论文标题
随机图形游戏的标签状态和大型网络上的近似平衡
A label-state formulation of stochastic graphon games and approximate equilibria on large networks
论文作者
论文摘要
本文在大图及其图形限制上研究了随机游戏。我们根据单个典型玩家的标签状态分发提出了一个新的Graphon游戏公式。相比之下，其他最近提出的Graphon游戏模型直接与连续的玩家合作，这涉及严重的措施理论技术。实际上，通过将标签视为状态流程的组成部分，我们在表述中表明，Graphon Games是平均现场游戏的特殊情况，尽管具有某些不可避免的脱模效和不连续性，这使得在平均野外游戏中无法实现的最现有结果无法实现。尽管如此，我们证明了马尔可夫图形平衡存在于相当笼统的假设下以及在单调条件下的唯一性。最重要的是，我们展示了如何使用Graphon平衡的概念来构建在任何（加权，有向）图上设置的大型有限游戏的近似平衡，从而在剪切的标准中收敛。缺乏参与者的交换性需要仔细定义近似平衡，从而允许玩家的近似错误之间的异质性，并且我们展示了模型输入的各种规则性能和基础图形如何自然地导致不同的近似强度。
This paper studies stochastic games on large graphs and their graphon limits. We propose a new formulation of graphon games based on a single typical player's label-state distribution. In contrast, other recently proposed models of graphon games work directly with a continuum of players, which involves serious measure-theoretic technicalities. In fact, by viewing the label as a component of the state process, we show in our formulation that graphon games are a special case of mean field games, albeit with certain inevitable degeneracies and discontinuities that make most existing results on mean field games inapplicable. Nonetheless, we prove existence of Markovian graphon equilibria under fairly general assumptions, as well as uniqueness under a monotonicity condition. Most imporantly, we show how our notion of graphon equilibrium can be used to construct approximate equilibria for large finite games set on any (weighted, directed) graph which converges in cut norm. The lack of players' exchangeability necessitates a careful definition of approximate equilibrium, allowing heterogeneity among the players' approximation errors, and we show how various regularity properties of the model inputs and underlying graphon lead naturally to different strengths of approximation.
