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.     

Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium

This paper revisits the minimum-effort coordination game with a continuum of Pareto-ranked Nash equilibria. Noise is introduced via a logit probabilistic choice function. The resulting logit equilibrium distribution of decisions is unique and maximizes a stochastic potential function. In the limit as the noise vanishes, the distribution converges to an outcome that is analogous to the risk-dominant outcome for 2 × 2 games. In accordance with experimental evidence, logit equilibrium efforts decrease with increases in effort costs and the number of players, even though these parameters do not affect the Nash equilibria. Journal of Economic Literature Classification Numbers: C72, C92.     

战略联盟的存在机理及其生命周期管理

战略联盟是企业间以价值链为纽带,以核心能力为基础展开的同盟搏弈.国内外学者对战略联盟的解释多借助于价值链理论、交易费用理论、博弈论和网络战略理论.尽管学界对战略联盟的生命周期少有论及,但作为“市场化组织”,战略联盟与其他生物体一样,具有自己的生命周期.论文根据战略联盟演绎进程和阶段性工作重点的差异,将其分为酝酿与组建期、震荡与磨合期、规范运作与联盟任务执行期以及联盟的解散与“升华”四个阶段,各阶段工作中心不同,风险存在差异.战略联盟具有“竞合”性质,联盟成员间合作博弈和非合作博弈共存.联盟成员的机会主义和欺诈悖德行为贯穿联盟始终,危及联盟存续,所以要提高联盟绩效,就必须加强联盟生命周期不同阶段的风险管理.     

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.     

Correlated Equilibrium in Stochastic Games

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and is drawn according to the same probability distribution at every stage). We prove that any n-player stochastic game admits an autonomous correlated equilibrium payoff. When the game is positive and recursive, a stationary correlated equilibrium payoff exists. Journal of Economic Literature Classification Numbers: C72, C73.     

The monoclus of a coalitional game

The analysis of single-valued solution concepts, providing payoffs to players for the grand coalition only, has a long tradition. Opposed to most of this literature we analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce several closely related allocation scheme rules, each resulting in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game with transferable utilities has a PMAS. Monotonicities, which measure the payoff difference for a player between two nested coalitions, are the driving force. These monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Variants are obtained by considering different domains and/or different collections of monotonicities. We deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues.     

Equilibrium in a Market Game

This paper studies the equilibrium of an exchange economy with the same number of agents and commodities. It is shown that under rather mild conditions on demand the market have a price equilibrium—independently of the divisibility of the commodities. The result extends Gale’s equilibrium theorem for indivisible commodities to the case where some commodities are perfectly divisible. The proof is based on a topological lemma contained in previous paper of one of the authors.     

Strategic complementarity in multi-stage games

We provide sufficient conditions in finite-horizon multi-stage games for the value function of each player, associated to extremal Markov perfect equilibria, to display strategic complementarities and for the contemporaneous equilibrium to be increasing in the state variables. The author is grateful to Federico Echenique, Rabah Amir and one anonymous referee for useful comments, project SEJ2005-08263 at UPF and Project Consolider-Ingenio CSD2006-00016 of the Spanish Ministry of Education and Science, and the Barcelona Economics Program of CREA, for financial support.     

Subgame Monotonicity in Extensive Form Evolutionary Games

A theory of subgame monotonicity is developed for finite extensive form games to model evolutionary processes that respect the subgame structure of the game. It is shown how these evolutionary processes can be decomposed into their evolution on smaller games and also recombined to simplify the analysis of the original game. When applied to the replicator dynamic, a generalization of the Wright manifold from population genetics is a natural consequence of monotonicity. Subgame monotonicity and the Wright manifold are also shown to arise naturally in imitation models based on the extensive form. Journal of Economic Literature Classification Numbers: C70, C72.     

Equilibrium selection in bargaining models

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.     

Strategic complexity in repeated extensive games

This paper studies a machine (finite automaton) playing a two-player repeated game of a simple extensive-form game with perfect information. We introduce a new complexity measure called multiple complexity which incorporates a strategyʼs responsiveness to information in the stage game as well as the number of states of the machine. We completely characterize the Nash equilibrium of the machine game. In the sequential-move prisonerʼs dilemma, cooperation can be sustained as an equilibrium.     

Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players. Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”. An anonymous referee of Economic Theory is acknowledged for his/her comments     

知识披露策略:专利竞赛中的厂商策略性行为

专利竞赛是产业组织理论的重要内容。在专利竞赛中,披露研发知识是落后厂商常用的策略性行为,其目的通常是延长竞赛时间,为其追赶领先厂商提供机会。落后厂商的知识披露策略能够降低领先厂商在专利竞赛中获胜的概率,并迫使领先厂商与落后厂商进行合作研发。我国企业的研发力量尽管在某些技术领域比国外大型企业弱,但可采取知识披露策略,迫使国外厂商与我国企业进行合作创新。     

收入、工作单位与主观幸福感——基于武汉市城镇居民的调查分析

基于2007年武汉市城镇居民的主观幸福感数据,本文对收入、工作单位与主观幸福感之间的关系进行考察。研究结果表明,绝对收入对主观幸福感有显著的正影响,而收入差距对主观幸福感有负影响,收入-幸福悖论并不成立。同时,在控制其他因素后,与在政府机关及国企事业单位工作的个体相比,在其他单位工作的群体的主观幸福感水平更低;如果考虑不同工作单位对个体主观幸福感所产生的影响,随着在其他单位工作的人的收入增加,由于工作单位的性质差异导致的主观幸福感差异在两者之间逐渐缩小。     

评香港策略性排污计划

香港策略性排污计划（ＳＳＤＳ），其污水处理的指导方针仍停留在“直排”阶段，因此该工程的指导思想存在着严重的失误；同时该计划未对实施后的环境影响进行科学论证，因此其可行性、科学性值得商榷；从经济方面看，ＳＳＤＳ也是一项浪费型的排污计划。在此分析的基础上，笔者对香港的污水处理提出了一些建议。     

Strategic Manipulation in Voting Games When Lotteries and Ties Are Permitted

A Gibbard-Satterthwaite type theorem is established for random decision rules and rules that permit ties. The rules use full information on how individuals rank lotteries and sets of outcomes. The theorem allows restrictions on the domain of rankings. Journal of Economic Literature Classification Numbers: D7, C7.     

Comparison of Scoring Rules in Poisson Voting Games

Scoring rules are compared by their equilibria in simple voting games with Poisson population uncertainty, using new techniques for computing pivot probabilities. Best-rewarding rules like plurality voting can generate discriminatory equilibria where the voters disregard some candidate as not a serious contender, although he may be universally liked, or may be symmetric to other candidates as in the Condorcet cycle. Such discriminatory equilibria are eliminated by worst-punishing rules like negative voting, but then even a universally disliked candidate may have to be taken seriously. In simple bipolar elections, equilibria are always majoritarian and efficient under approval voting, but not other scoring rules. Journal of Economic Literature Classification: D72.     

战略联盟组织的稳定性、组织治理与信用约束机制

本文运用博弈论的分析框架分析了战略联盟组织不稳定性的原因在于战略联盟组织的中间组织性质所导致的战略联盟组织对机会主义行为约束的弱化,进而揭示了战略联盟组织稳定的关键在于组织内成员的博弈支付结构和博弈者对未来的预期。在此基础上,从组织治理结构的角度提出了稳定战略联盟组织应建立有效的信用约束机制的结论,阐述了这一机制的目标和内容,并针对我国战略联盟组织所面临的问题提出了相应的对策。     

Pollution Control in Open Economies: Implications of Within-period Interactions for Dynamic Game Equilibrium

This paper examines a two-country, dynamic game model of pollution control in the presence of economic interactions between countries within a period, as well as the environmental interaction between periods (i.e., a change in the stock of global pollution). These economic interactions emerge because of changes in the terms of trade of polluting goods or the market share of domestic polluting industries. It is shown that if within-period externalities exist, a noncooperative equilibrium may result in a smaller stock of global pollution in the steady state than does international cooperation. Moreover, the properties of equilibrium paths depend on the direction and size of such externalities. In addition, trigger strategy equilibria that achieve the outcome of the collusive solution are examined.     

基于博弈机制的物流信息共享研究

供应链通过物流信息共享可以有效地促进资源共享与资源整合,从而提高服务的附加价值,增强持续增值能力。供应链相邻节点企业之间没有进行物流信息共享的主动性,往往表现为信息不共享。利用博弈模型的触发策略分析相邻节点在完全信息共享、部分信息共享、不进行信息共享以及存在信息共享率与节点企业长远期望等情况下的成本、收益状况,探讨物流信息共享机制有效地降低运作成本,提高服务效益,实现供应链的"共生"与"双赢"。