The theory of public goods: non-nash behaviour

Most treatments of equilibrium public goods provision assume zero conjectural variations in the sense that each individual regards the behaviour of the rest of the community as independent of his own. This paper introduces nonzero conjectural variations into the model. A diagram is introduced which can depict both the individual's and the community's equilibrium in the presence of nonzero conjectural variations. Equilibrium and optimal outcomes are compared, and a specific functional form is used to investigate the effect of community size on the nature of equilibrium. Finally, we discuss the requirement that conjectures should be consistent.     

ON THE CONSISTENT CONJECTURES EQUILIBRIUM OF EXPORT SUBSIDY GAME

This paper explores an export subsidy game in an international duopoly in which governments of countries as well as firms hold conjectures about the response of other governments. In the framework with linear demand/quadratic cost functions, a homogeneous good and no home consumption, I shall obtain the relations among the conjectural variation of firms, that of governments, and the optimal subsidies for countries. And I shall show that if and only if firms hold the consistent conjectures, Nash type behavior (zero conjectural variation) of governments is consistent.     

Finitely repeated games with monitoring options

We study finitely repeated games where players can decide whether to monitor the other players? actions or not every period. Monitoring is assumed to be costless and private. We compare our model with the standard one where the players automatically monitor each other. Since monitoring other players never hurts, any equilibrium payoff vector of a standard finitely repeated game is an equilibrium payoff vector of the same game with monitoring options. We show that some finitely repeated games with monitoring options have sequential equilibrium outcomes which cannot be sustained under the standard model, even if the stage game has a unique Nash equilibrium. We also present sufficient conditions for a folk theorem, when the players have a long horizon.     

Rational conjectures and evolutionary beliefs in public goods games

This paper applies conjectural variations (CVs) to a model of public good provision and shows that CVs are superior to Nash beliefs. In addition to imposing consistency, as Bresnahan, I show that consistent conjectures (CCs) are obtained from individual payoff maximization. CCs emerge as the unique subgame perfect Nash equilibrium (NE) in a two-stage game in which beliefs are chosen in Stage 1 and quantities in Stage 2. There is an individual payoff advantage to non-Nash behavior, generating a Prisoner's Dilemma in conjectures in addition to the usual free-rider problem associated with public goods. The correct and payoff maximizing conjecture is the unique equilibrium in an evolutionary framework against a player with Nash conjectures. The consistent conjecture equilibrium is the unique evolutionary equilibrium when both players conjectures evolve. Hence, the NE prediction is too optimistic when players have rational conjectures.     

Equilibrium selection in similar repeated games: experimental evidence on the role of precedents

We report on an experiment examining behavior and equilibrium selection in two similar, infinitely repeated games, Stag Hunt and Prisoner’s Dilemma under anonymous random matching. We are interested in the role that historical precedents may play for equilibrium selection between these two repeated games. We find that a precedent for efficient play in the repeated Stag Hunt game does not carry over to the repeated Prisoner’s Dilemma game despite the possibility that efficient play can be sustained as an equilibrium of the indefinitely repeated game. Similarly, a precedent for inefficient play in the repeated Prisoner’s Dilemma game does not extend to the repeated Stag Hunt game. We conclude that equilibrium selection between similar repeated games may have less to do with historical precedents and might instead depend more on strategic considerations associated with the different payoffs of these similar repeated games.     

Technology choice under duopoly

This paper presents a conjectural variation approach to demonstrate that competing firms will often distort their cost structures away from strict cost minimization for strategic reasons. In particular, it is shown that the nature of the desired distortions of production technology depends critically on the magnitudes of the firms' conjectural variations with respect to outputs as well as the firms' conjectural variations with respect to technology. These results are in sharp contrast to the conventional wisdom based on monopolized or perfectly competitive markets.     

Price or Quantity Competition? Oligopolistic Structures in International Commodity Markets

International commodity markets may be characterized by price or quantity competition and by product differentiation. As an illustration, this paper presents a set of models of the Japanese market for imported beef. The models are evaluated using a non-nested econometric test. The one which best fits the data is a Stackelberg model with price leadership by Australia. This result provides evidence on the explicit nature of the game being played by exporters, unlike the applied conjectural variations approach which provides only an index of how competitive the market is.     

Is Social Security Really Bad for Growth?

This paper develops a model of endogenous growth with overlapping generations to investigate the joint determination of social security, public investment, and growth in a small open economy. We show that a pure pay-as-you-go system with benefits indexed to wages provides taxpayers with incentives to support growth-oriented policies, which increase the future productivity of labor. We find that outcomes characterized by positive levels of intergenerational redistribution, public investment, and long-run growth can be sustained as subgame-perfect Nash equilibria of an infinitely repeated intergenerational game, if and only if the marginal productivity of public capital is large enough. Furthermore, we show that transfers comove with public investment and growth. Journal of Economic Literature Classification Numbers: E62, H55.     

Conjectural variations,risk aversion and price-cost margins

Summary We have shown that introduction of random conjectural variations and risk aversion into an oligopoly model leads to results in line with those derived earlier for competitive and monopolistic firms. In particular, a risk-averse firm has smaller output and higher expected price-cost margin than a risk-neutral firm. For a specific form of conjectural variations we have shown that under risk aversion the firm-level expected price-cost margins depend on the market structure, measured in terms of the Herfindahl index of the rest of the firms in the industry, as well as on the expected degree of correlation between the competitors' reactions.     

Overcoming coordination failure using a mechanism based on gradualism and endogeneity

We examine three tools that can enhance coordination success in a repeated multiple-choice coordination game. Gradualism means that the game starts as an easy coordination problem and moves gradually to a more difficult one. The Endogenous Ascending mechanism implies that a gradual increase in the upper bound of coordination occurs only if coordination with the Pareto superior equilibrium in a stage game is attained. The Endogenous Descending mechanism requires that when the game’s participants fail to coordinate, the level of the next coordination game be adjusted such that the game becomes simpler. We show that gradualism may not always work, but in such instances, its effect can be reinforced by endogeneity. Our laboratory experiment provides evidence that a mechanism that combines three tools, herein termed the “Gradualism with Endogenous Ascending and Descending (GEAD)” mechanism, works well. We discuss how the GEAD mechanism can be applied to real-life situations that suffer from coordination failure.     

Pure eclecticism—The tool kit of the constitutional economist

It is claimed here that the epistemics of constitutional economics has hitherto at best played a minor role but that dwelling on the epistemics might prove useful to understand why the positive branch of constitutional economics is not as far advanced as its normative counterpart. Four possible methods-namely comparative institutional analysis, economic history, conjectural history, and laboratory experiments-are analyzed with regard to their epistemic potential. It is hypothesized that conjectural history promises only little potential while the other three methods can be used to complement each other.     

A folk theorem for minority games

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.     

社会资本外部性的经济分析——以信任关系为例

以往理论研究与经验研究均指出社会资本具有正面的效应,但对这种效应是怎样取得的并无共识.我们尝试建立一个不完全信息动态博弈模型,说明社会资本-信任如何产生正的外部性,亦即产生超出个体理性计算之外的利益.我们的分析得出这样的结论,在一个多人互动的环境中,能否达到彼此合作或彼此信任,虽然会受到欺骗者所遭到的惩罚与欺骗利益多少的影响,但主要受到所处环境中具有社会资本者人数比例的影响.因此,可以说社会资本具有正的网络外部性,信任者人数越多,信任者所享受到的利益越大.     

Sustaining Collusion under Economic Integration*

In this paper, we aim at investigating from a game‐theory perspective whether trade liberalization can promote a collusive two‐way trade. We show that, under Cournot competition, economic integration is anti‐competitive if collusive trade is a possible outcome of the repeated game; under price competition, the likelihood of collusive trade is a necessary but not sufficient condition for trade liberalization to be pro‐competitive. Furthermore, we show that economic integration may increase the scope for collusion irrespective of the firms’ strategic variable.     

Exploring Duopoly Markets with Conjectural Variations

In this article, the authors investigate competitive firm behaviors in a two-firm environment assuming linear cost and demand functions. By introducing conjectural variations, they capture the different market structures as specific configurations of a more general model. Conjectural variations are based on the assumption that each firm believes its own strategy influences its rival's strategy. Firms derive their optimal choice from these exogenous conjectures, under the form of a conjectural best-response function. The authors’ approach fully encompasses the standard measures of market power (the Lerner Index) and concentration (the Herfindahl Index), both depending on the conjectural variations. They finally represent, analytically and graphically, the equilibrium strategies and the associated indexes in a unified framework for any level of competition, ranging from perfect competition to collusion.     

Successful Leadership in Global Public Good Provision: Incorporating Behavioural Approaches

In the standard model of voluntary public good provision and other game theoretic models, climate-friendly leadership of a country is not successful: A unilateral increase of this country’s greenhouse gas abatement measures, i.e., contributions to the global public good of climate protection, will not lead to a positive reaction by the other countries but instead trigger a reduction of their abatement efforts and thus a crowding-out effect. In this paper it is shown how this undesired consequence need no longer occur when elements of behavioral economics are incorporated in the otherwise standard model of public good provision. In particular, strategic complementarities between the public good contribution of the leading country and those of the follower may result either if the follower has specific non-egoistic or other-regarding preferences or if the leader’s contribution positively affects the follower’s beliefs, i.e., his conjectural variations, about the leader’s behaviour.     

Sowing Doubt Optimally in Two-Person Repeated Games

Consider a two-person repeated game, where one of the players, P1, can sow doubt, in the mind of his opponent, as to what P1's payoffs are. This results in a two-person repeated game with incomplete information. By sowing doubt, P1 can sometimes increase his minimal equilibrium payoff in the original game. We prove that this minimum is maximal when only one payoff matrix, the negative of the payoff matrix of the opponent, is added (the opponent thus believes that he might play a zero-sum game). We obtain two formulas for calculating this maximal minimum payoff. Journal of Economic Literature Classification Numbers: C7, D8.     

A further look at consistent conjectures and private provision of public goods

A model of private provision of a public good under conjectural variations is discussed and the rule for a symmetric consistent conjectures equilibrium (CCE) derived. It is shown that in a number of reasonable cases symmetric CCEs fail to exist in economies with identical individuals, while there may exist asymmetric ones. The relevance of these results for the use of the conjectural variations approach in public good theory is then discussed together with some suggestions for further research.     

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n  ≥  4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.” A previous version of this paper was circulated as Anderlini et al. (2005). We are grateful to Jeff Ely, Leonardo Felli, Navin Kartik, David Levine, Stephen Morris, Michele Piccione, Andrew Postlewaite, Lones Smith and to seminar audiences at Bocconi, Cambridge, CEPR-Guerzensee, Chicago, Columbia, Edinburgh, Essex, Georgetown, Leicester, LSE, Northwestern, Oxford, Rome (La Sapienza), Rutgers, SAET-Vigo, Stanford, SUNY-Albany, UCL, UC-San Diego, Venice and Yale for helpful feedback.     

基于法律风险损失的研究：CPA与客户之间的合作博弈

CPA与客户之间的合作关系因法律风险进而影响到审计质量,基于法律风险损失的视角,对CPA与客户之间的合作博弈进行重复博弈分析。结果表明：在法律风险损失足够大的情况下,CPA与客户各自理性的选择应是相互再合作,即CPA履行职责,客户提供真实的信息,从而提高审计质量。因此,规避法律风险损失对提高审计质量有积极作用,对我国相关法律政策也具有一定的借鉴意义。