Robust Stochastic Stability in Dynamic and Reactive Environments
Abstract
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 many settings of interest, agent utility functions themselves vary as a result of past agent choices. The ongoing COVID-19 pandemic provides an example: 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. This paper develops 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. As a case study, we 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.
Cite
@article{arxiv.2103.13475,
title = {Robust Stochastic Stability in Dynamic and Reactive Environments},
author = {Brandon C. Collins and Lisa Hines and Gia Barboza and Philip N. Brown},
journal= {arXiv preprint arXiv:2103.13475},
year = {2021}
}