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.

中文翻译：

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有限范式博弈纳什均衡算法综述

纳什均衡是博弈论中最有影响力的解决方案概念之一。随着计算机科学和人工智能的发展，对纳什均衡计算的需求越来越大，特别是互联网经济学和多智能体学习。本文从理论和实证角度回顾了有限范式博弈中计算纳什均衡及其近似解的各种算法。在理论部分，我们对文献中的算法进行了分类，并提出了算法设计和分析的基本思想。对于实证部分，我们对文献中的算法对不同类型的游戏进行了全面的比较。基于这些结果，我们为这些算法的实现和使用提供了实用的建议。最后，我们从理论和实践的角度提出了一系列开放性问题。