The theory of learning in games has extensively studied situations where agents respond dynamically to each other in light of a fixed utility function. However, in many settings of interest, agent utility functions themselves vary as a result of past agent choices. The ongoing COVID-19 pandemic has highlighted the need to formulate and analyze such models which feature game-environment feedback. For instance, a highly prevalent virus may incentivize individuals to wear masks, but extensive adoption of mask-wearing reduces virus prevalence which in turn reduces individual incentives for mask-wearing. What is the interplay between epidemic severity and the behaviors of a victim population? For initial answers, we develop a general framework using probabilistic coupling methods that can be used to derive the stochastically stable states of log-linear learning in certain games which feature such game-environment feedback. We then apply this framework to a simple dynamic game-theoretic model of social precautions in an epidemic and give conditions under which maximally-cautious social behavior in this model is stochastically stable.
翻译:游戏中的学习理论已经广泛研究了代理商根据固定的公用事业功能动态应对的情况。 但是,在许多感兴趣的环境中,代理商的功能本身因过去的代理商选择而不同。 正在发生的COVID-19大流行突出表明需要制定和分析以游戏-环境反馈为特点的模型。 例如,一种高度流行的病毒可能激励个人戴面具,但广泛采用戴面具的做法会减少病毒流行,这反过来又会减少个人戴面具的诱因。 流行严重程度与受害者群体行为之间的相互作用是什么? 对于最初的答案,我们开发了一个总体框架,使用概率性混合方法,可以用来在某些游戏-环境反馈为特点的游戏中得出逻辑-线性学习的随机稳定状态。 然后,我们将这一框架应用于一个简单的动态游戏-理论模式,在流行病中,社会防范措施的动态模式,并创造条件,在这个模式中,最审慎的社会行为是稳定的。