Cooperative Games

摘要该方案解决了合作和非合作动态博弈的算法问题。合作博弈：合营企业的共同成本如何在各受益者之间公平分配是一个普遍存在于私营企业和公共企业中的基本问题。虽然成本会计师和从业者坚持一些成本分配实践，但这些程序正在受到研究人员，特别是博弈论理论家的质疑，他们希望这些程序是公平的，公平的，并反映决策者在指导行动过程中的权力和影响力。合作博弈论恰恰解决了这些问题。直到最近，博弈论学者们提出了许多解决方案，但没有任何有效的解决方法来解决这些问题。通常，许多实际的成本分配问题和利润分享问题可以建模为博弈，其基本联盟仅随着参与者集的大小而多项式地增长。该项目旨在开发有效的算法，以解决许多模型的核仁和Shapley值。随机对策：在随机对策领域中，目的是研究有限和任意状态空间中限制平均收益的非零和对策，并寻找相关的纳什均衡。与零和博弈不同，非零和结构化随机博弈在限制平均收益时可能甚至不具有平稳纳什均衡。更重要的是开发算法来定位纳什均衡，至少对于结构化随机博弈。越来越多的行业和组织，甚至联邦资助机构都希望衡量共同努力的贡献。在环境问题中，通过合作博弈论的解决方案，可以准确地分配工业污染的成本或罚款。在民事诉讼和离婚诉讼中，法官根据个案作出的临时但直观的上诉判决可以通过合作博弈论解决方案的量化方法来支持。航空公司的价格战战略行为、税务机关的逃税和审计行为、汽车制造业的竞争都可以用随机博弈论的方法和模型进行分析。由有效的计算算法支持的解决方案对于将博弈论应用于现实生活问题至关重要。

Raghavan DMS 9704951 Cooperative Games NSF Abstract The proposal addresses algorithmic problems of cooperative and noncooperative dynamic games. Cooperative Games: How should the common costs be allocated fairly among the benefeciaries of a joint enterprise is a basic problem widespread in both private firms and in public enterprises. While cost accountants and practitioners have stuck to a few cost allocation practises , these procedures are being questioned by researchers especially by game theorists who would like the procedures to be fair, equitable and reflective of the decision makers power and influence in steering the course of actions. Cooperative game theory addresses precisely these issues. Till recently game theorists have been proposing many solutions without any efficient solution technique to solve for them. Often many practical cost allocation problems and profit sharing problems can be modeled as games whose essential coalitions grow only polynomially with he size of the player set. The project is aimed at developing efficient algorithms that will solve for the nucleolus and the Shapley value for many models. Stochastic games: In the area of stochastic games the aim is to study non-zero sum games in limiting average payoffs for finite and arbitrary state spaces and to look for correlated and Nash equilibria. Unlike zero-sum games, non-zero sum structured stochastic games may not possess even epsilon -stationary Nash equilibria in limiting average payoff. Even more important is to develop allgorithms to locate Nash equilibria, at least for structured stochastic games. Increasingly industries and organizations and even federal funding agencies want to measure the contributions of joint efforts. In environmental problems accurately allocating costs or fines for industrial pollutions will be possible with cooperative game theoretic solutions. In civil law suits and in divorce law suits, the ad hoc but intuitively appealing decisions by judges based on the individual cases can be backed up by quantifiable approaches using cooperative game theoretic solutions. The strategic behavior of price wars by airlines, the tax evasion and auditing by tax offices, auto manufacturing competitions can all be analyzed using stochastic game theoretic methods and models. The solutions backed up by efficient algorithms for computation is essential for the applicability of Game Theory to real life problems.