Deterministic multi-player Dynkin games

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff.We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than 1.We prove that a subgame-perfect ε-equilibrium in Markovian strategies exists. If the game is not degenerate this ε-equilibrium is actually in pure strategies.     

Weakly balanced contributions and the weighted Shapley values

We provide a concise characterization of the class of positively weighted Shapley values by three properties, two standard properties, efficiency and marginality, and a relaxation of the balanced contributions property called the weak balanced contributions property. Balanced contributions: the amount one player gains or loses when another player leaves the game equals the amount the latter player gains or loses when the former player leaves the game. Weakly balanced contributions: the direction (sign) of the change of one player’s payoff when another player leaves the game equals the direction (sign) of the change of the latter player’s payoff when the former player leaves the game. Given this characterization, the symmetric Shapley value can be “extracted”from the class of positively weighted Shapley values by either replacing the weak balanced contributions property with the standard symmetry property or by strengthening the former into the balanced contributions property.     

Learning games

This paper presents a model of learning about a game. Players initially have little knowledge about the game. Through playing the same game repeatedly, each player not only learns which action to choose but also constructs a personal view of the game. The model is studied using a hybrid payoff matrix of the prisoner's dilemma and coordination games. Results of computer simulations show that (1) when all the players are slow at learning the game, they have only a partial understanding of the game, but might enjoy higher payoffs than in cases with full or no understanding of the game; (2) when one player is quick in learning the game, that player obtains a higher payoff than the others. However, all can receive lower payoffs than in the case in which all players are slow learners.     

Coalitional games with veto players: Consistency, monotonicity and Nash outcomes

Following Dagan et al. [Dagan, N., Volij, O., Serrano, R. (1997). A non-cooperative view on consistent bankruptcy rules, Games Econ. Behav. 18, 55–72], we construct an extensive form game for veto-balanced TU games in which a veto player is the proposer and the other players are responders. The set of Nash outcomes of this extensive form game is described, and compared to solutions of TU games such as the nucleolus, kernel and egalitarian core. We find necessary and sufficient conditions under which the nucleolus of the game is a Nash outcome.     

网络游戏品质对玩家忠诚度的影响——沉浸体验的中介效应

中国网络游戏市场保持高速增长的势态，吸引了大量的竞争者进入这个行业。面对竞争，如何吸引玩家、保持玩家忠诚度己经成为网络游戏运营商最关心的问题。本文在回顾相关文献的基础上提出了研究假设，并通过网络调查方法收集数据，最后，通过回归分析验证假设，研究发现：网络游戏品质对玩家忠诚度有直接影响，同时有部分影响效应是通过沉浸体验间接实现的；在网络游戏品质、沉浸体验、运营商的可信度三者中，沉浸体验对网络游戏忠诚度的影响效应最大。     

Buying cooperation in an asymmetric environmental differential game

We consider a two-player asymmetric differential game of pollution control. One player is non-vulnerable to pollution, or unwilling to consider damages when choosing her production policy in a non-cooperative game. We characterize the feedback-Nash equilibrium and the cooperative solution. We establish conditions under which the vulnerable player can buy the cooperation of the non-vulnerable player to control her emissions. We further use the Nash bargaining solution to allocate the total cooperative dividend between the two players and propose a time-consistent decomposition overtime of the total payoff.     

篮球进攻队员假动作技术分析

进攻队员假动作在篮球比赛攻防对抗中产生,是完成篮球技战术必不可少的动作方法。文章通过对进攻队员假动作进行分类,探讨在其比赛中的具体运用,提出进攻假动作应具备的条件和注意的问题,为篮球教学与训练提供参考。     

矩阵对策中混合对策问题的数学模型及lingo求解

对策论是研究对抗问题的理论与方法。矩阵对策是最常见,也是最重要的对策。通过对矩阵对策中混合对策问题的分析,建立了局中人最优策略的线性规划模型,并给出了模型的lingo求解方法。     

Learning a population distribution

This paper introduces a dynamic Bayesian game with an unknown population distribution. Players do not know the true population distribution and assess it based on their private observations using Bayes׳ rule. First, we show the existence and characterization of an equilibrium in which each player׳s strategy is a function not only of the player׳s type but also of experience. Second, we show that each player׳s initial belief about the population distribution converges almost surely to a “correct” belief.     

Discussie bijdrage

An analysis is given of the character of games of chance and games of skill. It is shown that every game is influenced by stochastic effects. Whether a game should be classified as a game of pure skill or as a game of chance depends on the rules of the game, on the evaluation of the outcomes of the game and on the possibilities the player has by applying his skill to cope with the random effects of the particular game situations.     

On the formation of coalitions in infinite player games

This paper investigates the problem of determining when an infinite player game can be partitioned into countably many stable coalitions. An example is given of asuperadditive scalar measure game for which this is not possible and several positive results are presented. The final section of the paper takes up the problem of when a process of successive coalition formation can eventually lead to a division of all available resources. A theorem and a counterexample are presented for countable player games and the positive result is applied to the vector measure games considered earlier in the paper.     

Bayesian Nash equilibrium and variational inequalities

This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.     

Strategic behavior in non-atomic games

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

Equilibria in a class of aggregative location games

Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.     

重复占优策略博弈在团队培训中的应用及启发——基于一个体验式训练项目的思考

博弈论是研究决策主体行为发生直接相互作用时的决策以及这种决策的均衡问题的一门科学。占优策略博弈是指存在始终优于对方反应的博弈,占优策略博弈可能存在合作解和非合作解。在对一个基于重复非合作占优策略博弈而设计的培训项目进行分析的基础上,探讨有限重复占优策略博弈的非合作解和合作解的差别,并借鉴这种差别对于团队管理的启发,在管理实践中充分考虑主体的充分理性和最大化偏好,以团队利益为前提,尊重个体合理利益,设计科学的激励约束制度,促成一个良性的竞争合作团队氛围。     

探讨足球运动员的抢截球意识

足球比赛是一项整体的对抗项目,需要运动员不但具备良好的身体素质和团队的紧密配合,更需要每个人都有过硬的技术本领,同时要求运动员具有优良的足球意识。文章通过对足球比赛中的抢截球技术结构和特点的分析,阐明了如何培养运动员具备抢截球意识并在比赛中合理的运用该技术,从而提高比赛的获胜几率。     

A note on the evaluation of information in zero-sum repeated games

Two players play a zero-sum repeated game with incomplete information. Before the game starts one player receives a private signal that depends on the realized state of nature. The rules that govern the choice of the signal are determined by the information structure of the game. Different information structures induce different values. The value-of-information function of a game associates every information structure with the value it induces. We characterize those functions that are value-of-information functions for some zero-sum repeated game with incomplete information.     

Majority rule with dollar voting

Consider a majority game in which each player's voting strength is equal to the player's payoff. In this game, wealth is the only source of power, and any coalition with more than half the wealth can take everything. Only extreme concentrations of wealth, in which one player owns everything or two players each own half the total wealth are undominated, and thus constitute the core. However, the stable set (von Neumann-Morgenstern solution) is significantly larger. Allocations in which one player has half the wealth, or which divide the total wealth equally among a number of players equal to a power of two, constitute the unique stable set. The stable set thus provides a formal model of an endogenous balance of power.     

卡通物理游戏玩家心理体验研究——以《愤怒的小鸟》为例

近年来,卡通物理游戏《愤怒的小鸟》在全球范围内广受欢迎,本实验以该游戏为实验对象,通过主观体验法和面部表情法对玩家的情绪进行了测量,验证了游戏具有休闲、益智的作用,同时发现,游戏中物理机制的运用为玩家带来惊奇感和挑战感,也带给玩家一定的挫败感。