Oligopolistic equilibrium and financial constraints

• Date: 01 March 2020
• Published date: 01 March 2020
• Author: Yosuke Yasuda,Luis C. Corchón,Carmen Beviá
• DOI: http://doi.org/10.1111/1756-2171.12313

RAND Journal of Economics

Vol.51, No. 1, Spring 2020

pp. 279–300

Oligopolistic equilibrium and financial

constraints

Carmen Bevi´

a∗

Luis C. Corch´

on∗∗

and

Yosuke Yasuda∗∗∗

We model a dynamic duopoly in which firms can potentially drive their rivals from the market.

Forsome parameter values, the Cournot equilibrium outcome cannot be sustained in an infinitely

repeated setting. In those cases, there is a Markov perfect equilibrium in mixed strategies in

which one firm, eventually, will exit the market with probability one. Producer surplus in the

maximum collusive outcome is greater under bankruptcy consideration, because the outcome

that maximizes joint profits is skewed in favor of the more efficient firm. Consumer surplus and

social welfare also increase in many cases, although those effects are generally ambiguous.

1. Introduction

There is ample evidence that financial constraints play an important role in the behavior

of firms (Bernanke and Gertler, 1989; Kiyotaki and Moore, 1997). In particular, firms that lose

too much money (have negative profits) lose the capacity to compete and disappear (Bolton

and Scharfstein, 1990).1Firms might then have incentives to take actions that would make it

impossible for competitors to fulfill financial constraints in the hope of getting rid of them.

In this article, we model a quantity-setting duopoly in which firms take into account their and

their rivals’ financial limits, specifically that firms go bankrupt (exit) if they earn negative profits

∗Universidad de Alicante; carmen.bevia@ua.es.

∗∗Universidad Carlos III de Madrid; lcorchon@eco.uc3m.es.

∗∗∗Osaka University; yosuke.yasuda@gmail.com.

The authors wish to thank Antonio Robles as RA and D. Abreu, K. Bagwell,C. Ballester, P. Bolton, A. Brandenburger,

L. Cabral, A. Daughety, M. Escrihuela, M. Kandori, M. Katz, F. Maniquet, J. Mar´

ın, E. Maskin, A. Nicolo, G. P´

erez-

Quiros, I. Obara, J. Reinganum, S. Takahashi, A. Wolinsky, the two referees, and especially, B. Hermalin, for helpful

suggestions. Bevi´

a acknowledges financial support from ECO2014 53051, SGR2014-515, and PROMETEO/2013/037.

Corch´

on acknowledges financial support from MDM 2014-0431, ECO2017_87769_P, and S2015/HUM-3444. Yasuda

acknowledges research support from Grant-in-Aid for Scientific Research, 23683002 and 17K13702, administered by

the Japanese Ministry of Education.

1Even though firms can be reorganized after bankruptcy and continue business, the survival rate of firms after

bankruptcy is typically low,18% in the United States, 20% in the United Kingdom, and 6% in France; see Couwenberg

(2001).

C2020, The RAND Corporation. 279

280 / THE RAND JOURNAL OF ECONOMICS

in a period. Weintroduce the concept of bankr uptcy-free(BF, hereafter) outputs. These are output

pairs in which each firm’s profit is nonnegative (so no firm goes bankrupt) and in which no firm

could, by changing its output, bankrupt another without bankrupting itself. A critical insight of

our analysis is that static Cournot equilibrium outputs can fail to be BF when firms’ cost functions

are asymmetric. In particular, if firms have constant, but different, average costs, the Cournot

outcome can never be BF: a lower-costfir mcan bankr upt a higher-cost rivalwithout bankrupting

itself by increasing its output to the point that the price falls between their average costs. In a

dynamic game, such a move is profitable unless firms discount future too much, because it can

get rid of a competitor.

In our dynamic game, in which a quantity-setting game is played for infinitelymany periods

unless no firm goes bankrupt, the unique Markov Perfect Equilibrium (MPE) in pure strategies,

if it exists, is the Cournot equilibrium. However, if the Cournot outcome is not BF and firms have

incentives to predate for some discounts factors, MPE must entail mixed strategies. Inter alia,

this suggests that the commonly used constant-marginal-cost Cournot model could be misleading

if firms have different marginal costs and are financially constrained.

We show that a mixed-strategy MPE exists. Assuming constant average costs and concave

profit functions, we characterize the equilibrium. The support of each firm’s mixed strategy

contains exactly one interval. The support of the inferior firm has a mass point in the upper

extreme of the interval, which coincides with the best reply in the static game to the superior

firm’s mixed strategy. For the superior firm, the support also contains an isolated mass point,

which coincides with the best reply in the static game to the inferior firm’s mixed strategy. The

mass point lies strictly below the interval support. Because the superior firm would not produce a

larger output than the best reply unless bankruptcy occurs, outputs in the interval support reflect

the predatory activities of the superior firm. The inferior firm becomes bankrupt with positive

probability in each period. The introduction of financial constraints implies that monopolization

(by the efficient firm) will occur with positive probability in each period and thus, it will almost

surely occur in the long run. The probability of predation increases with the discount factor.

Moreover, anyof the outputs chosen by the superior firm are larger than the Cournot output, and

the outputs of the inferior firm are smaller than its Cournot output.

We consider the consequences of potential bankruptcy on the set of outcomes supportable

via tacit collusion. We show that producer surplus in the maximum collusive outcome is greater

under bankruptcy consideration than in the absence of bankruptcy. Thus, in this case, bankruptcy

considerations help collusion. However, this greater possibility of collusion does not imply a

greater social welfare loss. This is because the outcome that maximizes joint profits is skewed

in favor of the superior firm, and this firm produces more efficiently than the inferior firm.

When firms have large discount factors, predation pays off for the superior firm and the inferior

firm produces very little, fearing bankruptcy. Consequently, total output becomes larger under

bankruptcy consideration, and thus total welfare also increases.

We end this introduction with a preliminary discussion of the literature (see more on this

in the final section). Although a number of articles demonstrate that the financial structure does

affect market outcomes in an oligopoly, most previous studies adopt either static or two-stage

models. There are at least two exceptions, Spagnolo (2000) and Kawakami and Yoshida (1997).

Both articles make use of games with infinite time, like ours. The former examines the role of

stock options in repeated Cournot games. In that model, unlike standard repeated games, firms

do not necessarily maximize average discounted profits because stock options affect managers’

incentives. Taking this effect into consideration, Spagnolo (2000) shows that collusion becomes

easier to achieve.The latter ar ticle incorporates a simple exit constraint into the repeated prisoners’

dilemma. In their model, each firm must exit from the market no matter how it plays if the rival

deviates over certain number of periods, and hence, no output profile can be bankruptcy-free.

They show that predations inevitably occur when bankruptcy constraints are asymmetric and

firms are long-sighted.

C

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