of monopoly and bertrand

outcomes.

� Tells us that the cartel earns $11,000 more dollars in weeks when they are cooperating.

17

4 Nevo (2000, Ecmtra)

� wants to test di¤erent model�s of competition that can be nested in the BLP (1995)

model in the RTE cereal market

� the RTE cereal industry is characterized by

� high concentration (c3� 75%;c6� 90%)

� high price-cost margins (� 45%)

� large advertising to sales ration (� 13%)

� numerous introduction of new brands (67 new brands by top 6 in 80s), introduc-

tion and consumers�substituting will be great for identi�cation

� some have claimed that the high price-cost margins are evidence of collusive pricing

� The paper asks the question, is pricing in the industry collusive?

� it also decomposes the observed very high markups into di¤erent components

1. product di¤erentiation

2. multi-product �rms

3. potential price collusion

� the strategy is as follows

1. to �rst estimate a rich demand function

2. calculate the implied price cost margins from di¤erent models of competiton or

conduct ()

pt �mct = �1t st

the models he looks at is single product �rms, multi-product �rms (current setup),

and fully collusive pricing.

18

3. He then compares the predicted price cost margins to the observed price cost

margins (accounting cost data)

� Each element of can be decomposed into the product of two components, jl =

�jr�jr. The �rst component is the own or cross price responsiveness of demand

�jl =@slt@pjt

while the second component is an indicator of product ownership

�jl =

8<: 1 if fj; lg 2 F

0 otherwise

� In the single product case � is an identity matrix. In the multi-product case, � is

a block diagonal matrix where �rm�s only account for the impact of price changes on

their own pro�ts. In the fully collusive case, � is a matrix of ones.

� This allows him to say what portion of the markup is due to product di¤erentiation

(look at the single product markups which is only above cost due to di¤erentiation). It

also allows him to say what portion of the markups are due to �rms being multi-product

�rms (compare single product markups to multiproduct markups). He can then also

look at whether the collusive model can better explain the observed markups than the

multi-product model where �rms do not collude (compare collusive and multiproduct

markups to observed markups).

� Finds no evidence of collusion. The multi-product �rm model best explains observed

price cost margins.

� There are a couple issues with the paper

� Is choice discrete? Consumers very likely buy more than one box of cereal in a

quarter.

� Ignores the retailer, but uses retailer prices to study manufacturer competition.

19

�Why not actually estimate conduct parameters? He uses a "menu-based" ap-

proach. However, Nevo (1998) and more formally Berry and Haile (2009) shows

that the conduct parameters are identi�ed. This means that we could actually es-

timate the conduct parameters which would measure the degree of cooperation or

collusion. However, Nevo (2001) does not have adequate instruments to estimate

these additional parameters.

� Rather than apriori choosing a set of models to test, we could jointly estimate mc

along with the conduct parameters by parameterizing � and estimating this matrix.

Ciliberto andWilliams (2009) are working on this in the airline industry to test conduct

before and after the airline tarri¤ publishing case as well as the impact of multi-market

contact.

20

5 Ericson and Pakes (1995, ReStud), Pakes andMcGuire

(1994, Rand), and Doraszelski and Satterthwaite (2010,

Rand)

� A number of papers have build on the work of Maskin and Tirole (1987, 1988a, 1988b)

to build theoretical models that are adaptable to di¤erent aspects of various industries.

� These papers have also adapted the models in such a way as to make it possible to

econometrically estimate structural parameters of the model and compute equilibria

to perform counterfactual exercises.

� Doraszelski and Satterthwaite (2010, Rand) serves to correct some incorrect conclusions

in Ericson and Pakes (1995, ReStud) and Pakes and McGuire (1994, Rand) involving

existence of equilibria. In particular, it shows that mixed strategy equilibria must

be permitted in this type of game. However, they show how equilibrium puri�cation

is possible by allowing for private information. It also serves as a guide for how to

compute equilibria in MPE models in the presence of imperfect information.

5.1 Model

� Model assumes that �rms are hetergenous.

1. Sources of �rm heterogeneity is �rst encoded in a "state" vector which we will

discuss later. This state vector captures all the payo¤ relevant features of each

�rm (costs, capacity, product quality, etc). A �rm is able to change its state

over time through investment. The investment process is typically assumed to

be stochastic, a higher investment today guarantees a more favorable distribution

of states tomorrow, it does not ensure it.

2. Firms are allowed to di¤er in the opportunity cost of entry and exit. Essentially

�rms have random setup costs and scrap values.

21

� Time is assumed to be discrete and in�nite.

� Incumbent �rms must decide in each period whether to remain in the industry and

if so, how much to invest. Potential entrants have to decide whether to enter the

industry and, if so, how much to invest. Once these decisions are made, product

market competition takes place.

States and Firms

� Let N denote the number of �rms.

� Firm n is described by its state !n 2 , where = f1; :::::;M;M + 1g is the set of

possible states. States 1....M describe an active �rm while state M+1 identi�es a

�rm as being inactive. The degree of heterogeneity of a �rm is not limited to one

dimension. For example, if there are M1 levels of capacity and M2 levels of marginal

cost, then M =M1M2.

� At any point in time, the industry/market is characterized by the list of �rms�states

! = f!1:::::!Ng 2 S. where S = N . So we can refer to !i as a �rm�s state and ! as

the industry�s state.

� If N� is the number of incumbent �rms, then there are N-N� potential entrants. Thus,

once an incumbent �rm exits the industry, a potential entrant takes its slot and has

to decide whether or not to exit the industry. They are short-lived and base their

entry decisions on the net present value of entering today; potential entrants do not

take the option value of delaying entry into account. In contrast, incumbent �rms are

long-lived and solve intertemporal maximization problems to reach their exit decisions.

� All �rms are assumed to discount future pro�ts using a discount factor of �.

Timing

� In each period the sequence of events is as follows:

22

1. Incumbent �rms learn their scrap value and decide on exit and investment. Po-

tential entrants learn their setup cost and decide on entry and investment.

2. Incumbent �rms compete in the product market.

3. Exit and entry decisions are implemented.

4. The investment decisions of the remaining incumbents and new entrants are car-

ried out and their uncertain outcomes are realized.

� To simplify notation, we will use ! to denote the current industry state at the beginning

of the period and !0 to denote its state at the end of the period after state-to-state

transitions are realized.

� Firms observe the state at the beginning of the period as well as the outcomes of the

entry, exit, and investment decisions during the period.

� Entry, exit and investment decisions are made simultaneously, however, incumbents

(potential entrants) investment decisions are only carried out if they remain in (enter)

the industry.

Incumbent Firms

� Suppose !n 6=M + 1.

� At the beginning of each period each incumbent �rm draws a random scrap value �n

from a distribution F() with expectation E(�n) = �. Scrap values are assumed to be

independently and identically distributed across �rms and periods.

� Incumbent �rm n learns its scrap value �n prior to making its exit and investment

decisions but the scrap values of its rivals remain unknown to it (imperfect information

assumption).

� Let �n(!; �n) = 1, indicate that the decision of incumbent �rm n, who has drawn scrap

value �n , is to remain in the industry in state ! and let �(!; �n) = 0 indiate that its

decision is to exit the industry, collet the scrap value �n and perish.

23

� Since each �rms decision is conditioned on its private �n it is a random variable from

the perspective of other �rms. Let �n(!) =Z�n(!; �n)dF (�n) denote the probability

that incumbent �rm n remains in the industry in state !.

� If an incumbent �rm remains in the industry, it competes in the product market. Let

�n(!) denote the current pro�t of incumbent �rm n from product market competition

in state !. This could be the pro�t function from a capacity constrained cournot

game or di¤erentiated bertrand game. In addition to receiving a pro�t, the incumbent

realizes the investment xn(!) 2 [0; x] that it decided on at the beginning of the period

and moves from state !n to state !0n 6= M + 1 with some probability (we will specify

these probabilities later).

Potential Entrants

� Suppose !n =M + 1:

� We assume that at the beginning of the period each potential entrant draws a random

setup cost �en from a distribution Fe() with expectation E(�en) = �e. Set up costs are

assumed to be independent and identically distributed across �rms and periods and

private information to the individual �rm.

� If potential entrant n enters the market, it incurs the setup cost �en. If it stays out,

it recieves nothing and perishes.

� Let �en(!; �en) = 1 indicate that potential entrant n, who has drawn set up cost �en is

to enter the industry in state ! and �en(!; �en) = 0 indicate its decision to stay out.

� From the point of view of other �rms, �en(!) =Z�en(!; �

en)dF

e(�en) denote the proba-

bility that potential entrant n enters the industry in state !.

� Unlike an incumbent, the entrant does not compete in the product market. Instead it

undergoes a setup period upon committing to entry. The entrant realizes its previously

chosen investment xen(!) 2 [0; xe] and moves to state !0n 6=M+1 with some probability.

At the end of the setup period, the entrant becomes an incumbent.

24

� To simplify notation, if a �rm n is in state !n =M + 1, let

�en(!1; :::; !n�1; !n; !n+1; :::; !N ; �en) = �n(!1; :::; !n�1;M + 1; !n+1; :::; !N ; �

en)

�en(!1; :::; !n�1; !n; !n+1; :::; !N) = �n(!1; :::; !n�1;M + 1; !n+1; :::; !N)

xen(!1; :::; !n�1; !n; !n+1; :::; !N) = xn(!1; :::; !n�1;M + 1; !n+1; :::; !N)

because !n = M + 1 indicates a �rm is a potential entrant, we can drop the e super-

scripts from all our notation.

Transition Probabilities

� Let P (!0; !; �(!; �); x(!)) denote the probability that the industry moves from state

! to state !0 when �rms�s policies are given by �(!; �) = f�1(!; �1); ::::; �N(!; �N)g

and x(!) = fx1(!); ::::; �N(!)g. As with any probability, P (!0; !; �(!; �); x(!)) � 0

andX!02S

P (!0; !; �(!; �); x(!)) = 1.

� Suppose each �rm�s state transitioned independently, each �rm�s transition was un-

a¤ected by other �rms (similar to our consumption-saving problem), then we would

have

P (!0; !; �(!; �); x(!)) =Y

n=1;:::;N

Pn(!0n; !n; �(!n; �n); x(!n))

however, this will almost never be the case in any type of dynamic game we will study.

� More generally, since incumbents�scrap values and potential entrants setup costs are

private information, its exit or entry decision is a random variable from teh perspective

of an outside observer. Therefore, if we want the transition probability of one state to

another, we have to integrate out over all possible realizations of �rms�exit and entry

decisions to obtain the probability that the industry transits from state ! to state !0

as Z:::

ZP (!0; !; �(!; �); x(!))

Yn=1;:::;N!n 6=M+1

dF (�n)Y

n=1;:::;N!n=M+1

dF e(�en)

=X

�2f0;1gN

"P (!0; !; �; x(!))

Yn=1;:::;N

�n(!)�n(1� �n(!))(1��n)

#

25

Recall that scrap values and setup costs are independently and identically distributed

across �rms. Since from the point of view of other �rms, the probability that incumbent

�rm n remains in the industry or a potential entrant enters the industry in state ! is

�n(!). Therefore, a particular realization � = (�1; :::; �N) 2 f0; 1gN of �rms�exit and

entry decisions occurs with probabilityY

n=1;:::;N

�n(!)�n(1� �n(!))(1��n). If we then sum

across the probability of transitions from state ! to state !0 for all possible entry and

exit outcomes, we get P (!0; !; �(!; �); x(!)).

� The thing to take away from this discussion is that the transition probabilities from

one state to the next depend on the entry and exit probabilities of the �rms, which

are determined as part of equilibrium play. Therefore, when forming an expectation

over the industries future state, each �rm must take into account competitors�entry

and exit strategies as well as their stochastic investment outcomes.

Incumbent�s Problem

� Suppose that the industry is in state ! with !n 6=M + 1.

� Incumbent �rm n solves an intertemporarl maximization problem to reach its exit and

investment decisions. Let Vn(!; �n) denote the expected net present value of all future

pro�ts to incumbent �rm n, computated under the presumption that �rms behave

optimally, when the industry is in state ! and incumbent �rm n has drawn a scrap

value �n.

� Vn(!; �n) can be de�ned recursively by the solution to the following Bellman equation

Vn(!; �n) = sup�n(!;�n)xn(!)2[0;x]

24 �n(!) + (1� �n(!; �n))�n+

�n(!; �n)��xn(!) + �E

�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�35

where Vn(!) =RVn(!; �n)dF (�n) is the expected value function.

� Note that Vn(!; �n) is the value function after the �rm realizes the value of its scrap

value and Vn(!) is its expected value function before the �rm realizes its scrap value.

26

� If a �rm decides to exit the industry, it recieves this periods pro�ts, �n(!); and the

realization of their scrap value, �n.

� If a �rm decides to remain in the industry, it recieves this periods pro�ts, �n(!); and

realizes the cost of its optimal investment decision, �xn(!), and the expected value

of being an incumbent next period, �E�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�.

this implies that the cost of investment is realized only if the �rm stays in the industry.

Since next periods scrap value for �rm n has not yet been realized or the decisions or

other �rms regarding investment, entry, and exit, �rm n must take an expectation over

their actions.

� Since investment decisions are made conditional on remaining in the industry, incum-

bent �rm n�s problem can be broken up into two parts. First, the incumbent �rm

chooses the level of investment which is independent of the scrap value realization

(xn(!) does not depend on �n). Second, given the optimal investment choice, the �rm

makes the decision whether or not to remain in the industry.

� Therefore, we can write the optimal exit decision of an incumbent �rm n who has

drawn scrap value �n as a cuto¤ rule

�n(!; �n) =

8<: 1

0

if �n < �n(!)

if �n � �n(!)

where

�n(!) = supxn(!)2[0;x]

��xn(!) + �E

�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�

� Therefore, �n(!) is the scrap value that makes you indi¤erent between remaining an

incumbent or exiting the industry.

� We can thus represent the optimal exit decision rule as either

1. the cuto¤ scrap value �n(!) that makes the incumbent indi¤erent between re-

maining active or exiting, or

27

2. the probability �n(!) of an incumbent �rm n remaining in the industry in state !

� To see this, the probability of remaining in the industry is given by

�n(!) =

Z�n(!; �n)dF (�n) =

Z1[�n < �n(!)]dF (�n) = F (�n(!))

F�1(�n(!)) = �n(!)

� Using this reservation value to describe the exit rule, we can then express the expected

value function Vn(!) by taking the expectation of both sides of the expression for

Vn(!; �n) as

Vn(!) =

Z26666664

sup�n(!)2[0;1]xn(!)2[0;x]

�n(!) + (1� 1[�n < F�1(�n(!))])�n+

1[�n < F�1(�n(!))]

8<: �xn(!)+

�E�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�9=;

37777775 dF (�n)

Vn(!) =sup

�n(!)2[0;1]xn(!)2[0;x]

�n(!) + (1� �n(!))

8><>:Z

�n�F�1(�n(!))

�ndF (�n)(1��n(!))

9>=>;+�n(!)

��xn(!) + �E

�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�

� Thus, we can write a �rm�s problem in terms of choosing a probability of entry (which

implies a cuto¤ value) and an optimal investment decision. The second term in this

expression is the expectation of the scrap value conditional on accepting the scrap

value weighted by the probability that you accept the scrap value. The third term is

the expected value of remaining an incumbent weighted by the probability that you

remain an incumbent.

Entrant�s Problem

� Suppose that the industry is in state ! with !n =M + 1.

� The expected net present value of all future pro�ts for a potential entrant n when the

industry is in state ! and the entrant has drawn setup cost �en

Vn(!; �n) = sup�n(!;�

en)

xn(!)2[0;xe]

�n(!; �en)���en � xn(!) + �E

�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�

28

� Since the entrant is short-lived it does not solve an intertemporal maximization problem

to reach its decisions. Therefore, it enters this period and becomes an incumbent next

period or perishes. It is easy to add long-lived entrants into the model, the entry

problem then becomes intertemporal and similar to an optimal waiting problem.

� Similar to an incumbents problem, the entrant�s problem can be broken down into an

optimal investment problem followed by the decision to enter or not.

� Thus, we can write their entry decision rule as

�n(!; �en) =

8<: 1

0

if �en < �e

n(!)

if �en � �e

n(!)

where

�e

n(!) = supxn(!)2[0;xe]

��xn(!) + �E

�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�

� Imposing this reservation property on entry decisions and integration both sides of the

value function for the potential entrant gives us the expected value function for an

entrant

Vn(!) =sup

�n(!)2[0;1]xn(!)2[0;xe]

� (1� �n(!))

8><>:Z

�n<Fe�1(�n(!))

�endF (�en)(1��n(!))

9>=>;+�n(!)

��xn(!) + �E

�Vn(!

0)j!; !0n 6=M + 1; xn(!); ��n(!); x�n(!)�

Computing Equilibrium

� The solution concept that people use in these types of games is that of stationary

Markov Perfection. An equilibrium involves value and policy functions that solve the

Bellman Equations above for all n.

� A �rm thus behaves optimally in every state, irrespective of whether this state is on

or o¤ the equilibrium path.

29

� Further, since the horizon is in�nite, the in�uence of past play is captured in the current

state, there is a one-to-one correspondence between subgames and states. Therefore,

any MPE is subgame perfect.

Simple "Exit" Example

� Here we will consider a simple example of an exit game similar to the Fudenburg and

Tirole (198?) paper on exit.

� Suppose that there are 2 �rms, N=2.

� Let M=1, so their is one state if a �rm is active in the market. So !n = 1 implies a

�rm is active and if !n = 2 implies that a �rm is out of the industry.

� Therefore, the industry is either in state: (1,2), (2,1), (1,1), or (2,2).

� Since there is only one state for an active �rm, we are going to abstract from investment.

� We are also going to abstract from entry, just assume that it is prohibitively costly

to enter the industry, so (2,2) is an absorbing state for the industry. This is actually

similar to a student on the market this year, Takahashi (UW, 2010).

� Let �(!1; !2) denote the pro�ts of �rm 1 in state ! = (!1; !2):

� We will assume that scrap values �n are idd across �rms and time

� Let �n = �+ �� where

�~F ()

E(�) = 0

so that � > 0 can be thought of as a scale factor capturing the importance of the

imperfect information in the model.

30

� With this information, we can write the Bellman equations of �rm 1 as

V (1; 2) = sup�1(1;2)2[0:1]

�(1; 2) + (1� �1(1; 2))E[�1j�1 > �1(1; 2)]

+�1(1; 2)�V (1; 2)

V (1; 1) = sup�1(1;1)2[0:1]

�(1; 1) + (1� �1(1; 1))E[�1j�1 > �1(1; 1)]

+�1(1; 1)� f�2(1; 1)V (1; 1) + (1� �2(1; 1))V (1; 2)g

where

E[�1j�1 > �1(1; 2)] =

8><>:Z

�1�F�1(�1(1;2))

�ndF (�n)

(1� �1(1; 2))

9>=>;� We know the cuto¤ scrap values just make the �rm indi¤erent between exiting and

remaining

�1(1; 2) = �V (1; 2)

�1(1; 1) = � f�2(1; 1)V (1; 1) + (1� �2(1; 1))V (1; 2)g

� These expressions for the cuto¤ values can be rewritten

�1(1; 2) = P (�+ �� < �V (1; 2)) = F

��V (1; 2)� �

�

��1(1; 2) = P (�+ �� < � f�2(1; 1)V (1; 1) + (1� �2(1; 1))V (1; 2)g)

= F

�� f�2(1; 1)V (1; 1) + (1� �2(1; 1))V (1; 2)g � �

�

�

� If we restrict our attention to a symmetric equilibrium

�1(1; 2) = �2(1; 2) = �(1; 2)

�1(1; 1) = �2(1; 1) = �(1; 1)

� Further, if we make a distributional assumption on �, we can work out an expression

for E[�1j�1 > �1(1; 2)]. For simplicity, assume that �~U [�1; 1], which implies we can

31

work out the expectation of �1 conditional on accepting it as1

E[�1j�1 > �1(1; 2)] = E[�+ ��j�+ �� > �1(1; 2)]

= �+ �E

��j� > �1(1; 2)� �

�

�= �+ �

�1 + F�1(�(1; 2))

2

�= �+ �

�1 + (2�(1; 2)� 1)

2

�= �+ ��(1; 2)

� We now have four equations and four unknowns

V (1; 2) = �(1; 2) + (1� �(1; 2))(�+ ��(1; 2)) + �(1; 2)�V (1; 2)

V (1; 1) = �(1; 1) + (1� �(1; 1))(�+ ��(1; 1)) + �(1; 1)� f�(1; 1)V (1; 1) + (1� �(1; 1))V (1; 2)g

�(1; 2) = F

��V (1; 2)� �

�

�= :5 + :5

��V (1; 2)� �

�

��(1; 1) = F

�� f�(1; 1)V (1; 1) + (1� �(1; 1))V (1; 2)g � �

�

�= :5 + :5

�� f�(1; 1)V (1; 1) + (1� �(1; 1))V (1; 2)g � �

�

�that we can solve for V (1; 2); V (1; 1); �1(1; 2); �1(1; 1):

Algorithm for Computing an Equilibrium

� Note, you could solve this system of nonlinear equations directly. However, this is due

to the symmetry assumption (would be eight equations in eight unknowns) and also

the very small state space.

� Recursive methods will be necessary to solve larger models, with entry and investment

and a larger state space, so we will discuss this methodology.

1This uses the fact that

�(1; 2) = F

��1(1; 2)� �

�

�F�1(�(1; 2)) =

�1(1; 2)� ��

32

� Let the lth iteration of the value function and policy function be denoted by V l and

�l, respectively. If you have no idea what values these functions should take on, set

V l = 0 and �l = :5.

� The way the algorithm works in two steps. First update the policy functions, �l+1,

given V l, then given �l+1 update V l+1.

1.

�l+1(1; 2) = :5 + :5

��V l(1; 2)� �

�

��l+1(1; 1) = :5 + :5

���l(1; 1)V l(1; 1) + (1� �l(1; 1))V l(1; 2)

� �

�

!2.

V l+1(1; 2) = �(1; 2) + (1� �l+1(1; 2))(�+ ��l+1(1; 2)) + �l+1(1; 2)�V l(1; 2)

V l+1(1; 1) = �(1; 1) + (1� �l+1(1; 1))(�+ ��l+1(1; 1))

+�l+1(1; 1)���l+1(1; 1)V l(1; 1) + (1� �l+1(1; 1))V l(1; 2)

� We want to continue updating V l and �l until, the successive steps that we take are

very small. Typically, 10�8 is regarded as close enough.

� As we will see when we implement this code in matlab, the larger � the easier it is to

compute an equilibrium. Remember, if � = 0, we would be searching for an equilibrium

in pure strategies that does not exist which explains the issue. However, as � ! 0,

the pure strategy equilibrium approaches the mixed strategy equilibrium (equilibrium

probabilities of exit converge to mixed-strategy equilibrium).

� A useful tip in computing equilibria in these models is to add a dampening scheme (see

Chapter 3 of Judd 1998). Such a dampening scheme, limits the steps that the algo-

rithm takes when updating policy functions (and subsequently value functions). This

prevents the algorithm from over-prescribing changes in the policy function (cyclying

or jumping back and forth on either side of the true solution), particularly when the

algorithm is a long ways from converging.

33

� For example, one would choose a � 2 (0; 1) and policy functions in our example would

be updated as

�l+1(!) = �F

��(!)� �

�

�+ (1� �)�l(!)

so we are only going part way towards the next point suggested by the algorithm,

F��(!)��

�

�.

� As we get closer to the solution, we can allow � to approach 1. However, for early

steps, it is very useful to to employ such a dampening scheme.

34

6 Bajari, Benkard, and Levin (Ecmtra, 2009)

6.1 General Model

All the discussion here will be for one market. However, the state space can and will

need to be enriched to take into account heterogeneity across markets in my application.

There are N �rms, denoted i=1....N, who make decisions at times t = 1; 2; ::::;1. Market

conditions at time t are completely summarized by a commonly observed vector of state

variables st 2 S � <L. Given the state st, �rms choose actions simultaneously. Let

ait 2 Ai denote �rm i0s action at time t, and at = (a1t; a2t; ::::::; ant) 2 A the vector of time

t actions. Each �rm i recieves a private shock �it, drawn independently from a distribution

Gi(�jst) with support i � <M . The vector (or matrix) of private shocks is denoted as

�t = (�1t; �2t; :::::; �Nt). In my model this vector will represent shocks to marginal, �xed,

and entry and exit costs.

Each �rm�s pro�ts at time t can depend on the state, the actions of all the �rms, and

the �rm�s private shock. Firm i0s pro�t function is denoted as �i(at; st; vit) (remember the

actions of others take into account their own private shock so it is not an argument here).

Assuming that �rms share a constant discount factor � l 1, and taking a current state st as

given, �rm i0s expected future pro�ts (prior to the realization of the private shock) are

E

" 1X�=t

���t�i(at; st; vit) j st

#

Here the expectation is over i0s private shock and the �rms�actions in the current period, as

well as future values of the state variables, actions, and private shocks. The state variable

at date t + 1, st+1 is drawn from a probability distribution P (st+1jat; st). This allows for

time t actions, at to a¤ect future payo¤s.

Behavior is assumed to follow a pure strategy Markov Perfect Equlibria (MPE). There-

fore, each �rm�s behavior depends only on the current state and their own private shock. A

Markov strategy for �rm i is a function �i : S � i ! Ai. A pro�le of Markov strategies

is a vector � = (�1;�2; ::::; �N), where � : S � 1 � 2 � :::: � N ! A. If �rms behave

35

according to a pro�le �, �rm i0s expected pro�t given a state s can be written recursively:

Vi(sj�) = E��i(�(s; v); s; vi) + �

ZVi(s

0j�)dP (s0j�(s; v); s) j s�

Here Vi(sj�) is �rm i0s ex ante value function, since it represents expected pro�ts at the

beginning of a period before the realization of private shocks.

The pro�le is a MPE if, given the opponent�s pro�le ��i, each �rm i prefers it�s strategy

�i to all alternative Markov strategies �0i. That is, � is a MPE if for all �rms i, states s,

and Markov strategies �0i,

Vi(sj�) � Vi(sj�0i; ��i) = E

24 �i(�0i(s; vi); ��i(s; v�i); s; vi)+

�RVi(s

0j�0i; ��i)dP (s0j�0i(s; vi); ��i(s; v�i); s)j s

35An equivalent de�nition of MPE will be useful for the discussion on how to proceed with

estimation. The above de�nition requires that each �rm i and state s, �i performs at least

as well as any alternative Markov strategy �0i. An equivalent set of inequalities is that for

each �rm i and state s, �i outperforms the use of the alternative strategy �0i in the current

period, followed by the use of �i in future period. That is, for all �rms i, states s, and

Markov strategies �0i:

Vi(sj�) � Vi(sj(�0i; �i); ��i) = E

24 �i(�0i(s; vi); ��i(s; v�i); s; vi)+

�RVi(s

0j�)dP (s0j�0i(s; vi); ��i(s; v�i); s)j s

35Therefore, if no �rm has a pro�table deviation from the strategy pro�le �, then it is a MPE.

This idea will be used in estimation, by perturbing the strategy pro�les of the �rm and

using the resulting set of inequalities to construct an objective function to be minimized.

The parameters to be estimated include the discount factor �, the pro�t functions �1::::�N ,

and the distribution of the private shocks G1::::::GN . Denote the entire vector of unknown

parameters to be estimated by � ( so that one can write �i(a; s; �i; �) and Gi(�ijs; �) ).

6.2 Estimation

The �rst stage of BBL estimates the state transition probabilities Pr(s0ja; s) and equilibrium

policy functions �(s; �). The second stage uses the set of inequalities for equilibrium de-

scribed above to estimate all the remaining structural parameters. The data set available

36

must include the actions of �rms and the complete vector of state variables. It is also

required that the data for a given market be generated by the same MPE. The state space

can be enriched at the market level to allow for di¤erent MPE to be played across dissimilar

markets. However, unless one includes market dummies then one is still making some fairly

strong assumptions on behavior across markets. This will be a major issue, which I have to

adress in examining the airline industry.

6.2.1 First Stage Estimates

Policy Functions

Discrete Choice BBL propose nothing new in the case where the choice variable

must belong to a �nite discrete set each period. In this case they recommend estimating

the policy functions using a Hotz and Miller like approach. This approach requires one to

assume that the �rm�s choice speci�c private shocks (� 0s) enter the pro�t function additively

and a distributional form for these shocks. With these assumptions one can do a state by

state inversion to calculate the choice speci�c value functions, which allows recovery of the

policy functions �(s; �).

Continuous Choice BBL�s technique for estimation of the policy functions with a

continuous choice is something new. Here the policy functions take the form ai = �(s; �i),

where ai 2 Ai � < and �i is a single dimensional private shock (multiple actions and shocks

are also allowed in their framework but not discussed in detail due to the complications

to notation). To estimate the policy function in the one dimensional case the following

condition must be satis�ed.

Condition 1 For each agent i, Ai and i are single-dimensional and �i(a; s; �i) has in-

creasing di¤erences in (ai; �i). If �i(a; s; �i) is di¤erentiable this implies that@2�i(a;s;�i)@ai@�i

� 0

This assumption implies that �i is a shock to the marginal return to the action. Under

this condition, one is guarenteed that �rm i0s equilibrium policy �i(s; �i) is monotonically

increasing and can exploit this to estimate it. To do so, let Fi(aijs) denote the probability

37

that �rm i takes an action less than or equal to ai at state s. This proportion is assumed to

be observed in the data. Since �i(s; �i) is monotone in �i, Fi(aijs) = Pr(�i(s; �i) � aijs) =

Pr(�i � ��1i (ai; s)js) = Gi(��1i (ai; s)js; �). Letting ai = �i(s; �i) for all (s; �i) yields:

�i(s; �i) = F�1i (Gi(vijs; �)js)

Therefore, to estimate the policy function we need the distribution of actions at every

state Fi(aijs) and knowledge of the functional form of Gi. This allows the policy functions to

depend on any unknown parameters of G1::::GN . When estimating these policy functions in

practice BBL suggest smoothing the Fi(aijs) estimates across states and imposing symmetry

where ever possible.

Simulating Value Functions The estimated policy functions and state transistion prob-

abilities allow one to construct estimates of the equilibrium value functions. One can use

the �forward simulation�procedure suggested by Hotz et al.(1994) to estimate �rm�s value

functions for any strategy pro�le. If Vi(sj�i; ��i; �) is the expected future pro�ts of �rm i

from following strategy �i and competitors following strategy ��i then

Vi(sj�i; ��i; �) = E" 1Xt=0

���t�i(�(st; �t); st; vit; �) j s0 = s; �#

Here the expectation is again over current and future values of the private shocks � and

states s. The expectation can depend on � as well through the distribution of the private

shocks G1::::GN .

With estimates of policy functions and transition probabilities across states one can

compute the value function for an inital guess of the parameter vector. The algorithm

described below provides a simple way to simulate the value functions for any �rm-state

combination.

1. Starting at state s0 = s, draw a private shock �io from Gi(�js0; �) for each �rm i.

2. Calculate the speci�ed action ai0 = b�(s0; �i0) for each �rm i, and the resulting pro�ts

�i(a0; s0; �i0; �).

38

3. Draw a new state s1 using the estimated transition probabilities cPr(s1js0; a0).4. Repeat steps 1-3 for a large number of periods (until �rm i exits or �T is su¢ ciently

small).

One can then average over the simulated paths to get an estimate of the value function,

Vi(sj�i; ��i; �) for state s. This simulation procedure can be done for any pro�le of strategies

including non-equlibrium ones, ex. (�0i; ��i). As discussed below, this allows one to construct

a set of inequalities that must hold in equilibrium by comparing the equilibrium strategy

pro�le to a perturbed pro�le.

6.2.2 Second Stage Estimation

Assume one has estimates of the policy functions and state transition probabilities. Let

these functions be parameterized by a vector �, which can be consistently estimated in the

�rst stage with a known asymptotic distribution. More formally, BBL assume the policy

functions �i(s; �i;�) and transition probabilities Pr(st+1jst; at;�) are parameterized by a

�nite parameter vector �, and there exists a consistent estimator b�n with the property thatpn(b�n � �0) d! N(0; V�)

where �0 is the true parameter value generating the data.

Recall that the strategy pro�le � is a MPE if and only if for all �rms i, states s, and

alternative Markov policies �0i,

Vi(s; �i; ��i; �) � Vi(s; �0

i; ��i; �)

Given the state transitions Pr(s0js; a), these equilibrium inequalities de�ne a set of parame-

ters that rationalize the strategy pro�le � being played. Let �0 denote this set:

�0(�;Pr(s0js; a)) = f� : �; �;Pr(s0js; a) satisfy the MPE inequalities for all s; i; �0ig

The goal of estimation is then to learn � given � and Pr(s0js; a). If one�s modeling assump-

tions are not su¢ ciently strong this set need not be a singleton. However, this set can still

be consistently estimated and convey useful information about the parameters of interest.

39

Estimation in both the point and set identi�ed cases proceeds by constructing empirical

counterparts for some or all of the MPE conditions (or inequalities). One then minimizes

the squared distance of the violations. Let x 2 � be an index for the set of equilibrium

conditions, so that each x denotes a particular combination (i; s; �0i). Let

g(x; �; �) = Vi(s; �i; ��i; �)� Vi(s; �0

i; ��i; �)

The dependence on � comes from recalling that the Markov pro�les and the state transition

probabilities are a function of these (�rst stage) parameters. The inequality is satis�ed at

�; � if g(x; �; �) � 0. One can then de�ne an econometric objective function to be minimized

as

Q(�; �) =

Z�

(minfg(x; �; �); 0g)2dH(x)

Here H(�) is the distribution over the set of inequalities chosen by the researcher. One can

construct the simulated sample counterpart to this objective function by replacing the value

functions with simulated estimates and using b�n in place of �. This corresponds to a sampleobjective function

Qn(�; b�n) = 1

nI

nIXk=1

(minfeg(xk; �; b�n); 0g)2To construct the sample counterpart one takes nI iid draws from the distribution H (over

�rms-state-alternative strategy combinations). To do so requires simulating ns paths to

get the simulated value functions for each of those �rm-state-strategy combinations. The

alternative policies which one examines can simply be perturbations of the estimated policy

functions, �0i(s; �i; b�n) = �i(s; �i; b�n) + �. The choice of which inequalities to include in the

estimation a¤ect only e¢ ciency and not consistency.

For the case of point identifcation, BBL prove the estimated parameters are consistent

and asymptotically normal and suggest that one use bootstrap techniques to estimate the

variance covariance matrix. For the case of set identi�cation, BBL provide a proof of

consistency, which follows closely those of Manski and Tamer (2002) and Haile and Tamer

(2003). The distribution theory for this type of estimator is discussed in Chernozhukov,

Hong, and Tamer (2004).

40

BBL note some special cases that may be relevant in some applications. In particular,

if all of the parameters to be estimated in the second stage enter the value function linearly,

then the value functions need only be simulated once. This will often be the case if one

assumes a static model of competition and is only interested in estimating �xed, entry, or

exit costs. However, this will not be true in many other simple examples. One common case

of non-linearity is when the policy function depends on the unknown distribution of private

shocks. This will be the case in a dynamic pricing model with private shocks to marginal

cost. Therefore, the majority of the gains in my setting will be from avoiding computation

of the equilibrium. I will still have to re-simulate the value functions for each new guess of

the parameters.

7 Gowrisankaran (Rand, 1999)

� most merger analysis that is performed is static. this paper was intended to show that

these dynamic models can be used to model mergers in an industry.

� the most cutting edge work was done by Nevo (Rand, 2000) on merger analysis and

this ignored the endogeneity of merger process.

� �rms don�t simply randomly decide to merge, rather there is typically something to be

gained by doing so (market power, cost e¢ ciencies, etc).

� he models entry, exit, investment and mergers

� by writing down a detailed model which endogenizes the merger process, he is able to

point out some dynamic issues that a static model misses.

� one part that a static merger analysis misses, is the entry/exit process. with one

dominnant �rm there may be room for an additional entrant or this �rm may be so

dominant that it forces the remaining incumbents out of the market.

� these two e¤ects have di¤erent impacts on welfare that are important and should not

be ignored when examining the competitive e¤ects of a merger.

41

8 Fershtman and Pakes (Rand, 2000)

� provide a collusive framework with heterogeneity among �rms, investment, entry, and

exit.

� they model collusion as a simple repeated pricing game, just like the super games we

have seen in the past

� they show that when an incumbent �rm is likely to exit in the near future, collusion is

very hard to support. this makes sense, because if I get this guy out there is one less

competitor until another entrant comes along. the cost is that I give up the di¤erence

between my collusive and nash reversion pro�ts this period.

� they show that this framework can be used to generate "price wars" or deviations from

the collusive agreement, where �rms try to force out competitors by reverting to the

nash outcome.

� however, they show that a collusive outcome can actually be consumer welfare improv-

ing.

� if collusion encourages additional entry and these �rms o¤er a su¢ ciently rich set

of products, then consumers may actually bene�t despite the higher prices from the

collusive regime.

9 Doraszelski and Markovich (Rand, 2007)

� Looks at the impact of advertising on competitive advantage

� in 2006 �rms spent $280 billion dollars on advertising in the US, about 2% of GDP.

� therefore, it is important that we build models that can capture the di¤erent incentives

and impact of advertising on equilibrium outcomes.

� they build a model of entry, exit, static pricing, and advertising which serves as an

investment

42

� they model two di¤erent reasons for advertising, to build up "goodwill" with consumers

and to make consumers "aware" of their products.

� they show how �rms can use advertising to deter entry as well as induce exit in a

dynamic setting.

10 Benkard (ReStud, 2004)

� one of the �rst papers to empirically estimate a model in the spirit of Ericson and

Pakes

� examines dynamic elements of the commercial aircraft industry

� endogenizes entry, exit, prices, and quantities as part of a Markov Perfect Equilibrium

� wants to explain a few empirical facts with the model

1. very high concentration levels (only a few manufacturer�s world-wide)

2. pricing well below static marginal cost

� the way in which he gets at this idea is by allowing for scale economies which makes it

hard for many small �rms to compete and he also adds learning by doing

� �rms in a static model would have no incentive at all to price below marginal cost.

� however, in a dynamic model with learning by doing (costs that fall as you produce

more aircraft), a �rm has an incentive to aggressively price in the �rst periods and

drive down costs so that markups in subsequent periods are substantial.

� Benkard �nds that there is a very large degree of cost reducing investment in learning

and that this "unconstrained" MPE outcome is very close to the e¢ cient one which a

social planner would obtain.

43

11 Ryan (Ecmtra, 2010)

� this is the paper on environmental regulation that david covered last semester

12 Williams (JMP, 2009)

� looks at the airline industry and tries to explain aggressive responses to entry (doubling

and tripling of capacity following entry by smaller �rms).

� builds a model in which �rms invest in capacity, enter/exit, and compete in a capacity

constrained pricing game

� shows that the very intense competition following entry is not welfare improving be-

cause it often leads to exit in a short number of periods as compared to an outcome

where �rms are restricted to investing to maximize static pro�ts

13 Takahashi (JMP, 2010)

� estimates the impact of competition and exogenous demand decline on the exit process

of movie theaters in teh US from 1950-1965.

� he modi�es the Fudenberg and Tirole (1986) model from a duopoly to a oligopoly

� shows that tv penetration lead to dramatic decline in �rms payo¤s over time

� however, the dynamic model allows for �rms earning negative pro�ts to remain in the

market if they expect to bene�t from outlasting their competitors at which time their

pro�ts would incrase.

� he shows this strategic delay of exit creastes a signi�cant delay in the exit process.

44