Inverse Learning in $2\times2$ Games: From Synthetic Interactions to Traffic Simulation

TL;DR

This paper introduces two inverse game-theoretic learning methods for $2\times2$ games, demonstrating their effectiveness in synthetic and traffic simulation scenarios, and analyzing trade-offs between interpretability and realism.

Contribution

It develops a closed-form CE-ML estimator and a dynamic LBR-ML estimator for inverse learning in $2\times2$ games, bridging static and dynamic modeling approaches.

Findings

Effective parameter recovery in synthetic games

Successful application to traffic interaction scenarios

Trade-offs identified between interpretability and behavioral realism

Abstract

Understanding how agents coordinate or compete from limited behavioral data is central to modeling strategic interactions in traffic, robotics, and other multi-agent systems. In this work, we investigate the following complementary formulations of inverse game-theoretic learning: (i) a Closed-form Correlated Equilibrium Maximum-Likelihood estimator (CE-ML) specialized for $2\times2$ games; and (ii) a Logit Best Response Maximum-Likelihood estimator (LBR-ML) that captures long-run adaptation dynamics via stochastic response processes. Together, these approaches span the spectrum between static equilibrium consistency and dynamic behavioral realism. We evaluate them on synthetic "chicken-dare" games and traffic-interaction scenarios simulated in SUMO, comparing parameter recovery and distributional fit. Results reveal clear trade-offs between interpretability, computational tractability, and behavioral expressiveness across models.