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arXiv · 2607.22865

Structured Coordination Games on Planar Graphs: a Dual Approach

John S. McAlister
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Abstract

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.

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John S. McAlister. 2026-07-24. Structured Coordination Games on Planar Graphs: a Dual Approach. https://arxiv.org/abs/2607.22865

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