The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic environment varies as a result of past agent choices. Unfortunately, the analysis techniques that enabled a rich characterization of the emergent behavior in static environment games fail to cope with dynamic environment games. To address this, we develop a general framework using probabilistic couplings to extend the analysis of static environment games to dynamic ones. Using this approach, we obtain sufficient conditions under which traditional characterizations of Nash equilibria with best response dynamics and stochastic stability with log-linear learning can be extended to dynamic environment games. As a case study, we pose a model of cyber threat intelligence sharing between firms and a simple dynamic game-theoretic model of social precautions in an epidemic, both of which feature dynamic environments. For both examples, we obtain conditions under which the emergent behavior is characterized in the dynamic game by performing the traditional analysis on a reference static environment game.
翻译:游戏中学习理论广泛研究了代理商通过优化固定的实用功能来积极应对对方的情况。 但是,在现实情况下,战略环境因过去的代理商选择而不同。 不幸的是,能够对静态环境游戏中的突发行为进行丰富定性的分析技术无法应对动态环境游戏。 为了解决这个问题,我们开发了一个总体框架,利用概率结合法将静态环境游戏的分析扩大到动态环境游戏。 使用这种方法,我们获得了足够的条件,可以将具有最佳响应动态和逻辑线性学习稳定性的传统纳什平衡特征扩展至动态环境游戏。作为案例研究,我们提出了公司之间分享网络威胁情报的模式,以及一种简单的动态游戏理论模式,即一种流行病的社会防范模式,两者都具有动态环境特征。我们通过对参考静态环境游戏进行传统分析,获得了动态游戏中新兴行为特征的条件。