English

A Finite Population Destroys a Traveling Wave in Spatial Replicator Dynamics

Populations and Evolution 2021-04-28 v3 Computer Science and Game Theory Analysis of PDEs Pattern Formation and Solitons

Abstract

We derive both the finite and infinite population spatial replicator dynamics as the fluid limit of a stochastic cellular automaton. The infinite population spatial replicator is identical to the model used by Vickers and our derivation justifies the addition of a diffusion to the replicator. The finite population form generalizes the results by Durett and Levin on finite spatial replicator games. We study the differences in the two equations as they pertain to a one-dimensional rock-paper-scissors game.

Cite

@article{arxiv.2006.00397,
  title  = {A Finite Population Destroys a Traveling Wave in Spatial Replicator Dynamics},
  author = {Christopher Griffin and Riley Mummah and Russ deForest},
  journal= {arXiv preprint arXiv:2006.00397},
  year   = {2021}
}

Comments

17 pages, 7 figures

R2 v1 2026-06-23T15:56:10.735Z