The Game Model Analysis between the Individual and the Group

This paper analyses the game model between the individual and the group that has the characteristics of Stackelberg model in traditional game theory and replicator dynamic model in evolutionary game theory. In the first phase of game, the bounded rationality group players adopt the replicator dynamic behavior. Secondly, the full rationality individual player decides the own response function by the strategies distribution of group players. The shortsighted individual player will take the risk-dominant strategy. This model has some unique characteristics.     

Inductive reasoning about unawareness

We develop a model of games with awareness that allows for differential levels of awareness. We show that, for the standard modal-logical interpretations of belief and awareness, a player cannot believe there exist propositions of which he is unaware. Nevertheless, we argue that a boundedly rational individual may regard the possibility that there exist propositions of which she is unaware as being supported by inductive reasoning, based on past experience and consideration of the limited awareness of others. In this paper, we provide a formal representation of inductive reasoning in the context of a dynamic game with differential awareness. We show that, given differential awareness over time and between players, individuals can derive inductive support for propositions expressing their own unawareness. We consider the ecological rationality of heuristics to guide decisions in problems involving differential awareness.     

A THEORY OF MAN AS A CREATOR OF THE WORLD*

The present paper proposes a theory of man, wherein man constructs models of the world based on past experiences in social situations. The present theory considers experiences, or chunks of impressions, as primitives instead of an objective game, which is assumed to be given in the standard game theory. Agents construct models of the world based on direct and indirect experiences. Each model comprises a structural part and a factual part. The structural part is represented as a game, while the factual part is represented as a strategy profile of this game. In constructing a model, an agent might use certain axioms—for example coherence, according to which the model should be able to explain his or her own experiences; conformity to a solution concept; and minimality with respect to some simplicity measure. A few applications are presented to demonstrate how this theory works.     

Partial memories, inductively derived views, and their interactions with behavior

We explore the inductively derived views obtained by players with partial temporal (short-term) memories. A player derives his personal view of the objective game situation from his accumulated (long-term) memories, and then uses it for decision making. A salient feature that distinguishes this paper from others on inductive game theory is partiality of a memory function of a player. This creates a multiplicity of possibly derived views. Although this is a difficulty for a player in various senses, it is an essential problem of induction. Faced with multiple possible views, a player may try to resolve this using further experiences. The two-way interaction between behavior and personal views is another distinguishing feature of the present paper.     

Racial Discrimination in English football

This paper examines data on the racial composition and financial and sporting performance of professional English soccer teams between 1974 and 1993. In an earlier paper, Szymanski showed that teams with an above average proportion of black players would tend to perform better on average that would have been expected given the aggregate wage bills of these clubs. Since players are more or less freely traded in soccer this presents strong market‐based evidence of discrimination. In the present paper we explore the source of such discrimination. In particular we are concerned to test the hypothesis that discrimination is attributable to the fans rather than the owners. If fans were racially prejudiced then the owners of a team might expect to generate a smaller marginal revenue product from a black player compared to an equally skilled white player. We assess the presence of fan discrimination by examining relationships between attendance, revenues, performance and the proportion of black players in the team. We also incorporate evidence regarding statements of racial prejudice (from the British Social Attitudes Survey) in particular regions. We find little evidence that the discrimination against black players has its source in fan discrimination.     

低碳经济下煤炭企业排污行为的博弈分析

基于我国长期处于"政府主导型"的环保模式中,运用博弈论方法,建立简单的政企双方完全信息静态博弈模型,在局中人混合策略解的基础上,对影响政府监管与企业排污概率的因素进行重点分析。研究结果表明,通过控制企业排污处罚金及政府监管成本等参数,是提高政府监管概率、降低企业排污概率的有效途径。进而,为相关政府部门提供若干指导性建议。     

基于户籍制度的教育回报差异:对工资歧视的再考察

利用2005年全国1%人口抽样调查数据,分析了我国东南部十一个省份就业者基于户籍制度的收入差异。户口类型对于工资的影响可以被不同户口类型人群的教育回报差距所解释。不同户口类型人群间教育回报的差距随着教育年限的下降而显著扩大。这一结果支持了在解释基于户籍制度的工资歧视的合理性方面信息经济学的有关理论。我国城乡间义务教育水平的差距引起了基于户籍制度的教育回报差异,进而导致了基于户籍类型的工资歧视。     

Learning by trial and error

A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are erroneous in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. We introduce a learning rule in which behavior is conditional on whether a player experiences an error of the first or second type. This rule, called interactive trial and error learning, implements Nash equilibrium behavior in any game with generic payoffs and at least one pure Nash equilibrium.     

Gender discrimination in China: Experimental evidence from the job market for college graduates

This paper examines employment-related gender discrimination during the initial stages of a hiring process. It specifically focuses on recent college graduates in China. By examining firms’ responses to fictitious resumes with randomly generated information on gender and other key attributes of applicants (e.g., school reputation, student's academic achievement, and leadership experiences), this study is able to separate the effect of gender on a student's potential for getting an on-site interview from the confounding effects of other factors. The findings reveal that, with all other factors remaining constant, female applicants, on average, are less likely to be invited by hiring firms to on-site interviews as compared with their male counterparts. Furthermore, gender discrimination in computer and mathematics, architecture and engineering, and sales occupations appears to be driving the results of this study. The qualitative evidence based on interviews with firm recruiters suggests that the findings of this study are generally consistent with the role congruity theory of prejudice in psychology literature. While the finding that the quality of a job candidate (academic achievement and leadership experience) does not reduce gender discrimination offers some evidence to support a taste-based discrimination view, we do not have enough evidence to support a statistical discrimination view.     

Bounded interpersonal inferences and decision making

Summary. Individual decision making is based on predictions about other players' choices as well as on valuations of reactions to predictions. In this sense, a player has a prediction-decision criterion for decision making. We develop a theory of prediction-decision criteria, which enables us to capture new phenomena on individual decision making in games. The decision making situation is described in the epistemic logic GL of shallow depths. There, each player considers his and other players' decision making down to some shallow depths. It is a point of our theory to investigate inferential complexities of interpersonal introspections. In particular, we can discuss a minimal epistemic inferential structure for prediction-decision making. We will find parallel structures in decision making and prediction making, which is called an inner parallelism. The climax of the paper is the consideration of inner parallelisms of prediction-decision making. Received: August 31, 2000; revised version: April 9, 2001     

A TEST OF EMPLOYER DISCRIMINATION IN THE NBA

This paper presents a test of an important implication of Becker's theory of employer discrimination: when institutional change enhances labor mobility, employer discrimination falls because it becomes more costly for employers to indulge tastes for discrimination. The test case is the National Basketball Association (NBA). This paper specifically addresses the following question about the NBA: why did black/white player salary differentials vanish by the early 1990s? Previous studies claim that NBA wage gaps in the 1980s are attributable to customer discrimination and monopsonistic wage discrimination. This study argues that employer discrimination was an important source of those gaps and that one reason they vanished was because reduced monopsony power eradicated employer discrimination. Monopsony power fell because the 1988 NBA Collective Bargaining Agreement and the entry of four new teams in the league enhanced player mobility and increased the amount of labor market competition. Using data for the 1985-86 and 1990-91 seasons, employer discrimination was proxied by the race of the team's general manager. Empirical results strongly suggest that a major reason the NBA wage gap vanished in the later period was because of a reduction in employers' ability to discriminate. This is in contrast to earlier literature on the NBA, which has tended to emphasize the role of customer discrimination. (JEL J71)     

Learning to play games in extensive form by valuation

Game theoretic models of learning which are based on the strategic form of the game cannot explain learning in games with large extensive form. We study learning in such games by using valuation of moves. A valuation for a player is a numeric assessment of her moves that purports to reflect their desirability. We consider a myopic player, who chooses moves with the highest valuation. Each time the game is played, the player revises her valuation by assigning the payoff obtained in the play to each of the moves she has made. We show for a repeated win-lose game that if the player has a winning strategy in the stage game, there is almost surely a time after which she always wins. When a player has more than two payoffs, a more elaborate learning procedure is required. We consider one that associates with each move the average payoff in the rounds in which this move was made. When all players adopt this learning procedure, with some perturbations, then, with probability 1 there is a time after which strategies that are close to subgame perfect equilibrium are played. A single player who adopts this procedure can guarantee only her individually rational payoff.     

Dismissals and quits in repeated games

This paper studies repeated games, where player 1 can decide to let the opponent continue or replace her by a new player. We also allow for the possibility of player 2 quitting the game. When only layoffs can occur, a folk theorem for finite horizons obtains due to the threat that termination of the relationship imposes on player 2. However, quits limit this result to those cases in which the outside option for player 2 is small (lower than some Nash equilibrium payoff of the stage game).     

结构化多人博弈的分析框架

结构化多人博弈是一种把博弈方嵌入到具体的社会关系之中,在两两博弈的基础上求解整体博弈均衡状态的分析框架。和现有的合作博弈(Cooperative Game Theory)、网络博弈(Network Games)、进化图论(Evolutionary Graph Theory,EGT)、计算博弈论(Computational Game Theory)等多人博弈分析框架相比,结构化博弈既有和它们相似的地方,也有非常重要的差别。结构化博弈更适合用来分析政治问题和社会现象中的多人博弈局面。作为最简单的情况,本文先给出了一个三人结构化博弈的一般分析框架,然后根据这个分析框架对传统的联盟博弈进行了新的分析,发现经典的"三人分300元"博弈事实上有稳定的均衡解,即三人各分100元。作为一个简单的应用,文章分析了三个国家之间的"战争-同盟博弈",我们发现该博弈有两个稳定的均衡解,在这两个稳定的均衡解中,超级大国和小国总是选择结盟,而小国总是选择和地区大国进行战争。从这两个例子可以看出,结构化多人博弈在分析复杂的政治、经济、社会问题上具有传统博弈论方法所不具备的很多优势,其获得的均衡解也更符合社会实际。     

Arms Races and Negotiations

Two players simultaneously decide whether or not to acquire new weapons in an arms race game. Each player's type determines his propensity to arm. Types are private information, and are independently drawn from a continuous distribution. With probability close to one, the best outcome for each player is for neither to acquire new weapons (although each prefers to acquire new weapons if he thinks the opponent will). There is a small probability that a player is a dominant strategy type who always prefers to acquire new weapons. We find conditions under which the unique Bayesian–Nash equilibrium involves an arms race with probability one. However, if the probability that a player is a dominant strategy type is sufficiently small, then there is an equilibrium of the cheap-talk extension of the game where the probability of an arms race is close to zero.     

博弈论视角下的广泛竞争与社会稳定——基于鹰-鸽模型及两个扩展型的分析

鉴于人类社会和动物世界的广泛竞争以及有别于动物世界的人类社会独特的稳定性,通过采用鹰-鸽博弈的基本模型和扩展型,尝试以一种博弈的视角分析这种广泛的竞争性和人类社会独特的稳定性,以证明明晰道德基础(共识)对社会稳定的重要作用。     

The Colonel Blotto game

In the Colonel Blotto game, two players simultaneously distribute forces across n battlefields. Within each battlefield, the player that allocates the higher level of force wins. The payoff of the game is the proportion of wins on the individual battlefields. An equilibrium of the Colonel Blotto game is a pair of n-variate distributions. This paper characterizes the unique equilibrium payoffs for all (symmetric and asymmetric) configurations of the players’ aggregate levels of force, characterizes the complete set of equilibrium univariate marginal distributions for most of these configurations, and constructs entirely new and novel equilibrium n-variate distributions.I am grateful to Jason Abrevaya, Dan Kovenock, James C. Moore, Roger B. Nelsen, and three anonymous referees for very helpful comments. A version of this paper was presented at the 2005 Midwest Economic Theory Meetings. This paper is based on the first chapter of my Ph.D. dissertation     

基于演化博弈的和谐社会构建模型分析

经济学在社会科学中的主导性地位决定了经济和谐是和谐社会构建的基础。以"理性经济人"假设为基础的正统经济理论与和谐社会的本质内容存在着一定程度的差异性,因而不能够为和谐社会的存在性构建起科学的理论体系,而行为经济学为和谐社会的实现提供了现实性的理论依据。互惠性偏好是行为经济学的基础性假设之一,基于互惠性偏好的个体行为博弈可以改善博弈双方的经济利益,从而为演化博弈环境下群体经济行为从自利型向互惠型的演化创造了条件,最终为经济学视角下和谐社会微观经济理论体系的构建提供了坚实的理论基础。     

Walrasian analysis via two-player games

We associate to any pure exchange economy a game with only two players, regardless of the number of consumers. In this two-player game, each player represents a different role of the society, formed by all the individuals in the economy. Player 1 selects feasible allocations trying to make Pareto improvements. Player 2 chooses an alternative from the wider range of allocations that are feasible in the sense of Aubin. The set of Nash equilibria of our game is non-empty and our main result provides a characterization of Walrasian equilibria allocations as strong Nash equilibria of the associated society game.     

Do people make strategic commitments? Experimental evidence on strategic information avoidance

Game theory predicts that players make strategic commitments that may appear counter-intuitive. We conducted an experiment to see if people make a counter-intuitive but strategically optimal decision to avoid information. The experiment is based on a sequential Nash demand game in which a responding player can commit ahead of the game not to see what a proposing player demanded. Our data show that subjects do, but only after substantial time, learn to make the optimal strategic commitment. We find only weak evidence of physical timing effects.