生成式对抗均衡解算器
Generative Adversarial Equilibrium Solvers
摘要：
我们介绍了使用生成对抗学习来计算一般博弈论环境中的均衡，特别是伪博弈中的广义纳什均衡（GNE），以及其在Arrow-Debreu竞争经济中的竞争均衡（CE）的具体实例。伪博弈是博弈的一种推广，其中参与者的行为不仅影响其他参与者的收益，而且影响他们的可行行动空间。虽然GNE和CE的计算在最坏情况下是棘手的，即，PPAD困难，在实践中，许多应用程序只需要在问题实例的分布上具有高精度的解决方案。我们介绍了生成对抗平衡求解器（GAES）：生成对抗神经网络的家庭，可以学习GNE和CE仅从一个样本的问题实例。我们提供了计算和样本的复杂性界限，并应用该框架来寻找纳什均衡的正常形式的游戏，CE在阿罗德布鲁竞争性经济体，和GNE在京都机制的环境经济模型。
英文摘要：
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.
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