Collaborative Research: New Algorithms for Computing Equilibria of Stochastic Games

本研究的重点是动态战略行为模型，其中双方（个人，国家，公司，机构）在很长一段时间内反复互动，并做出对环境有持续影响的决策。pi正在开发算法来模拟这样的行为：每一方都对他人的行为有一致的信念，并根据这些信念最大化自己的福利。这些计算方法可以应用于广泛的模型，这些模型用于经济学的各个领域，以及其他学科，如国际关系和进化生物学。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。状态变量决定了代理在博弈的每个阶段可以采取的一系列行动以及由此产生的收益。根据参与者采取的行动，状态演变为马尔可夫链。研究的目的是开发计算玩家在每个状态下的子博弈完全均衡中可以获得的折现收益的算法。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.