PreprintCC BY 4.0arXiv
Myopic Best Response Replicates the Mean Curvature Flow
Abstract
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.
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BibTeX
@misc{mcalister2026myopic,
title = {{Myopic Best Response Replicates the Mean Curvature Flow}},
author = {John S. McAlister and Nathan Burns},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37803},
eprint = {2609.37803},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37803},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Myopic Best Response Replicates the Mean Curvature Flow
AU - John S. McAlister
AU - Nathan Burns
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37803
UR - https://arxiv.org/abs/2609.37803
AB - 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.
ER -