On the Global Convergence of Stochastic Fictitious Play

We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities.     

Games Played Through Agents

We introduce a game of complete information with multiple principals and multiple common agents. Each agent makes a decision that can affect the payoffs of all principals. Each principal offers monetary transfers to each agent conditional on the action taken by the agent. We characterize pure‐strategy equilibria and we provide conditions—in terms of game balancedness—for the existence of an equilibrium with an efficient outcome. Games played through agents display a type of strategic inefficiency that is absent when either there is a unique principal or there is a unique agent.     

Cooperation in Repeated Games When the Number of Stages is not Commonly Known

It is shown that an exponentially small departure from the common knowledge assumption on the number T of repetitions of the prisoners' dilemma already enables cooperation. More generally, with such a departure, any feasible individually rational outcome of any one-shot game can be approximated by a subgame perfect equilibrium of a finitely repeated version of that game. The sense in which the departure from common knowledge is small is as follows: (I) With probability one, the players know T with precision ±K. (ii) With probability 1 −ε, the players know T precisely; moreover, this knowledge is mutual of order εT. (iii) The deviation of T from its finite expectation is exponentially small.     

Information Independence and Common Knowledge

In Bayesian environments with private information, as described by the types of Harsanyi, how can types of agents be (statistically) disassociated from each other and how are such disassociations reflected in the agents' knowledge structure? Conditions studied are (i) subjective independence (the opponents' types are independent conditional on one's own) and (ii) type disassociation under common knowledge (the agents' types are independent, conditional on some common‐knowledge variable). Subjective independence is motivated by its implications in Bayesian games and in studies of equilibrium concepts. We find that a variable that disassociates types is more informative than any common‐knowledge variable. With three or more agents, conditions (i) and (ii) are equivalent. They also imply that any variable which is common knowledge to two agents is common knowledge to all, and imply the existence of a unique common‐knowledge variable that disassociates types, which is the one defined by Aumann.     

Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem

We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Reny (1999) that is not covered by his theorem. We use the main result to prove the existence of pure Nash equilibrium in a class of finite games in which agents' pure strategies are subsets of a given set, and in turn use this to prove the existence of stable configurations for games, similar to those used by Schelling (1971, 1972) to study residential segregation, in which agents choose locations.     

On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure‐strategy equilibria in Bayesian games. We allow action spaces to be compact locally complete metric semilattices and type spaces to be partially ordered probability spaces. Our proof is based on contractibility rather than convexity of best‐reply sets. Several examples illustrate the scope of the result, including new applications to multi‐unit auctions with risk‐averse bidders.     

译者博弈与翻译忠实

翻译是一项有目的的社会性活动,一次完整的翻译活动绝不是译者的独角戏,而是由原文作者、翻译委托人、译文读者、出版社及其他译者等共同参与完成,他们在翻译过程中有着各自的利益,彼此之间既有合作又有对抗。翻译实质上就是一场以译者为中心的多方博弈,其最终所实现的忠实只是译者与博弈各方达成的一个＂纳什均衡＂,而这种均衡是有效实现翻译效益和翻译交际功能的保证。译者博弈既是实现翻译忠实的必要,也是实现翻译忠实的必然。     

电子游戏对儿童心理发展影响的实证研究

电子游戏作为新技术和新文化发展的代表产物,已成为儿童的重要娱乐方式。与此同时,电子游戏对儿童尤其是儿童心理发展的影响已引起了社会各界的关注。实证研究表明,电子游戏如果合理利用,可以培养儿童的多元智能,成为一种很好的教育资源。不同类型电子游戏对开发和培养儿童单项智能具有不同的优势。游戏设计开发人员和教育工作者应设计开发适合儿童多元智能发展的电子游戏作品,发挥电子游戏所具有的智能开发的优势,减少电子游戏对儿童智能发展的不利影响。     

Game-Based Cognitive-Behavioral Therapy (GB-CBT) Group Program for Children Who Have Experienced Sexual Abuse: A Preliminary Investigation

This preliminary investigation examined the efficacy of a game-based cognitive-behavioral therapy group program for elementary school-aged children who have experienced sexual abuse. Treatment aimed to improve: (a) internalizing symptoms, (b) externalizing behaviors, (c) sexually inappropriate behaviors, (d) social skills deficits, (e) self-esteem problems, and (f) knowledge of healthy sexuality and self-protection skills. Results indicate that game-based cognitive-behavioral therapy was effective for improving internalizing and externalizing symptoms, reducing sexually inappropriate behaviors, and improving children's knowledge of abuse and self-protection skills. Although results pointed in a positive direction for social skills and self-perception, these findings were not statistically significant. Clinical significance was also evaluated to assess the clinical utility of treatment effects. Treatment implications of the findings and future research directions are discussed.