Cooperative Games

Raghavan DMS 9704951合作游戏NSF摘要 该建议解决了合作和非合作动态博弈的算法问题。 合作游戏：如何在合资企业的受益人之间公平地分配共同成本，是一个普遍存在于私营企业和公营企业中的基本问题。虽然成本会计师和从业人员坚持一些成本分配的方法，但这些程序受到研究人员的质疑，特别是游戏理论家，他们希望程序公平，公正，反映决策者在指导行动过程中的权力和影响力。 合作博弈论正好解决了这些问题。 直到最近，博弈理论家一直在提出许多解决方案，但没有任何有效的解决方案技术来解决它们。 通常，许多实际的成本分配问题和利润分配问题可以建模为博弈，其基本联盟仅随参与者集的大小多项式增长。 该项目旨在开发高效的算法，以求解许多模型的核仁和沙普利值。 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甚至不可能具有双稳态纳什均衡。甚至更重要的是开发所有出租车定位纳什均衡，至少对于结构化的随机游戏。 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，精确分配工业污染的成本或罚款将有可能与合作博弈论的解决方案。在民事诉讼和离婚诉讼中，特别但直觉上上诉的决定 法官根据个别案件作出的决定，可以通过使用合作博弈论解决办法的量化方法得到支持。 航空公司的价格战战略行为、税务机关的逃税稽查行为、汽车制造业的竞争行为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博弈论应用于真实的生活问题是必不可少的。

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.