A survey on algorithms for Nash equilibria in finite normal-form games
It addresses the need for efficient Nash equilibrium computation in fields like Internet economics and multi-agent learning, but is incremental as it surveys existing methods.
This paper reviews and compares algorithms for computing Nash equilibria and approximations in finite normal-form games, providing theoretical classifications and empirical evaluations to offer practical implementation suggestions.
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.