A survey on algorithms for Nash equilibria in finite normal-form games

TL;DR

This survey reviews algorithms for computing Nash equilibria in finite normal-form games, covering theoretical classifications, empirical comparisons, and practical recommendations for implementation.

Contribution

It provides a comprehensive classification and comparison of existing algorithms, along with practical insights and open problems in the field.

Findings

Algorithms vary significantly in efficiency across game types.

Empirical results highlight strengths and weaknesses of different approaches.

Practical suggestions improve algorithm implementation and application.

Abstract

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet economics and multi-agent learning. This paper reviews various algorithms computing the Nash equilibrium and its approximation solutions in finite normal-form games from both theoretical and empirical perspectives. For the theoretical part, we classify algorithms in the literature and present basic ideas on algorithm design and analysis. For the empirical part, we present a comprehensive comparison on the algorithms in the literature over different kinds of games. Based on these results, we provide practical suggestions on implementations and uses of these algorithms. Finally, we present a series of open problems from both theoretical and practical considerations.