Social Indeterminacy

An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict‐preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to arbitrary neutral monotone social welfare functions that can be described by a strong simple game G if the voting power of each individual, measured by the Shapley–Shubik power index, is sufficiently small. Our proof is based on an extension to another classic result concerning the majority rule. Condorcet studied an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is p>1/2. Condorcet's jury theorem asserts that if the number of voters tends to infinity then the probability that the first candidate will be elected tends to one. We prove that this assertion extends to a sequence of arbitrary monotone strong simple games if and only if the maximum voting power for all individuals tends to zero.     

虚拟世界经济收益模式研究

虚拟世界经济收益模式分为直接收益模式和间接收益模式,前者主要包括时间销售和虚拟物品销售等,后者主要包括现实货币交易和微型服务外包.其中间接收益模式对服务贸易发展、产业结构升级、增加低水平劳动力就业都具有特殊意义,更适合中国目前的形势.通过对虚拟世界收益模式新形式的初步分析.为政策制定提供参考.     

手机游戏产业繁荣背后社会负面效应的规避

伴随智能手机的逐渐普及,手机游戏产业日益成为数字娱乐文化产业中的主力军。由于国内手机游戏用户数量大、年龄低的特点,以及智能手机使手机游戏呈现出游戏载体智能化、游戏软件多样化、厂商利益链条化、政府监管复杂化等新特点,手机游戏产业存在游戏软件安全性、合法性以及游戏内容健康性等社会负面问题。为使手机游戏产业健康发展,制作商应把效益与文化建设相融合;用户提高安全意识,家长转变对游戏的态度,重视但不过分夸大游戏的负面效应;政府制定游戏分级制度、加大对公益类、教育类游戏软件开发的支持、保护手机游戏软件知识产权,争取把手机游戏产业打造成文化产业链中新的“金蛋”。     

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.     

新规则对湖南省第八届大学生运动会武术比赛的影响

运用采献资料法,临场统计法和数理统计法对湖南省第八届大学生运动会武术比赛中使用的新规则做了研究,其中动作质量、演练水平和难度得分对最后的成绩影响大相径庭,对金牌分布的影响是显而易见的,通过研究分析,最后提出了相关建议,旨在为湖南省高校武术训练提供理论和实践依据。     

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.