We introduce the use of generative adversarial learning to compute equilibria in general game-theoretic settings, specifically the generalized Nash equilibrium (GNE) in pseudo-games, and its specific instantiation as the competitive equilibrium (CE) in Arrow-Debreu competitive economies. Pseudo-games are a generalization of games in which players' actions affect not only the payoffs of other players but also their feasible action spaces. Although the computation of GNE and CE is intractable in the worst-case, i.e., PPAD-hard, in practice, many applications only require solutions with high accuracy in expectation over a distribution of problem instances. We introduce Generative Adversarial Equilibrium Solvers (GAES): a family of generative adversarial neural networks that can learn GNE and CE from only a sample of problem instances. We provide computational and sample complexity bounds, and apply the framework to finding Nash equilibria in normal-form games, CE in Arrow-Debreu competitive economies, and GNE in an environmental economic model of the Kyoto mechanism.

翻译：我们引入生成对抗学习来计算一般博弈论设定中的均衡，具体包括伪博弈中的广义纳什均衡及其在阿罗-德布鲁竞争经济中作为竞争均衡的特例。伪博弈是博弈的一种推广形式，其中玩家的行动不仅影响其他玩家的收益，还影响其可行行动空间。尽管广义纳什均衡和竞争均衡在最坏情况下的计算是棘手的（即PPAD-难），但在实际应用中，许多问题仅需在问题实例分布上具有高期望精度的解。我们提出生成对抗均衡求解器（GAES）：一类生成对抗神经网络，能够仅从问题实例样本中学习广义纳什均衡和竞争均衡。我们给出了计算复杂度和样本复杂度的界限，并将该框架应用于正则形式博弈中的纳什均衡求解、阿罗-德布鲁竞争经济中的竞争均衡求解，以及基于京都机制的环境经济模型中的广义纳什均衡求解。