Algorithms for Computing the Equilibrium Payoff Sets of Dynamic Games with Perfect Monitoring

该奖项资助计算战略均衡的新方法和算法的研究。许多经济情况涉及代理人之间的重复相互作用。这些重复的战略互动也出现在社会科学的其他领域，包括政治和国际关系。这种互动的最基本的形式化是重复的博弈。这提供了一个数学框架，其中正在进行的互动可以被量化，并且可以以一致的方式同时评估诸如短视的作弊诱惑、参与者的数量、参与者在计划他们的行动和反应时可获得的信息、当前与未来关切的迫切性等因素的影响。在这项工作中，一个不可或缺的工具是均衡的概念。然而，除了在最微不足道的公式中，实际计算可能的均衡是一项困难的任务。即使在相对简单的程式化环境中，社会科学家也很难调查潜在条件变化的影响(如果某些投入的价格发生变化会发生什么，如果制定法规限制公司掌握的关于竞争对手的信息，如果贸易关税改变，等等)。这个项目的目的就是解决这个计算问题。Pi和他的团队试图开发出使用标准笔记本电脑快速得出答案的方法。初步结果包括一些很有前途的新方法。总体目标是将这些结果扩展到其他重复交互的重要类别，从而为学生、研究人员和从业者提供重要的新工具，以促进他们对正在进行的交互的分析。

This award funds research in new methods and algorithms for computing strategic equilibria. Many economic situations involve repeated interactions between agents. These repeated strategic interactions also appear in other realms of social science including politics and international relations.The most basic formalization of such interactions is a repeated game. This provides a mathematical framework in which ongoing interactions can be quantified and the impact of such factors as the myopic temptations to cheat, the number of participants, the information available to participants when they plan their moves and responses, the compellingness of present versus future concerns, and so on, can be simultaneously assessed in a coherent way. An indispensable tool in this endeavor is the notion of equilibrium.However, except in the most trivial formulations, the actual computation of possible equilibria is a difficult task. Even in relatively simple stylized settings it is difficult for the social scientist to investigate the impact of changes in underlying conditions (what happens if the price of certain inputs changes, what if regulations are put in place which limit the information firms have about their rivals, what if trade tariffs are altered, and so on). This project aims squarely at this computational problem.The PI and his team seek to develop methods that yield answers rapidly using standard laptop computers. Preliminary results include a number of promising new methods. The overall goal is to extend these results to other important classes of repeated interactions and thereby provide students, researchers and practitioners, important new tools to facilitate their analysis of ongoing interactions.