Folk theorems for the observable implications of repeated games

The fact that infinitely repeated games have many different equilibrium outcomes is known as the Folk Theorem. Previous versions of the Folk Theorem have characterized only the payoffs of the game. This paper shows that over a finite portion of an infinitely repeated game, the concept of perfect equilibrium imposes virtually no restrictions on observable behavior. The Prisoner's Dilemma is presented as an example and discussed in detail.I would like to thank an anonymous referee, Sushil Bikhchandani, David Hirshleifer, David Levine, Thomas Voss, and participants in the UCLA Game Theory Seminar for helpful comments.     

Game Trees For Decision Analysis

Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the game tree representation and solution technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks.     

Resolving the Trust Predicament: A Quantum Game-theoretic Approach

Developing a good theoretical understanding of the role of trust in IR (such as in the events leading to the end of the Cold War) is still an open problem. Most game-theoretic studies of trust do not go beyond the limitations of an (ontologically) individualistic paradigm, thus assuming a pre-defined set of individual strategies. Yet, it is a fact that the predicament of collective trust is empirically resolved in many situations. This paper suggests a new game-theoretic approach—Quantum Game Theory (QGT)—to understand and explain how the predicament of trust is resolved. In a quantum game of trust the actors play the game by simultaneously collectively reconstructing the strategic environment in such a way as to become mutually strategically entangled. Quantum strategic entanglement allows trust to emerge between the two actors without assuming a need for signaling, prior “contract” type of arrangement, or any form of third-party communication. The paper develops and solves such a model of quantum game of trust     

作为偶缘性的游戏--伽达默尔游戏观解析

伽达默尔的游戏概念与偶缘性联系密切。偶缘性首先从文本阐释中表现出来 ,是对不同阐释境域的关注。游戏将偶缘性演化为一种客体性的边缘状态 ,抽除了游戏中的主体因素 ,从伽达默尔阐释学的游戏概念 ,可以演化到后现代主义无主体的观念。实际上 ,正是通过游戏概念 ,阐释学成为后现代主义的入口     

博弈·平衡·控制——中国传统法和谐价值解读

对于中国传统法的和谐价值的认识,可以将博弈、平衡、控制三个层面作为解读新法。博弈是传统法所面对的各种矛盾与冲突,这是传统法具有和谐价值的成因;平衡是传统法在博弈中解决矛盾与冲突的手段,这是传统法和谐价值的实际样态;控制是传统法所追求的目标价值,是经过博弈、平衡后的一种政治期许的实际效果。立足当今和谐社会与法治建设,以扬弃的态度解读传统法,这是传统法和谐价值的现代意义所在。     

结合案例分析游戏在儿童社会工作个案辅导中的运用

游戏是儿童表达想法和感受的重要媒介,在儿童的成长生活中占据着非常重要的地位。社会工作实务辅导有必要重视游戏对儿童的意义,将之融合进实务辅导之中。但目前我国社会工作专业领域中尚缺乏相关的理论和实践经验。本文结合自身实务经验,提出专业社工可在三个层面借鉴西方儿童游戏治疗理论的经验,指导个案辅导中的游戏运用,以期可以促进儿童个案社会工作实务的新发展。     

结合案例分析游戏在儿童社会工作个案辅导中的运用

游戏是儿童表达想法和感受的重要媒介,在儿童的成长生活中占据着非常重要的地位。社会工作实务辅导有必要重视游戏对儿童的意义,将之融合进实务辅导之中。但目前我国社会工作专业领域中尚缺乏相关的理论和实践经验。本文结合自身实务经验,提出专业社工可在三个层面借鉴西方儿童游戏治疗理论的经验,指导个案辅导中的游戏运用,以期可以促进儿童个案社会工作实务的新发展。     

Endogenizing the order of moves in matrix games

Players often have flexibility in when they move and thus whether a game is played simultaneously or sequentially may be endogenously determined. For 2 × 2 games, we analyze this using an extended game. In a stage prior to actual play, players choose in which of two periods to move. A player moving at the first opportunity knows when his opponent will move. A player moving at the second turn learns the first mover's action. If both select the same turn, they play a simultaneous move subgame.If both players have dominant strategies in the basic game, equilibrium payoffs in the basic and extended games are identical. If only one player has a dominant strategy or if the unique equilibrium in the basic game is in mixed strategies, then the extended game equilibrium payoffs differ if and only if some pair of pure strategies Pareto dominates the basic game simultaneous play payoffs. If so, sequential play attains the Pareto dominating payoffs. The mixed strategy equilibrium occurs only when it is not Pareto dominated by some pair of pure strategies.In an alternative extended game, players cannot observe delay by opponents at the first turn. Results for 2×2 games are essentially the same as with observable delay, differing only when only one player has a dominant strategy.     

中美在南海问题上的外交博弈及其路径选择

中美围绕南海问题的较量类似"囚徒困境"博弈。由于利益冲突、缺乏互信以及联盟因素,中美在南海问题上的合作出现困境。如果上述问题得不到解决,该博弈就有可能转化为"谁是懦夫"博弈。南海问题的前景不容乐观。要解决中美南海博弈的外交困境,需要采取有效措施建立互信,并进行利益协调。     

Spatial externalities and risk in interdependent security games

Individuals regularly invest in self-protection to reduce the risk of an adverse event. The effectiveness of self-protection often depends on the actions of other economic agents and can be modeled as a stochastic coordination game with multiple Pareto-ranked equilibria. We use lab experiments to analyze tacit coordination in stochastic games with two kinds of interdependencies in payoffs: “non-spatial” in which every agent’s action has an impact on the risk faced by every other agent, and “spatial” in which agents only impact the risk faced by their immediate neighbors. We also compare behavior in the stochastic games to deterministic versions of the same games. We find that coordination on the payoff-dominant equilibrium is significantly easier in the deterministic games than in the stochastic games and that spatial interdependencies lead to greater levels of coordination in the deterministic game but not in the stochastic game. The difficulty with coordination observed in the stochastic games has important implications for many real-world examples of interdependent security and also illustrates the importance of not relying on data from deterministic experiments to analyze behavior in settings with risk.     

On social utility payoffs in games: a methodological comparison between Behavioural and Rational Game Theory

Are the recent findings of Behavioural Game Theory (BGT) on unselfish behaviours relevant for the progress of game theory? Is the methodology of BGT, centred around the attempt to study theoretically players’ utility functions in the light of the feedback that experimental evidence can produce on the theory, a satisfactory one? Or is the creation of various types of ‘social preferences’ just wasteful tinkering? This article compares BGT with the methodology of Rational Game Theory (RGT). BGT is viewed as a more promising and constructive approach, with regard to the relationship between experimental data and theoretical modelling. However, I also argue that today RGT and BGT are closer to one another than often thought.     

Unilateral Family Therapy with the Spouses of Alcoholics

The design and development of a unilateral family therapy for alcohol abuse is reported from a study of 25 spouses. Subjects were recruited from newspaper advertisements in which spouses of partners who had a drinking problem and refused to enter treatment were solicited to receive free professional assistance. Treatment embraced treatment orientation, clinical assessment, spouse role induction, abuser-directed interventions, spouse-directed interventions, and maintenance. Results indicated that the unilateral treatment program can be implemented, the spouses of uncooperative alcohol abusers can be assisted to function as a positive rehabilitative influence with their alcoholic mates, and that important positive gains for the abusers and spouses can be achieved. It is concluded that the unilateral approach should be experimentally evaluated and, if results are favorable, applied with other populations.     

日本游戏批评思想地图——兼论游戏批评的向度

游戏批评包含不少向度,其中有两个向度常被运用,即指向文艺鉴赏的第一向度,与指向超越性问题意识的第二向度。日本的游戏批评起步于20世纪80年代,这些批评对当时流行的宇宙类游戏给予了高度关注,并从游戏文本中解读日本社会的深层构造。之后的游戏批评,把注意力转向游戏中普遍存在的故事性,批评的向度也由超越性的问题意识移向文艺鉴赏,逐渐成为市场机制的一部分。2000年以后,东浩纪与大冢英志的学术论争,催生了“游戏现实主义”,成就了日本游戏批评的最高峰,游戏批评逐渐被引回学术领域。如今,在日本政府与游戏业界的协助下,日本学界正在厘清已有的游戏研究成果,并着力于游戏批评史的建构。     

Non-strict ordinal 2 × 2 games: A comprehensive computer-assisted analysis of the 726 possibilities

Game theory has provided many tools for the study of social conflict. The 2 × 2 game has been found to be a particularly useful model. This paper describes the enumeration and analysis of all 726 distinct 2 × 2 games. A computer is used to generate the complete set, and a wide variety of maximin, equilibrium and stability calculations is performed for each player for every outcome in every game. The resulting data set is of great value for both the modeling and analysis of social conflict.     

Belief formation in a signaling game without common prior: an experiment

Using belief elicitation, the paper investigates the process of belief formation and evolution in a signaling game in which a common prior is not induced. Both prior and posterior beliefs of Receivers about Senders’ types are elicited, as well as beliefs of Senders about Receivers’ strategies. In the experiment, subjects often start with diffuse uniform beliefs and update them in view of observations. However, the speed of updating is influenced by the strength of initial beliefs. An interesting result is that beliefs about the prior distribution of types are updated slower than posterior beliefs, which incorporate Senders’ strategies. In the medium run, for some specifications of game parameters, this leads to outcomes being significantly different from the outcomes of the game in which a common prior is induced. It is also shown that elicitation of beliefs does not considerably change the pattern of play in this game.     

Rule utilitarianism,rights, obligations and the theory of rational behavior

The paper first summarizes the author's decision-theoretical model of moral behavior, in order to compare the moral implications of the act-utilitarian and of the rule-utilitarian versions of utilitarian theory. This model is then applied to three voting examples. It is argued that the moral behavior of act-utilitarian individuals will have the nature of a noncooperative game, played in the extensive mode, and involving action-by-action maximization of social utility by each player. In contrast, the moral behavior of rule-utilitarian individuals will have the nature of a cooperative game, played in the normal mode, and involving a firm commitment by each player to a specific moral strategy (viz. to the strategy selected by the rule-utilitarian choice criterion) — even if some individual actions prescribed by this strategy, when considered in isolation, should fail to maximize social utility.The most important advantage that rule utilitarianism as an ethical theory has over act utilitarianism lies in its ability to give full recognition to the moral and social importance of individual rights and personal obligations. It is easy to verify that action-by-action maximization of social utility, as required by act utilitarianism, would destroy these rights and obligations. In contrast, rule utilitarianism can fully recognize the moral validity of these rights and obligations precisely because of its commitment to an overall moral strategy, independent of action-by-action social-utility maximization.The paper ends with a discussion of the voter's paradox problem. The conventional theory of rational behavior cannot avoid the paradoxical conclusion that, in any large electorate, voting is always an irrational activity because one's own individual vote is extremely unlikely to make any difference to the outcome of any election. But it can be shown that, by using the principles of rule-utilitarian theory, this paradox can easily be resolved and that, in actual fact, voting, even in large electorates, may be perfectly rational action. More generally, the example of rule utilitarianism shows what an important role the concept of a rational commitment can play in the analysis of rational behavior.     

Korean and American Children's Concepts of Adult and Peer Authority

The primary purpose of this research was to examine Korean children's concepts of authority. Children's judgments about commands of persons with varying age, social position, and knowledge were assessed. 48 subjects from the first, third, and fifth grades were presented with portrayals of persons giving children commands regarding two types of events: fighting and a game rule dispute. Subjects evaluated the legitimacy of commands and chose between different persons giving opposing commands. With regard to a command to stop fighting, subjects accepted the legitimacy of adult and peer authorities, as well as an adult without a position of authority. Subjects rejected commands that failed to prevent harm even when given by an adult authority. With regard to a game rule dispute, subjects most heavily weighted knowledge in evaluating the authority commands. The findings show that Korean children do not have a unitary orientation to adult authority, and have implications for an understanding of individuals' conceptions in the context of a cultural ideology emphasizing reverence for authority. A second study, with a group of fifth graders from the United States, was conducted to determine how the game event task or cultural influences accounted for some differences between previous findings in the U.S. and the findings with the Korean children. The second study showed that whereas the U.S. children mainly respond in ways similar to the Korean children, the U.S. children gave more priority to pragmatic considerations; the Korean children gave more priority to the attribute of the authority's knowledge.     

依势博弈：基层社会维权行为的新解释框架

基层社会的维权行为研究保持着延续性的沟通对话,但需要发展一种更为综合的解释框架来消解已有解释之间的张力。本文借用本土资源性概念“势”的含义,汲取各种解释的合理内核,基于乡镇场域的现实案例提出一种融合性的解释框架--依势博弈,包含知势、造势、借势、用势四个方面,与博弈对象的以势摆平、调解方的中庸调势处于同一维权行为系统中。依势博弈解释框架体现了维权行动的主体多元性、博弈平等性、策略权宜性、因素多样性、内容丰富性等特征,反应了中国基层社会变迁的倾向,拓展基层维权抗争的视角,体现了从官民或者说强弱维权中走向多元化利益博弈,具有更高层次的概括解释力。     

A differential approach to the repeated prisoner's dilemma

The repeated prisoner's dilemma game is converted into a differential game by assuming that the players, instead of making decisions individually for each repetition of the prisoner's dilemma game, make decisions on the ratio of cooperative and noncooperative games that they wish to play over the next few moves, and that the actual plays are then determined using this ratio and a randomizing procedure. Although it sounds like a significant departure, this assumption is probably not too different from reality.Since each player can always obtain by his own action at least the payoff which he would receive from the noncooperative-noncooperative pair of strategies, that part of the differential game which is dominated by such a dual noncooperative strategy for either player is an unlikely outcome. This dominated area can be readily computed for any game, including those with more than two players.Formal testing with empirical data was impossible because of uncertainty about the proper null hypothesis. Nevertheless, experimental results reported by Rapoport are consistent with the theory.The authors are, respectively, Graduate Research Asistant in Economics and Professor of Economics and Public Choice at Virginia Polytechnic Institute and State University.     

Learning strategic environments: an experimental study of strategy formation and transfer

I present an experiment on learning about a game in an initially unknown environment. Subjects play repeatedly simple 2 × 2 normal-form coordination games. I compare behavioral learning algorithms for different feedback information. Minimal feedback only informs about own payoffs, while additional feedback informs about own payoffs and the opponent’s choice. Results show that minimal feedback information leads to a myopic learning algorithm, while additional feedback induces non-myopic learning and increases the impulse with which players respond to payoff differences. Finally, there is evidence for a strategy transfer across games which differ only according to the relabel of actions, but not according to permutation in the payoff matrix.