Strategically Robust Game Theory via Optimal Transport

2025-07-21

AI Summary

Decision-making in games is challenged by multi-source uncertainties—including incomplete information, bounded rationality, and computational constraints—undermining the reliability of conventional equilibria. Method: This paper introduces “strategic robust equilibrium,” a novel equilibrium concept that constructs an ambiguity set over opponents’ behavioral distributions via optimal transport, parameterized by a tunable robustness level. Contribution/Results: The equilibrium interpolates naturally between Nash equilibrium and maximin (security) strategies, guarantees existence, and admits computation at complexity no higher than that of Nash equilibrium. Theoretically, we establish the “robustification facilitates coordination” phenomenon. Empirically, across bimatrix, congestion, and Cournot games, strategic robust equilibrium achieves significantly higher equilibrium payoffs and robustness under uncertainty compared to standard Nash equilibrium, while remaining compatible with mainstream game models.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In many game-theoretic settings, agents are challenged with taking decisions against the uncertain behavior exhibited by others. Often, this uncertainty arises from multiple sources, e.g., incomplete information, limited computation, bounded rationality. While it may be possible to guide the agents' decisions by modeling each source, their joint presence makes this task particularly daunting. Toward this goal, it is natural for agents to seek protection against deviations around the emergent behavior itself, which is ultimately impacted by all the above sources of uncertainty. To do so, we propose that each agent takes decisions in face of the worst-case behavior contained in an ambiguity set of tunable size, centered at the emergent behavior so implicitly defined. This gives rise to a novel equilibrium notion, which we call strategically robust equilibrium. Building on its definition, we show that, when judiciously operationalized via optimal transport, strategically robust equilibria (i) are guaranteed to exist under the same assumptions required for Nash equilibria; (ii) interpolate between Nash and security strategies; (iii) come at no additional computational cost compared to Nash equilibria. Through a variety of experiments, including bi-matrix games, congestion games, and Cournot competition, we show that strategic robustness protects against uncertainty in the opponents' behavior and, surprisingly, often results in higher equilibrium payoffs - an effect we refer to as coordination via robustification.

Problem

• Addressing decision-making under uncertain opponent behavior
• Modeling joint uncertainty from multiple sources effectively
• Ensuring robust equilibria with no computational overhead

Innovation

• Uses optimal transport for robust equilibrium
• Introduces strategically robust equilibrium concept
• Ensures Nash equilibrium computational efficiency