A new look for Stackelberg-Cournot equilibria in oligopolistic markets

Summary. This note deals with Cournot type oligopolies in which the market clearing price occasionally may be non-unique. A Stackelberg leading producer is present. Given that setting we explore continuity properties of the followers' reaction and provide sufficient conditions for existence of equilibrium. Received: June 20, 2000; revised version: April 24, 2001     

Coalition-proof Bertrand equilibria

Summary. This paper examines the coalition-proof Nash equilibria of a Bertrand model of price competition where firms supply all demand. When firms are asymmetric we prove existence and provide a sufficient condition for uniqueness. For symmetric firms, we show that an equilibrium is necessarily unique. We also examine whether this unique equilibrium outcome is implementable through a sequential move game where the firms take turns at announcing prices. Finally we examine the limiting property of such equilibria as the number of firms go to infinity.Received: 20 March 2002, Revised: 5 August 2003JEL Classification Numbers: D43, D41, L13.Correspondence to: Kunal SenguptaWe are deeply indebted to an anonymous referee for very helpful and incisive comments that led to substantial improvements in the paper. We also gratefully acknowledge the hospitality of the Department of Finance, Hong Kong University of Science and Technology where much of the work on this paper was carried out.     

Welfare economics and bounded rationality: the case for model-based approaches

In this paper, we examine the problems facing a policy maker who observes inconsistent choices made by agents who are boundedly rational. We contrast a model-less and a model-based approach to welfare economics. We make the case for the model-based approach and examine its advantages as well as some problematic issues associated with it.     

Trust in triads: effects of exit, control, and learning

This paper provides theoretical background for some effects of social networks on trust. We study the implications of a model with rational actors in two settings with three actors. In the first setting, there are two trustees who are involved in transactions with one truster implying that the truster has an exit option. In the second setting, two trusters play with one trustee, which gives the trusters options for voice, i.e., complaining and informing each other about the trustee's behavior. We compare these models with a baseline model in which there is only one truster and one trustee. It turns out that the opportunities for placing and honoring trust do not change for the exit model compared to the baseline model. The opportunities for trust in the voice model differ from the baseline model only if both trusters inform each other at a rate that is high enough. Only if the possibilities for receiving information and transmitting information are large enough for both trusters, trust will increase due to the information exchange possibilities in the voice model.     

Long run equilibria in an asymmetric oligopoly

Summary. Consider an oligopolistic industry composed of two groups (or populations) of firms, the low cost firms and the high cost firms. The firms produce a homogeneous good. I study the finite population evolutionarily stable strategy defined by Schaffer (1988), and the long run equilibrium in the stochastic evolutionary dynamics based on imitation and experimentation of strategies by firms in each group. I will show the following results. 1) The finite population evolutionarily stable strategy (ESS) output is equal to the competitive (or Walrasian) output in each group of the firms. 2) Under the assumption that the marginal cost is increasing, the ESS state is the long run equilibrium in the stochastic evolutionary dynamics in the limit as the output grid step, which will be defined in the paper, approaches to zero. Received: September 19, 1997; revised: June 18, 1998     

Mixed-strategy equilibria and strong purification for games with private and public information

This paper shows the existence of mixed-strategy equilibria for games with private and public information under general conditions. Under the additional assumptions of finiteness of action spaces and diffuseness and conditional independence of private information, a strong purification result is obtained for the mixed strategies in such games. As a corollary, the existence of pure-strategy equilibria follows. I am very grateful to Yeneng Sun, Nicholas C. Yannelis and M. Ali Khan for helpful discussions and suggestions. I also wish to thank an anonymous referee whose comments led to many improvements in the paper.     

Bargaining with asymmetric information in non-stationary markets

Summary. The Rubinstein and Wolinsky bargaining-in-markets framework is modified by the introduction of asymmetric information and non-stationarity. Non-stationarity is introduced in the form of an arbitrary stochastic Markov process which captures the dynamics of market entry and pairwise matching. A new technique is used for establishing existence and characterizing the unique outcome of a non-stationary market equilibrium. The impact of market supply and demand on bilateral bargaining outcomes and matching probabilities is explored. The results are useful for examining such questions as why coordination failures and macroeconomic output fluctuations are correlated with real and monetary shocks. Received: July 22, 1994; revised version: January 21, 1998     

Imperfectly competitive factor markets and price normalization

A two-sector general equilibrium model with imperfectly competitive labor markets is set up. Noncooperative equilibria with wage setting at the sectoral level are shown to depend on the choice of price-normalization rule even though all agents behave fully rationally. Hence, imposing rationality is not sufficient to deprive the choice of price-normalization rule of its importance. It is argued that the importance of the choice of price-normalization rule may follow from the strategic interaction of agents and not from imperfectness of competition per se, and some examples are provided.     

Optimal policy for environmental goods trade in asymmetric oligopolistic eco-industries

In this paper, we examine the optimal structure of an environmental tax to pollution, a production subsidy to a domestic eco-industry, and an import tariff on environmental goods (EGs) in a two-country model where the home country imports EGs from the foreign country. Home and foreign firms that produce EGs engage in Cournot competition. We then assume that the number of the home local firms which produce EGs is constant, but that of the foreign firms is variable. Our main findings are as follows: (I) The optimal environmental tax level may be lower than the Pigouvian level even if the tax has a positive impact on the output of EGs produced by a domestic firm. (II) The optimal tariff level may be positive when the country implements the first best policy combination in a closed economy regarding the environmental tax and the subsidy. (III) The optimal subsidy level may be positive, and then the subsidy may be substitutive for the import tariff on EGs.     

Secret information acquisition in Cournot markets

Summary. Two-stage game models of information acquisition in stochastic oligopolies require the assumption that firms observe the precision of information chosen by their competitors before determining quantities. This paper analyzes secret information acquisition as a one-stage game. Relative to the two-stage game firms are shown to acquire less information. Policy implications based on the two-stage game yield, therefore, too high taxes or too low subsidies for research activities. For the case of heterogeneous duopoly we briefly discuss comparative statics results. Received: August 9, 1999; revised version: May 31, 2000     

On the computation of stable sets and strictly perfect equilibria

Summary. In this paper a procedure is described that computes for a given bimatrix game all stable sets in the sense of Kohlberg and Mertens (1986). Further the procedure is refined to find the strictly perfect equilibria (if any) of such a game. Recieved: December 29, 1999; revised version: February 17, 2000     

Reciprocity and Cooperation in Repeated Coordination Games: The Principled-Player Approach

Two long-lived players play a repeated coordination game. I show the restrictions on players' beliefs which imply that cooperation is optimal play. Journal of Economic Literature Classification Number: D83.     

Renegotiation-Proof Climate Agreements with Full Participation: Conditions for Pareto-Efficiency

Recent contributions show that climate agreements with broad participation can be implemented as weakly renegotiation-proof equilibria in simple models of greenhouse gas abatement where each country has a binary choice between cooperating (i.e., abate emissions) or defecting (no abatement). Here we show that this result carries over to a model where countries have a continuum of emission choices. Indeed, a Pareto-efficient climate agreement can always be implemented as a weakly renegotiation-proof equilibrium, for a sufficiently high discount factor. This means that one need not trade-off a “narrow but deep” treaty with a “broad but shallow” treaty.     

A Suggested Interpretation of Some Experimental Results on Preplay Communication

M. Rabin (1994, J. Econ. Theory63, 370-391) proposes a model of behavior in two-person complete-information games with preplay communication, using non-equilibrium notions in the spirit of rationalizability to derive lower bounds on players' expected payoffs when players have unlimited communication opportunities. This paper adapts Rabin's model so that it can be used to analyze the results of the experiments of R. Cooper et al. (1989, Rand J. Econ.20, 568-587) on structured preplay communication in the Battle of the Sexes and the results of the unstructured bargaining experiments of Roth, Malouf, and Murnighan. Adding empirically motivated restrictions that allow the model to predict the payoff effects of changes in bounded communication possibilities like those in the experiments, it is shown that the data from both experiments are generally consistent with Rabin's model, and with the predictions of the extended model. Journal of Economic Literature Classification Numbers: C70, C72, C78, C91.     

Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining

We did experiments in a three-round bargaining game where the (perfect) equilibrium offer was $1.25 and an equal split was $2.50. The average offer was $2.11. Patterns of information search (measured with a computerized information display) show limited lookahead rather than backward induction. Equilibrium theories which adjust for social utilities (reflecting inequality-aversion or reciprocity) cannot explain the results because they predict subjects will make equilibrium offers to “robot” players, but offers to robots are only a little lower. When trained subjects (who quickly learned to do backward induction) bargained with untrained subjects, offers ended up halfway between equilibrium and $2.11. Journal of Economic Literature Classification Numbers: C7, C9.     

寡头垄断:优化产业市场结构的选择

长期以来,人们从微观经济理论出发,认为竞争是有效的,垄断是无效的。但从世界范围内的产业发展来看,寡头垄断是当今国际市场结构发展的主流,为了优化中国产业市场结构,改善产业组织绩效,本文认为应对市场结构的效率进行重新认识,并提出了优化中国产业市场结构的选择。     

Correlated equilibria, incomplete information and coalitional deviations

This paper proposes new concepts of strong and coalition-proof correlated equilibria where agents form coalitions at the interim stage and share information about their recommendations in a credible way. When players deviate at the interim stage, coalition-proof correlated equilibria may fail to exist for two-player games. However, coalition-proof correlated equilibria always exist in dominance-solvable games and in games with positive externalities and binary actions.     

Walras and Darwin: an odd couple?

General equilibrium theory and the evolutionary branches of economics and game theory take rather opposite positions in the spectrum covered by the economic science. However, we reveal and explore analogies between Darwinian dynamics and Walrasian tatonnement processes for pure exchange economies, as well as further analogies implied by these.     

On perfect equilibria in stochastic models of growth with intergenerational altruism

Summary. The well-known model of altruistic growth/strategic bequest is studied. A stochastic transition function is considered and fairly general sufficient conditions for the existence of Markov-stationary subgame-perfect equilibrium are given. Also some special cases in which the equilibrium policy is continuous and nondecreasing are discussed.Received: 20 September 2003, Revised: 11 December 2004, JEL Classification Numbers: C73, D91, O40.Research was partially supported by KBN grant 5 PO3A 01420.     

Quantal Response Equilibria for Extensive Form Games

This article investigates the use of standard econometric models for quantal choice to study equilibria of extensive form games. Players make choices based on a quantal-choice model and assume other players do so as well. We define an agent quantal response equilibrium (AQRE), which applies QRE to the agent normal form of an extensive form game and imposes a statistical version of sequential rationality. We also define a parametric specification, called logit-AQRE, in which quantal-choice probabilities are given by logit response functions. AQRE makes predictions that contradict the invariance principle in systematic ways. We show that these predictions match up with some experimental findings by Schotter et al. (1994) about the play of games that differ only with respect to inessential transformations of the extensive form. The logit-AQRE also implies a unique selection from the set of sequential equilibria in generic extensive form games. We examine data from signaling game experiments by Banks et al. (1994) and Brandts and Holt (1993). We find that the logit-AQRE selection applied to these games succeeds in predicting patterns of behavior observed in these experiments, even when our prediction conflicts with more standard equilibrium refinements, such as the intuitive criterion. We also reexamine data from the McKelvey and Palfrey (1992) centipede experiment and find that the AQRE model can account for behavior that had previously been explained in terms of altruistic behavior. This revised version was published online in August 2006 with corrections to the Cover Date.