Collaborative Research: New Algorithms for Computing Equilibria of Stochastic Games

本研究的重点是动态战略行为的模型，其中双方（个人，国家，公司，机构）在很长一段时间内反复互动，并做出对环境产生持久影响的决策。PI正在开发算法来模拟行为，其中每一方都对其他人的行为有一致的信念，并在这些信念的基础上最大化自己的福利。这些计算方法可以应用于各种经济学领域以及国际关系和进化生物学等其他学科中使用的广泛模型。更具体地说，PI研究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。状态变量决定了在游戏的每个阶段中代理人可以采取的一组行动以及由此产生的收益。在参与者采取行动的条件下，状态演化为马尔可夫链。研究的目的是开发算法，用于计算的折扣收益，球员可以获得在子博弈完美均衡开始在每个国家。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.