Perturbing Best Responses in Zero-Sum Games

TL;DR

This paper explores how perturbing utility functions in zero-sum game algorithms like Double Oracle and Fictitious Play can significantly reduce the number of iterations needed to approximate Nash equilibria, especially with structured strategies.

Contribution

It introduces a method for utility perturbation that accelerates convergence of best-response algorithms in zero-sum games, with efficient techniques for structured strategies.

Findings

Perturbations can reduce iteration count in best-response algorithms.

Logarithmic iteration bounds achieved with suitable perturbations.

Efficient utility perturbation methods for structured strategies.

Abstract

This paper investigates the impact of perturbations on the best-response-based algorithms approximating Nash equilibria in zero-sum games, namely Double Oracle and Fictitious Play. More precisely, we assume that the oracle computing the best responses perturbs the utilities before selecting the best response. We show that using such an oracle reduces the number of iterations for both algorithms. For some cases, suitable perturbations ensure the expected number of iterations is logarithmic. Although the utility perturbation is computationally demanding as it requires iterating through all pure strategies, we demonstrate that one can efficiently perturb the utilities in games where pure strategies have further inner structure.