A Coupling Approach to Analyzing Games with Dynamic Environments

TL;DR

This paper introduces a probabilistic coupling framework to analyze dynamic environment games, extending static game analysis techniques to account for environment changes driven by agent actions.

Contribution

It develops a general probabilistic coupling approach that allows traditional static game analysis methods to be applied to dynamic environment games.

Findings

Extended Nash equilibrium analysis to dynamic environments

Derived conditions for stochastic stability in dynamic games

Applied framework to cyber threat sharing and epidemic social precautions

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 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.