Structured Coordination Games of Planar Graphs: a Dual Approach
Preprint, 2026
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.
Recommended citation: McAlister, J. S. (2026) Structured Coordination Games of Planar Graphs: a Dual Approach. preprint. https://doi.org/10.48550/arXiv.2607.22865
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