AI 中文总结
研究结构化协调博弈中纳什均衡问题，利用势函数和平面图对偶关系定义拟度量空间，证明纳什均衡是全局目标函数局部极小值，在两种策略时可构建动态子图过程概括近视最优反应动态。
AI 中文摘要
在纯协调博弈中，若每个参与者与其他参与者均匀互动，找到纳什均衡很简单。但当参与者具有关系结构时，问题变得更难回答。本文表明，结构化协调博弈的纳什均衡通过势函数代表最小割划分的局部概念。利用平面图对偶中划分与子图的标准关系，定义一个拟度量空间，其中纳什均衡是全局目标函数局部极小值。当博弈限于两种策略且这些结论使我们能构建一个动态子图过程，概括协调博弈的近视最优反应动态。
英文摘要
Finding Nash equilibria in the pure coordination game is trivial when every player interacts with every other player evenly. However, when players have a relational structure, the question becomes harder to answer. Here, we show that Nash equilibria to the structured coordination game represent a local notion of the Min-cut partition by way of the potential function. Using the standard relationship between partitions and subgraphs in the planar dual, we define a quasimetric space for which Nash equilibria are local minimizers of a global objective. When the game is restricted to only two strategies, these results allow us to construct a dynamic subgraph process which recapitulates the Myopic Best Response dynamics of the coordination game.
