Myopic Best Response Replicated the Mean Curvature Flow
Published in Preprint, 2026
“In a continuous coordination game, under myopic best response, players change strategies, and thus strategic communities change their shapes in time. We show that the boundaries of these strategic communities evolve according to Free Boundary Mean Curvature Flow in the continuous time limit. The convergence relies on an approximation scheme for the Mean Curvature Flow, which has previously been used to describe other threshold dynamics. With this equivalence, we can characterize Nash equilibria of the continuous coordination game as minimal surfaces and explore related consequences in biased versions of the same game.”
In a continuum of players, when each player updates their strategy by MBR, the boundary of the strategic communites evolves according to Mean Curvature Flow.
Recommended citation: McAlister J. S., Burns N.(2026) Myopic Best Response Replicates the Mean Curvature Flow. preprint. https://doi.org/10.48550/arXiv.2609.37803
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