Information structures and decentralizability of equilibria

Summary Decentralizability with respect to an equilibrium concept means that those equilibria for an extensive game and its agent normal form game coincide for any given payoffs. We consider decentralizability of Nash equilibrium, subgame perfect equilibrium, and perfect equilibrium. For each equilibrium concept we give a necessary and sufficient condition on the information structure of an extensive game for decentralizability to hold. When it holds it does not matter if agents with the same objectives decide independently or have someone coordinate their actions.The author thanks Satish Chand, Mamoru Kaneko, Akira Okada and participants at seminars at the Australian National University, Kyoto University, University of Tsukuba, and The First Decentralization Conference in Japan held at Keio University for valuable suggestions and comments.     

Endogenous property rights regimes, common-pool resources and trade

A model is developed where opening to trade affects a dynamic common-pool resource stock and welfare through a community's voting decision to institute a property rights regime regulating the stock. The model finds that resource stock levels can decline even when a Markov perfect equilibrium path for labor and property rights regimes are chosen to maximize welfare. Thus, opening to trade can be welfare maximizing even when resource stock declines. Experimental results show that under certain conditions, subjects briefly follow a Markov perfect equilibrium path for property rights regime choice but labor allocations are myopically chosen indicating that some resource dynamics may be considered by subjects.     

A Common Pool Resource Game with Sequential Decisions and Experimental Evidence

We describe a common pool resource game in which players choose how much of the stock to extract in a sequential manner. There are two choices and one represents taking a larger proportion of the stock than the other. After a player makes a choice, the remaining stock grows at a constant rate. We consider a game with a finite number of alternating moves. It is shown that changes in the larger proportion of the stock that the players are allowed to take and the growth rate affect equilibrium, but have little effect on behavior in the laboratory. In addition to observing more cooperation than predicted, we observe that parameters that are strategically irrelevant affect behavior. The results of this research might help policy makers in developing adequate policies to prevent overexploitation of some natural renewable resources.     

Stochastic bequest games

In this paper, we prove the existence of a stationary Markov perfect equilibrium for a stochastic version of the bequest game. A novel feature in our approach is the fact that the transition probability need not be non-atomic and therefore, the deterministic production function is not excluded from consideration. Moreover, in addition to the common expected utility we also deal with a utility that takes into account an attitude of the generation towards risk.     

Finitely repeated games with social preferences

A well-known result from the theory of finitely repeated games states that if the stage game has a unique equilibrium, then there is a unique subgame perfect equilibrium in the finitely repeated game in which the equilibrium of the stage game is being played in every period. Here I show that this result does in general not hold anymore if players have social preferences of the form frequently assumed in the recent literature, for example in the inequity aversion models of Fehr and Schmidt (Quartely Journal of Economics 114:817–868, 1999) or Bolton and Ockenfels (American Economic Review 100:166–193, 2000). In fact, repeating the unique stage game equilibrium may not be a subgame perfect equilibrium at all. This finding should have relevance for all experiments with repeated interaction, whether with fixed, random or perfect stranger matching.     

Dynamic common agency

A general model of dynamic common agency with symmetric information is considered. The set of truthful Markov perfect equilibrium payoffs is characterized and the efficiency properties of the equilibria are established. A condition for the uniqueness of equilibrium payoffs is derived for the static and the dynamic game. The payoff is unique if and only if the payoff of each principal coincides with his marginal contribution to the social value of the game. The dynamic model is applied to a game of agenda setting.     

Coordination need not be a problem

In a game of common interest there is one action vector that all players prefer to every other. Yet there may be multiple Pareto-ranked Nash equilibria in the game and the “coordination problem” refers to the fact that rational equilibrium play cannot rule out Pareto-dominated equilibria. In this paper, I prove that two elements — asynchronicity and a finite horizon — are sufficient to uniquely select the Pareto-dominant action vector (in subgame perfect equilibrium play). Asynchronicity may be exogenously specified by the rules of the game. Alternatively, in a game where players choose when to move, asynchronicity may emerge as an equilibrium move outcome.     

Extinction in common property resource models: an analytically tractable example

We discuss an analytically tractable discrete-time dynamic game in which a finite number of players extract a renewable resource. We characterize a symmetric Markov-perfect Nash equilibrium of this game and derive a necessary and sufficient condition under which the resource does not become extinct in equilibrium. This condition requires that the intrinsic growth rate of the resource exceeds a certain threshold value that depends on the number of players and on their time-preference rates.     

Which border taxes? Origin and destination regimes with fiscal competition in output and emission taxes

This paper posits a two-stage game in tax regime and tax rates to study the property of second-best emission and output taxes in a two-country world with an atmospheric externality. It shows that (i) either the destination–destination or the origin–origin tax regime may constitute the subgame perfect Nash equilibrium of this game; (ii) either regime may Pareto-dominate the other; (iii) it is possible to have a prisoner's dilemma game where the origin–origin regime Pareto-dominates but the choice of the destination regime is the dominant strategy for each country. Other results include (iv) under origin–origin regime: the output tax is used for fiscal competition; the emission tax is set at a rate equal to the (national) marginal social damage of emissions; and public goods are provided suboptimally. (v) Under destination–destination regime: the output tax is ineffective as an instrument for fiscal competition; the emission tax is used not only for combating pollution but also for tax competition; the tax is set at a rate below the (national) marginal social damage of emissions; emissions are pushed above their closed-economy level; the provision of public goods are optimal.     

Markov equilibria in dynamic matching and bargaining games

Rubinstein and Wolinsky [Rev. Econ. Stud. 57 (1990) 63] show that a simple homogeneous market with exogenous matching has a continuum of (non-competitive) perfect equilibria; however, the unique Markov-perfect equilibrium of this model is competitive. By contrast, in the more general case of heterogeneous markets, even the Markov property is not enough to guarantee the perfectly competitive outcome. We define a market game that allows for heterogeneous values on both sides of the market and exhibit a number of examples of (non-competitive) Markov-perfect equilibria, with and without discounting. Unlike the homogeneous case, these equilibria allow for inefficient trades and for trade at non-uniform prices. The non-competitive equilibrium may be unique.     

Subgame Perfect Equilibria in Stage Games

It is well known that a stage game with infinite choice-sets, unless it contains a public coordination-device in each stage, may have no subgame perfect equilibria. We show that if a game with public coordination-devices has a subgame perfect equilibrium in which two players in each stage use non-atomic strategies, then the game without coordination devices also has a subgame perfect equilibrium. Journal of Economic Literature Classification Numbers: C6, C7, D8.     

Computing a quasi-perfect equilibrium of a two-player game

Refining an algorithm due to Koller, Megiddo and von Stengel, we show how to apply Lemke’s algorithm for solving linear complementarity programs to compute a quasi-perfect equilibrium in behavior strategies of a given two-player extensive-form game of perfect recall. A quasi-perfect equilibrium is known to be sequential, and our algorithm thus resolves a conjecture of McKelvey and McLennan in the positive. A quasi-perfect equilibrium is also known to be normal-form perfect and our algorithm thus provides an alternative to an algorithm by von Stengel, van den Elzen and Talman. For the case of a zero-sum game, we devise variants of the algorithm that rely on linear programming rather than linear complementarity programming and use the simplex algorithm or other algorithms for linear programming rather than Lemke’s algorithm. We argue that these latter algorithms are relevant for recent applications of equilibrium computation to artificial intelligence.     

Infinite horizon common interest games with perfect information

We consider infinite horizon common interest games with perfect information. A game is a K-coordination game if each player can decrease other players' payoffs by at most K times his own cost of punishment. The number K represents the degree of commonality of payoffs among the players. The smaller K is, the more interest the players share. A K-coordination game tapers off if the greatest payoff variation conditional on the first t periods of an efficient history converges to 0 at a rate faster than K^−t as t→∞. We show that every subgame perfect equilibrium outcome is efficient in any tapering-off game with perfect information. Applications include asynchronously repeated games, repeated games of extensive form games, asymptotically finite horizon games, and asymptotically pure coordination games.     

Representing equilibrium aggregates in aggregate games with applications to common agency

An aggregate game is a normal-form game with the property that each playerʼs payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games.     

浅析知识产权保护中混合策略纳什均衡模型的应用

知识产权保护不但受制于立法的完善和执法的力度,而且取决于自觉维权的意识和守法的环境。我国企业和科研机构知识产权保护意识薄弱,缺乏维护自身合法权益的能力,尊重他人知识产权的观念尚未形成社会主流。本文运用博弈论方法,分析了一个知识产权保护博弈案例中的混合策略纳什均衡解,得出从增加知识产权主体自觉维权意识和加大侵权者成本两方面实现知识产权有效保护的结论。     

Union–firm bargaining: Order of play and efficiency

This paper shows that a modified alternating offers Rubinstein model can provide a Pareto superior outcome in the context of the right-to-manage union–firm bargaining. Two examples of bargaining protocols that yield a superior outcome are provided. In the first example, the parties engage in a game in which the order of play is determined as part of the bargaining. We show that the game has a unique subgame perfect equilibrium in which the firm always moves first in the wage bargaining game. The equilibrium wage is, therefore, unique. In the second example, we examine a two-part-tariff alternating offers bargaining protocol, where the parties bargain over the wage and transfer payments. We show that this bargaining protocol has a Pareto efficient, unique subgame perfect equilibrium. Thus, although the parties do not bargain over the level of employment, the outcome under this protocol is, nevertheless, socially optimal.     

Undominated (and) perfect equilibria in Poisson games

In games with population uncertainty some perfect equilibria are in dominated strategies. We prove that every Poisson game has at least one perfect equilibrium in undominated strategies.     

员工反生产行为组织控制的演化博弈分析

基于演化博弈理论和员工反生产行为组织控制的行为博弈演化过程,构建企业与员工共同参与的演化博弈模型.博弈的复制动态方程表明:员工选择显性反生产行为的比例、员工因选择反生产行为所获得的额外收益、企业对员工的反生产行为进行监管所投入的成本,企业观测到员工选择反生产行为时所作出的处罚都将对博弈均衡的结果产生影响.对此,应加强人力资源管理,加大组织支持力度,建立有效的控制机制.     

Secrecy, two-sided bias and the value of evidence

We provide necessary and sufficient conditions on players' preferences for a verifiable message game to possess a separating equilibrium and/or a pooling equilibrium, as well as sufficient conditions for every equilibrium of such a game to be pooling. We also characterize all nonseparating equilibria, and use this property to show that less information might be conveyed in any equilibrium of a verifiable message game than in some equilibrium of the cheap talk game with the same parameters.     

Existence of equilibrium in common agency games with adverse selection

We establish the existence of subgame perfect equilibria in general menu games, known to be sufficient to analyze common agency problems. Our main result states that every menu game satisfying enough continuity properties has a subgame perfect equilibrium. Despite the continuity assumptions that we make, discontinuities naturally arise due to the absence, in general, of continuous optimal choices for the agent. Our approach, then, is based on (and generalizes) the existence theorem of [Simon, L., Zame, W., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58 (4), 861–872] designed for discontinuous games.