I n this article, we show how dissipativity and passivity theory impacts game theory, in particular, learning in multiplayer games. Over the years, a plethora of algorithms/dynamics have been proposed in the game theoretic literature for learning (or seeking) a Nash equilibrium. From the best-response play, proximal dynamics and (projected) gradient-play to fictitious-play, payoff-based play or Q-learning (reinforcement-learning), the list is long. Herein, we consider some these popular game-theoretic algorithms and show how the principle of balancing passivity can explain their operation, as well as the trade-off between game properties and learning dynamics properties. We discuss how passivity and basic properties of interconnected systems lead to simplified proofs of convergence of such algorithms, and furthermore, how by leveraging them, novel algorithms and game dynamics with better properties can be generated.

中文翻译：

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博弈论中的耗散理论：论耗散和被动在纳什均衡寻求中的作用

在本文中，我们展示了耗散性和被动性理论如何影响博弈论，特别是多人游戏中的学习。多年来，博弈论文献中已经提出了大量算法/动力学来学习（或寻求）纳什均衡。从最佳响应游戏、近端动力学和（预计）梯度游戏到虚构游戏、基于收益的游戏或 Q 学习（强化学习），列表很长。在这里，我们考虑了一些流行的博弈论算法，并展示了平衡被动性原理如何解释它们的操作，以及博弈属性和学习动态属性之间的权衡。我们讨论了互连系统的被动性和基本属性如何导致此类算法收敛的简化证明，此外，如何利用它们，