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