Beyond Bayesian Nash: Learning Minimax-Regret Equilibria for Adversarial Team Games under Asymmetric Information

2026-07-10

AI Summary

This work addresses the sensitivity of existing equilibria—such as Bayesian Nash equilibrium—to strategic perturbations in the opponent’s type distribution within adversarial team games under asymmetric information. To enhance robustness against such distributional shifts, the paper introduces the Probabilistic Robust Minimax Regret Equilibrium (PR-MRE), which uniquely integrates a distribution-agnostic minimax regret criterion with a nominal type distribution by minimizing worst-case regret over a high-confidence subset of types. The authors develop a scalable learning framework, PRMRE-PSRO, combining robust bilinear programming, semidefinite relaxation, and deep reinforcement learning, augmented with a robust double-oracle mechanism. Empirical results demonstrate that PR-MRE substantially outperforms conventional risk-neutral equilibria in graph-based games, exhibiting significantly greater robustness in worst-case performance under hidden types.

Abstract

Adversarial team games (ATGs) with asymmetric information, such as adversarial path-finding, goal search, and reachability games on graphs, require strategies that are robust to hidden opponent types, such as a hidden goal flag, and to deception. Under asymmetric information, deception is seen as strategic shifts in the type distribution such that the omniscient opponent can collude with Nature and condition its play on the observed type. Existing risk-neutral solution concepts, such as Bayesian Nash equilibrium (BNE), are sensitive to distribution shifts, while distributionally robust approaches provide guarantees only within a prescribed ambiguity set. To address these limitations, we introduce Probabilistically Robust Minimax-Regret Equilibrium (PR-MRE), a novel equilibrium concept that combines the distribution-free robustness of minimax-regret reasoning with probabilistic information from a nominal type distribution. PR-MRE minimizes worst-case regret over a high-confidence subset of the type space, providing protection against strategic redistribution of probability mass while avoiding the conservatism of fully distribution-free approaches. We show that, for normal-form Bayesian games, PR-MRE can be formulated as a robust bilinear program and derive a tractable semidefinite relaxation. We then adapt this relaxation into a novel meta-solver within a robust double-oracle framework, PRMRE-PSRO, enabling population-based learning of approximate PR-MRE strategies via deep reinforcement learning best responses. Experiments on graph-structured adversarial team games demonstrate that PR-MRE discovers strategies with substantially improved worst-case performance across hidden types compared to risk-neutral equilibrium solutions, resulting in more robust behavior under strategic distribution shifts.

Problem

• Adversarial Team Games
• Asymmetric Information
• Minimax Regret
• Distributional Robustness
• Strategic Deception

Innovation

• minimax regret
• asymmetric information
• distributional robustness
• adversarial team games
• robust equilibrium