Cooperative Games

Raghavan DMS 9704951合作博弈国家科学基金会摘要该提案解决了合作和非合作动态博弈的算法问题。合作博弈：如何在合资企业的受益者之间公平分配共同成本是一个普遍存在于私营企业和公共企业中的基本问题。尽管成本会计师和从业者一直坚持少数几种成本分配做法，但这些程序正受到研究人员的质疑，尤其是博弈论者，他们希望这些程序公平、公平，并反映出决策者在指导行动过程中的权力和影响力。合作博弈理论就是针对这些问题提出的。直到最近，博弈论者一直在提出许多解决方案，但没有任何有效的求解技术来解决这些问题。通常，许多实际的成本分配问题和利润分享问题可以被建模为博弈，其本质联盟仅随着参与者集合的大小而以多项式增长。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。随机博弈：在随机博弈领域，目标是研究有限和任意状态空间中限制平均收益的非零和博弈，并寻找相关和纳什均衡。与零和博弈不同，非零和结构随机博弈在限制平均收益时可能不具有甚至是epsilon平稳的纳什均衡。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是这样。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，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，法官根据个别案件作出的临时但直观的上诉决定，可以用合作博弈论解决方案的量化方法来支持。航空公司价格战的战略行为、税务机关的逃税审计、汽车制造业的竞争都可以用随机博弈论的方法和模型来分析。由有效的计算算法支持的解决方案对于博弈论在现实生活中的应用是至关重要的。

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.