Asymmetric Nash Seeking via Best Response Maps: Global Linear Convergence and Robustness to Inexact Reaction Models

2026-03-17

AI Summary

This work addresses the computation of Nash equilibria in two-player constrained games under asymmetric information, where one player lacks full knowledge of the other’s objective and constraints and can only interact via a best-response mapping. The authors propose an iterative algorithm that combines projected gradient descent with best-response updates, requiring no complete disclosure of either player’s optimization problem and applicable to settings with decoupled feasible sets. Under standard regularity conditions, they establish—for the first time—the global linear convergence of the algorithm in such an asymmetric regime relying solely on best-response access. Moreover, when the best-response is subject to uniformly bounded errors of magnitude ε, the iterates converge to an O(ε)-neighborhood of the equilibrium, with an explicit error bound provided. Numerical experiments corroborate the theoretical convergence rates and sensitivity to response inaccuracies.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Search and Optimization: Non-convex Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and constraints, an assumption that is often unrealistic in practice. This letter studies a class of asymmetric-information two-player constrained games with decoupled feasible sets, in which Player 1 knows its own objective and constraints while Player 2 is available only through a best-response map. For this class of games, we propose an asymmetric projected gradient descent-best response iteration that does not require full mutual knowledge of both players' optimization problems. Under suitable regularity conditions, we establish the existence and uniqueness of the Nash equilibrium and prove global linear convergence of the proposed iteration when the best-response map is exact. Recognizing that best-response maps are often learned or estimated, we further analyze the inexact case and show that, when the approximation error is uniformly bounded by $\varepsilon$, the iterates enter an explicit $O(\varepsilon)$ neighborhood of the true Nash equilibrium. Numerical results on a benchmark game corroborate the predicted convergence behavior and error scaling.

Problem

• asymmetric information
• Nash equilibrium
• best-response map
• constrained games
• multi-agent decision-making

Innovation

• asymmetric information
• best-response map
• global linear convergence
• robustness to inexact models
• Nash equilibrium