A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

基于深度和广度的博弈学习模型

信息和理性在博弈学习中具有重要作用.博弈历史反映了博弈参与者的策略选择倾向,在一定程度上预示了博弈主体的行动规律.从主题、事件类型以及事件概率三个方面来描述历史的概念.由于博弈主体是有限理性人,他不能掌握全部的历史,也不能掌握全部博弈主体的博弈信息.深度就是指在时间轴上的纵向研究尺度.广度是指在每一期的博弈中,博弈者所能学习的对象的范围.由于博弈学习者的理性差异,他们在学习中往往采用不同的学习深度和广度.同样,也正是由于学习差异性的存在,才使得整个群体社会得以多样发展、共同繁荣.     

Transversality of the Shapley value

A few applications of the Shapley value are described. The main choice criterion is to look at quite diversified fields, to appreciate how wide is the terrain that has been explored and colonized using this and related tools. The title is inspired by a tutorial that one of the authors planned to deliver at the 7th meeting on Game Theory and Practice (Montreal, 2007), but was unable to do it for personal reasons. Thanks to Georges Zaccour whose invitation sparked the present survey.     

On implementation via demand commitment games

A simple version of the Demand Commitment Game is shown to implement the Shapley value as the unique subgame perfect equilibrium outcome for any n-person characteristic function game. This improves upon previous models devoted to this implementation problem in terms of one or more of the following: a) the range of characteristic function games addressed, b) the simplicity of the underlying noncooperative game (it is a finite horizon game where individuals make demands and form coalitions rather than make comprehensive allocation proposals and c) the general acceptability of the noncooperative equilibrium concept. A complete characterization of an equilibrium strategy generating the Shapley value outcomes is provided. Furthermore, for 3 player games, it is shown that the Demand Commitment Game can implement the core for games which need not be convex but have cores with nonempty interiors. Received March 1995/Final version February 1997     

航空客票销售渠道的博弈研究

为研究航空公司和机票代理人之间的博弈过程,在分析航空公司和代理人在不同策略下各自的得益基础上,建立了静态博弈模型,并运用演化博弈理论对航空公司的机票直销策略选择与代理人策略选择的互动机制进行了分析.博弈分析结果显示,航空公司和代理商在以下情况时存在进化稳定策略:当代理销售成本高于直销成本时,航空公司会加大直销力度;而航空公司的直销策略比较强势时,当代理商抵制策略的概率会大大增加;航空公司缓和推进直销时,代理会也会采取缓和策略.     

A dynamic approach to the Shapley value based on associated games

We propose a dynamic process leading to the Shapley value of TU games or any solution satisfying Inessential Game (IG) and Continuity (CONT), based on a modified version of Hamiache's notion of an associated game. The authors are very grateful to William Thomson and two anonymous referees for valuable comments which much improve the paper. They provide better statements and proofs of several major results than the original ones.     

排污监察博弈与策略选择

针对当前排污监察的现状,提出了环境监察部门聘用环境监察员与排污单位之间的监察与反监察博弈观点.就监察员不同的收入结构,分别建立了监察排污静态博弈模型和查处排污动态博弈模型,探讨了监察员固定收入结构与罚款提成收入结构对那什均衡的影响,得出了监察员与排污单位的期望得益.通过分析有关参数,提出了排污监察中信息不对称问题的解决方法,探求了环境监察部门的策略选择.     

博弈论在打假中的运用

运用博弈论的方法对个人打假、政府打假及举报制度进行假设、建模和分析 ,结果显示 :无论在个人打假中 ,还是在政府打假中 ,单纯依靠经济手段显然无法达到预期效果 ,而应该同时运用行政手段、法律手段、精神手段等 ,同时为了减少信息不对称对打假者的影响 ,有必要建立举报制度 .我们期望我们的分析结果能为有效开展打假活动提供一种思路 .     

Game Theory applied to gene expression analysis

This is a summary of the author’s Ph.D. thesis supervised by Fioravante Patrone and Stefano Bonassi and defended on 25 May 2006 at the Università degli Studi di Genova. The thesis in written in English and a copy is available from the author upon request. This work deals with the discussion and the application of a methodology based on Game Theory for the analysis of gene expression data. Nowadays, microarray technology is available for taking “pictures” of gene expressions. Within a single experiment of this sophisticated technology, the level of expression of thousands of genes can be estimated in a sample of cells under given conditions. Roughly speaking, the starting point is the observation of a “picture” of gene expressions in a sample of cells under a biological condition of interest, for example a tumor. Then, Game Theory plays a primary role to quantitatively evaluate the relevance of each gene in regulating or provoking the condition of interest, taking into account the observed relationships in all subgroups of genes.      

博弈训练及其对均衡的影响

训练和学习是博弈中的一对统一体.博弈学习是通过降低博弈语境的不确定性来提高博弈收益,而博弈训练则是针对博弈学习的一种策略.训练者通过可信的信号传递来影响对手的博弈学习结果,改变受训者的信念,从而提高博弈收益.博弈训练的目标可分为事实隐藏和事实揭示.在使用博弈训练时,应遵循"利已、利他、可信、可辩"的原则,从全局的角度审视整个博弈环境,选择利己利他的训练方法,最终取得较优的训练效果.     

失业保险制度的博弈分析

完善失业保险制度是解决我国失业问题的有效手段。在失业保险制度的制定中。失业保险金支付水平的确定是关键。本文从博弈的角度建立模型对此问题进行了分析，并据此对失业问题的解决提出一些建议。     

PREFERENCE AND EVOLUTION IN THE ITERATED PRISONER＇S DILEMMA

Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner＇s dilemma. In this article, a preference parameter k was introduced in the payoff matrix, wherein the value of k denotes the player＇s degree of egoism and altruism （preference）. Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how preference influences the evolutionary equilibrium and behaviors of players. The authors get the general results： egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.     

Minimal large sets for cooperative games

We analyze the concept of large set for a coalitional game v introduced by Martínez-de-Albéniz and Rafels (Int. J. Game Theory 33(1):107–114, 2004). We give some examples and identify some of these sets. The existence of such sets for any game is proved, and several properties of largeness are provided. We focus on the minimality of such sets and prove its existence using Zorn’s lemma. Institutional support from research grants (Generalitat de Catalunya) 2005SGR00984 and (Spanish Government and FEDER) SEJ2005-02443/ECON is gratefully acknowledged, and the support of the Barcelona Economics Program of CREA.     

三级供应链合作利润博弈与分配机制构建

基于变形需求函数建立了多向主从式三级供应链下游成员合作利润博弈模型,运用Stackelberg博弈法求解,对成员及渠道利润随合作关系程度变化进行深入的经济分析;构建了具有理性、转移性、协商性的供应链下游合作利润分配机制定量模型,其由合作利润结构性分配和合作利润运行性分配组成,阐明了之间的互动关系与内在运行方式,得出当合作关系程度高于2/3时才进行合作利润运行性分配的结论,且对分配机制的内在运行方式进行了数学解析。     

A new approach to the core and Weber set of multichoice games

Multichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. We show that the precore coincides with the definition proposed by Faigle, and that the set of imputations may be unbounded, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex compact set. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their coincidence in the convex case remain valid. A last section makes a comparison with the core defined by Van den Nouweland et al. A preliminary and short version of this paper has been presented at 4th Logic, Game Theory and Social Choice meeting, Caen, France, June 2005 (Xie and Grabisch 2005).     

Hedging of game options in discrete markets with transaction costs

Game options introduced in [10] in 2000 were studied, by now, mostly in frictionless both complete and incomplete markets. In complete markets the fair price of a game option coincides with the value of an appropriate Dynkin's game, whereas in markets with friction and in incomplete ones there is a range of arbitrage free prices and superhedging comes into the picture. Here we consider game options in general discrete time markets with transaction costs and construct backward and forward induction algorithms for the computation of their prices and superhedging strategies from both seller's (upper arbitrage free price) and buyer's (lower arbitrage free price) points of view extending to the game options case most of the results from [12].     

PREFERENCE AND EVOLUTION IN THE ITERATED PRISONER''S DILEMMA

Game theory is extensively used to study strategy-making and actions of play-ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner's dilemma. In this article, a pref-erence parameter k was introduced in the payoff matrix, wherein the value of k denotes the player's degree of egoism and altruism (preference). Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how prefer-ence influences the evolutionary equilibrium and behaviors of players. The authors get the general results: egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.     

Computing power indices: Multilinear extensions and new characterizations

Johnston [Johnston, R.J., 1978. On the measurement of power: some reactions to Laver. Environment and Planning A 10, 907–914], Deegan and Packel [Deegan, J., Packel, E.W., 1979. A new index of power for simple n-person games. International Journal of Game Theory 7, 113–123], and Holler [Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262–271] proposed three power indices for simple games: Johnston index, Deegan–Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.     

Complex adaptive systems and game theory: An unlikely union

A Complex Adaptive System is a collection of autonomous, heterogeneous agents, whose behavior is defined with a limited number of rules. A Game Theory is a mathematical construct that assumes a small number of rational players who have a limited number of actions or strategies available to them. The CAS method has the potential to alleviate some of the shortcomings of GT. On the other hand, CAS researchers are always looking for a realistic way to define interactions among agents. GT offers an attractive option for defining the rules of such interactions in a way that is both potentially consistent with observed real‐world behavior and subject to mathematical interpretation. This article reports on the results of an effort to build a CAS system that utilizes GT for determining the actions of individual agents. © 2009 Wiley Periodicals, Inc. Complexity, 16,24–42, 2010     

Additive stable solutions on perfect cones of cooperative games

Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described. Received: December 2001/Revised: July 2002 RID="*" ID="*"  This note contains the new results, which were presented by the first author in an invited lecture at the XIV Italian Meeting on Game Theory and Applications in Ischia, July 2001. The lecture was dedicated to Irinel Dragan on the occasion of his seventieth birthday.