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The theory of learning in games has extensively studied situations whereagents respond dynamically to each other by optimizing a fixed utilityfunction. However, in real situations, the strategic environment varies as aresult of past agent choices. Unfortunately, the analysis techniques thatenabled a rich characterization of the emergent behavior in static environmentgames fail to cope with dynamic environment games. To address this, we developa general framework using probabilistic couplings to extend the analysis ofstatic environment games to dynamic ones. Using this approach, we obtainsufficient conditions under which traditional characterizations of Nashequilibria with best response dynamics and stochastic stability with log-linearlearning can be extended to dynamic environment games. As a case study, we posea model of cyber threat intelligence sharing between firms and a simple dynamicgame-theoretic model of social precautions in an epidemic, both of whichfeature dynamic environments. For both examples, we obtain conditions underwhich the emergent behavior is characterized in the dynamic game by performingthe traditional analysis on a reference static environment game.

A Coupling Approach to Analyzing Games with Dynamic Environments