Best Experienced Payoff Dynamics and Cooperative Play in Extensive Form Games

该奖项用于博弈论的研究。调查者试图开发和分析新的人口动态模型，在这种情况下，随着时间的推移，个人在战略环境中与其他人互动。该项目的第一部分考虑了这样一种情况，即当个人随机与伴侣配对时，他们对自己经历的结果做出理性反应。这里的目标是展示由此产生的动态如何导致合作行为，即使参与其中的个人知道他们只会在设定的时间内与同一个人互动。在设定的结束日期的重复关系中保持合作行为的可能性是博弈论中的一个基本问题，与许多社会科学和许多政策应用直接相关。本项目中研究的动力学可以为合作行为的持续性提供一种解释，并可能有助于我们制定支持合作的政策和制度。PI还将开发新的公共领域软件，并将演示如何使用该软件通过在线教科书/课程对游戏动力学进行建模。该软件、在线书籍和课程将使不同学科的学生和研究人员能够试验进化游戏动力学，而不需要这些学生具有广泛的博弈论或数学背景。该项目的第一个组成部分研究了最有经验的收益动态，在此动态下，修订代理选择一组策略进行测试，将每个策略与固定数量的随机选择的对手进行比较，并切换到实现收益最高的策略。基于逆向归纳的分析预测了完全不合作的行为，而实验证据表明更高水平的合作。基本的想法是，动态拥有一个几乎具有全球吸引力的休息点，展示了高水平的合作。这个休止点对模型的变化非常稳健。由于动力学采用具有有理系数的多项式方程的形式，计算代数的技术对于证明结果和描述合作博弈可以持续的游戏类别是有用的。第二个项目考虑了进化博弈动力学，它包含了不同策略之间的内在关系。这些关系可能反映了玩策略所需要的相似之处，反映了某些策略具有相似性质的看法，或者游戏所处的背景。当模仿代理通过将其收益不仅与外部标准比较，而且与类似策略的平均收益进行比较来评估策略时，就会出现嵌套复制者动态。这些动态零售了复制者动态的所有基本收敛和稳定性特性，并且可以通过强化学习模型与离散选择理论中的模型相关联。

This award funds research in game theory. The investigator seeks to develop and analyze new models of population dynamics in situations where individuals interact with others in strategic situations over time. The first part of the project considers a situation in which individuals respond rationally to the outcomes they experience when randomly matched with a partner. The goal here is to demonstrate how the resulting dynamics lead to cooperative behavior even when the individuals involved know that they will only interact with the same person for a set time. The possibility of maintaining cooperative behavior in repeated relationships with a set end date is a basic question in game theory, one with direct relevance to many social sciences and many policy applications. The dynamics studied in this project can provide one explanation for the persistence of cooperative behavior and may help us develop policies and institutions that support cooperation. The PI will also develop new public domain software, and will demonstrate how to use that software to model game dynamics via an online textbook/course. The software, online book, and course will enable students and researchers in a wide variety of disciplines to experiment with evolutionary game dynamics, without requiring that these students have extensive backgrounds in game theory or mathematics. The first component of the project studies best experienced payoff dynamics, under which revising agents select a set of strategies to test, play each strategy against fixed numbers of randomly chosen opponents, and switch to the strategy with the highest realized payoff. Analysis based on backward induction predict fully uncooperative behavior, while experimental evidence points to higher levels of cooperation. The basic idea is that the dynamics possess an almost globally attractive rest point exhibiting high levels of cooperation. This rest point is quite robust to variations of the model. Because the dynamics take the form of polynomial equations with rational coefficients, techniques from computational algebra are useful to prove results and in describing the classes of games in which cooperative play can be sustained. The second project considers evolutionary game dynamics which incorporate intrinsic relations among different strategies. These relations may reflect similarities in what playing the strategies entails, perceptions that certain strategies are of a similar nature, or the contexts in which the game is played. Nested replicator dynamics arise when imitating agents evaluate strategies by comparing their payoffs not only to an exogenous standard, but also to the average payoff earned by similar strategies. These dynamics retail all basic convergence and stability properties of the replicator dynamic, and can be lined to models from discrete choice theory via models of reinforcement learning.