Correlated Quantal Response Equilibrium: A New Equilibrium Notion for Human-AI Strategic Interactions

Abstract

The modeling of the behavior of agents in strategic environments and the prediction of the resulting outcomes has long been a challenging problem; this has been the focus of game theory. The introduction of AI agents as human-aids or as sole decision-makers expands the underlying question: Can we model behavior and predict outcomes of strategic games that involve a mix of AI agents and human players? As an initial answer, we propose Correlated Quantal Response Equilibrium (CQRE) that combines and generalizes classical solution concepts such as Quantal Response Equilibrium and Correlated Equilibrium. We answer questions of existence and propose a method for computing the CQRE that is a best fit to a given joint action distribution. We demonstrate the empirical effectiveness of CQRE predictions using a diverse collection of complex general-sum games, including high-rank and large-action two-player games, challenging multiplayer games, and a large-scale extension of the Selten--Chmura setting to AI--AI and human--AI play.