Cartel size and collusive stability with non-capitalistic players

A well established belief both in the game-theoretic IO and in policy debates is that market concentration facilitates collusion. We show that this piece of conventional wisdom relies upon the assumption of profit-seeking behaviour, for it may be reversed when firms pursue other plausible goals. To illustrate our intuition, we investigate the incentives to tacit collusion in an industry formed by labour-managed (LM$LM$) enterprises. We characterise the perfect equilibrium of a supergame in which LM$LM$ firms play an infinitely repeated Cournot game under grim trigger strategies. We show that the critical threshold of the discount factor above which collusion is stable (i) is lower in the LM$LM$ industry than in the capitalistic one; (ii) monotonically decreases with the number of firms.     

The critical discount factor as a measure for cartel stability?

This paper considers the stability of tacit collusion in price setting duopolies with repeated interaction. The minimum discount factor above which tacit collusion can be sustained in a subgame perfect equilibrium is called the critical discount factor δ*. In addition, δ* is often used as an intuitive measure for the stability of a tacit cartel, assuming that a collusive equilibrium is more difficult to sustain when δ* increases. However, according to standard theory the distance δ − δ* between the actual and the critical discount factor does not matter for stability as long as δ > δ*. This paper contributes experimental evidence that supports the intuitive idea that a larger critical discount factor makes collusion a less likely outcome.      

FINITELY REPEATED PRISONERS' DILEMMA WITH SMALL FINES: THE PENANCE CONTRACT*

This paper investigates finitely repeated prisoners' dilemma games with explicit contractual devices. It shows that full collusion can be achieved in a unique manner by incentivizing the players' final‐period play with small fines. The incentivizing modality is the penance contract, by which a player is penalized if and only if he deviates from the penance strategy in the final period. Using this contractual agreement brings the penance strategy profile into unique subgame perfect equilibrium in the entire game and achieves full collusion without being invalidated by renegotiation.     

Communication in repeated games with costly monitoring

We study repeated games with discounting where perfect monitoring is possible, but costly. It is shown that if players can make public announcements, then every payoff vector which is an interior point in the set of feasible and individually rational payoffs can be implemented in a sequential equilibrium of the repeated game when the discount factor is high enough. Thus, efficiency can be approximated even when the cost of monitoring is high, provided that the discount factor is high enough.     

R&D COOPERATION BETWEEN IMPATIENT RIVALS

We analyse R&D cooperation between product‐market competitors within a repeated‐game framework with imperfect monitoring. When firms are patient enough, R&D cooperation is attainable without product‐market collusion. However, if firms are less patient, we show that collusion in the product market is necessary to sustain R&D cooperation. Moreover, consumers can be better off when collusion is allowed in this case.     

Interlinkage and Generous Tit‐for‐Tat Strategy

We investigate an infinitely‐repeated prisoners' dilemma with imperfect monitoring and consider the possibility that the interlinkage of the players' distinct activities enhances implicit collusion. We show a necessary and sufficient condition for the existence of a generous tit‐for‐tat Nash equilibrium. Such an equilibrium, if it exists, is unique. This equilibrium achieves approximate efficiency when monitoring is almost perfect, where the discount factors are fixed.     

SOCIAL NORMS,LOCAL INTERACTION,AND NEIGHBORHOOD PLANNING*

This article examines optimal social linkage when each individual's repeated interaction with each of his neighbors creates spillovers. Each individual's discount factor is randomly determined. A planner chooses a local interaction network or neighborhood design before the discount factors are realized. Each individual then plays a repeated Prisoner's Dilemma game with his neighbors. A local trigger strategy equilibrium (LTSE) describes an equilibrium in which each individual conditions his cooperation on the cooperation of at least one “acceptable” group of neighbors. Our main results demonstrate a basic trade‐off in the design problem between suboptimal punishment and social conflict. Potentially suboptimal punishment arises in designs with local interactions since in this case monitoring is imperfect. Owing to the heterogeneity of discount factors, however, greater social conflict may arise in more connected networks. When individuals' discount factors are known to the planner, the optimal design exhibits a cooperative “core” and an uncooperative “fringe.”“Uncooperative” (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when the planner knows only the ex ante distribution over individual discount factors, then in some cases the optimal design partitions individuals into maximally connected cliques (e.g., cul‐de‐sacs), whereas in other cases incomplete graphs with small overlap (e.g., grids) are possible.     

Conjectural Variations and Voluntary Public Good Provision in a Repeated Game Setting

The purpose of this paper is to show how conjectural variations can be derived as a reduced form in an infinitely repeated game of private provision of public goods. We obtain explicit closed forms of conjectural variations associated with maximal sustainable equilibria in which the sum of the utilities of all of a community's members is maximized for both quadratic and Cobb–Douglas preferences, provided that the resulting sequence of contributions can be sustained as a Nash (or subgame perfect) equilibrium in the underlying repeated game. We also show that positive conjectural variations will emerge as long as people place positive weight on the future, and that those conjectures are positively related to the discount factor.     

Repeated games with present-biased preferences

We study infinitely repeated games with perfect monitoring, where players have β-δ preferences. We compute the continuation payoff set using recursive techniques and then characterize equilibrium payoffs. We then explore the cost of the present-time bias, producing comparative statics. Unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set is not monotonic in β or δ. Finally, we show how the equilibrium payoff set is contained in that of a repeated game with smaller discount factor.     

The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments

In the infinitely repeated Prisoners' Dilemma with side payments, we characterize the Pareto frontier of the set of subgame perfect equilibrium payoffs for all possible combinations of discount factors. Play paths implementing Pareto dominant equilibrium payoffs are uniquely determined in all but the first period. Full cooperation does not necessarily implement these payoffs even when it maximizes total stage game payoffs. Rather, when the difference in players' discount factors is sufficiently large, Pareto dominant equilibrium payoffs are implemented by partial cooperation supported by repeated payments from the impatient to the patient player. When both players are sufficiently patient, such payoffs, while implemented via full cooperation, are supported by repeated payments from the impatient to the patient player. We characterize conditions under which public randomization has no impact on the Pareto dominant equilibrium payoffs and conditions under which such payoffs are robust to renegotiation.     

产业垂直关联、转售价控制与合谋非效率：来自中国公司的经验证据*

产业组织间合谋问题包含产业垂直间及水平间合谋。转售价控制作为产业垂直间合谋竞争者地位主要差异表现,其整体经济价值的决定在动态竞争环境下面临着原有合谋解的瓦解和新合谋解达成的可能。本文理论证明,动态竞争环境下两家同质化的制造商分别使用各自的服务商体系其结果可能会带来更大的行业整体利润。本文应用动态面板技术,以中国最具活力的两个三角地区为实证对象进行验证,从社会整体福利角度证明这种非合谋方式是更有效率的。本文得出的结论主要有两个：一是从组织间的垂直联系看,合谋是一种非效率活动,且各自服务商有非合谋的冲动,其冲动能力大小与企业创新外部性和服务商的谈判力密切相关;二是间接证明了制造业与服务业的合谋更多的是一种经济价值分割而非创造,现有的产业间垂直关联是脆弱非平衡态,这种非平衡态存在着临界条件。本文基于上述结论提出了相应的建议和对策。     

The Castle on the Hill

A simple example of a stochastic game with irreversibility is studied and it is shown that the folk theorem fails in a robust way. In this game of Castle on the Hill, for a broad range of discount factors, including those close to one, equilibrium is unique. Moreover, the equilibrium for large discount factors is Pareto dominated by the equilibrium for low discount factors. A unique cyclic equilibrium is also possible for intermediate ranges of discount factors. Journal of Economic Literature Classification Numbers: C7, C6.     

Product differentiation,price discrimination and collusion

The existing literature which analyses the relationship between the product differentiation degree and the sustainability of a collusive agreement on price assumes that firms cannot price discriminate, and concludes that there is a negative relationship between the product differentiation degree and the critical discount factor. This paper, in contrast, assumes that firms are able to price discriminate. Within the Hotelling framework, three different collusive schemes are studied: perfect collusion on discriminatory prices; perfect collusion on a uniform price; collusion not to discriminate. We obtain that the critical discount factor of the first and the third collusive scheme does not depend on the product differentiation degree, while the critical discount factor of the second collusive scheme depends positively on the product differentiation degree. Moreover, we show that imperfect collusion is more difficult to sustain than perfect collusion.     

On the efficiency of ex ante and ex post pricing institutions

Summary This paper compares the performance of three pricing institutions in a decentralized matching model in which random matching occurs. In the first, sellers make public ex ante commitments to trade at pre-specified prices before matching occurs. In the second, the buyer and seller engage in an alternating offer bargaining game once a match has occurred. In the final pricing institution, one party is chosen at random to make a take it or leave it price offer. The steady state equilibrium with ex ante pricing pareto dominates the steady state equilibrium with ex post take it or leave it offers, which in turn pareto dominates the steady state equilibrium with alternating offers. As the discount factor goes to one, the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level. The ex post pricing institutions generate participation rates that are bounded away from efficient levels. The surplus loss associated with switching from ex ante pricing to take it or leave it offers is small when the discount factor is close to one. Contrary to many models of decentralized trade, ex post pricing institutions encourage too much search by buyers.The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. The research for this paper was completed while the author was visiting the University of California at San Diego. The author thanks Douglas Gale for comments.     

On the limit perfect public equilibrium payoff set in repeated and stochastic games

This paper provides a dual characterization of the existing ones for the limit set of perfect public equilibrium payoffs in a class of finite stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg et al. (1994), Kandori and Matsushima (1998) and Hörner et al. (2011) obtain. As a second corollary, it is shown that this limit set of payoffs is a convex polytope when attention is restricted to perfect public equilibria in pure strategies. This result fails for mixed strategies, even when attention is restricted to two-player repeated games.     

On the Relationship Between Innovation and Product Market Competition

This paper considers a theoretical model where firms reduce their initial unit costs by spending on R&D activities in a collusive market and where firms are able to coordinate on distinct output levels other than that of the unrestricted joint profit maximization outcome. We show that, in our model, the degree of collusion (captured by the discount factor) reduces the incentive to innovate when innovation is made non‐cooperatively. The reason is that non‐cooperative R&D introduces a negative externality where firms overinvest beyond the effort required to minimize the cost in order to extract profits from the rival firm, and a reduction in product competition helps internalize the externality. In a research joint venture the absence of R&D rivalry leads to contrary results. The main implication is that the validity of the Schumpeterian hypotheses depends on the extent of cooperation at the R&D stage.     

A three-player dynamic majoritarian bargaining game

We analyze an infinitely repeated divide-the-dollar bargaining game with an endogenous reversion point. In each period a new dollar is divided among three legislators according to the proposal of a randomly recognized member—if a majority prefer so—or according to previous period's allocation otherwise. Although current existence theorems for Markovian equilibria do not apply for this dynamic game, we fully characterize a Markov equilibrium. The equilibrium is such that irrespective of the discount factor or the initial division of the dollar, the proposer eventually extracts the whole dollar in all periods. We also show that proposal strategies are weakly continuous in the status quo that equilibrium expected utility is not quasi-concave, and the correspondence of voters’ acceptance set (the set of allocations weakly preferred over the status quo) fails lower hemicontinuity.     

UNIQUENESS OF EQUILIBRIUM PAYOFFS IN FINITELY REPEATED GAMES WITH IMPERFECT MONITORING*

This paper examines when a finitely repeated game with imperfect monitoring has a unique equilibrium payoff vector. This problem is nontrivial under imperfect monitoring, because uniqueness of equilibrium (outcome) in the stage game does not extend to finitely repeated games. A (correlated) equilibrium is equilibrium minimaxing if any player's equilibrium payoff is her minimax value when the other players choose a correlated action profile from the actions played in the equilibrium. The uniqueness result holds if all stage game correlated equilibria are equilibrium minimaxing and have the same payoffs. The uniqueness result does not hold under weaker conditions.     

Cost‐Based Anti‐dumping as a Repeated Game

In this paper, we consider anti‐dumping (AD) duties as a tool to facilitate collusion between a domestic and a foreign firm in an infinitely repeated differentiated Bertrand game, where prices are publicly observable and each firm receives a privately observed i.i.d. cost shock in each period. We consider second‐best scenarios, where market‐share or production arrangement with sidepayments is not allowed. We show that there exist equilibrium‐path reciprocal ADs. The collusive (trigger) price is distorted downward compared with complete information benchmark as a trade‐off between diminishing the incentive to deviate and ensuring off‐schedule deviation gains when private cost shocks are highly favourable. The model differs from Green and Porter ( 1984 ) and Rotemberg and Saloner ( 1986 ) in that it is the private cost shocks as opposed to public demand shocks that necessitate modifications of collusion. In conclusion, AD policy may encourage collusion, and therefore, unless the source of market imperfection is carefully examined, laissez faire might be a better choice.     

Bid rotation and collusion in repeated auctions

This paper studies bidder collusion with communication in repeated auctions when no side transfer is possible. It presents a simple dynamic bid rotation scheme which coordinates bids based on communication history and enables intertemporal transfer of bidders’ payoffs. The paper derives a sufficient condition for such a dynamic scheme to be an equilibrium and characterizes the equilibrium payoffs in a general environment with affiliated signals and private or interdependent values. With IPV, it is shown that this dynamic scheme yields a strictly higher payoff to the bidders than any static collusion scheme which coordinates bids based only on the current reported signals.