Collaborative Research: New Algorithms for Computing Equilibria of Stochastic Games

本研究侧重于动态战略行为模型，在该模型中，双方(个人、国家、公司、机构)在长期内反复互动，并做出对环境有持续影响的决策。PI正在开发算法来模拟行为，在这种行为中，每一方都对其他人的行为有一致的信念，并在给定这些信念的情况下最大化自己的福利。这些计算方法可以广泛应用于经济学的各个领域，也可以应用于国际关系和进化生物学等其他学科。具体地说，PI研究了具有几何折扣和随机状态变量的无限重复博弈的纯策略子博弈完美均衡。状态变量决定了代理人在博弈的每个阶段可以采取的行动集以及由此产生的收益。根据玩家采取的行动，状态以马尔可夫链的形式演变。研究的目标是开发算法来计算参与者在每个状态开始的子博弈完美均衡中可以获得的贴现收益。PI还将开发和分发实现算法的软件包。

This research focuses on models of dynamic strategic behavior, in which two parties (individuals, nations, corporations, agencies) interact repeatedly over a long horizon and make decisions that have a persistent impact on the environment. The PIs are developing algorithms to simulate behavior in which each party has consistent beliefs about how others will behave and is maximizing their own welfare given those beliefs. These computational methods can be applied to a wide range of models that are used in various fields of economics, as well as in other disciplines such as international relations and evolutionary biology.More specifically, the PIs study the pure strategy subgame perfect equilibria of infinitely repeated games with geometric discounting and a stochastic state variable. The state variable determines the set of actions that can be taken by the agents in each period of the game and the resultant payoffs. Conditional on the actions taken by the players, the state evolves as a Markov chain. The objective of the research is to develop algorithms for computing the discounted payoffs that players can obtain in subgame perfect equilibria starting in each state. The PIs will also develop and distribute software packages that implement the algorithms.