Nicolas Lanchier
University of Arizona
Best-response dynamics
[When and where]
The best-response dynamics is an example of evolutionary game where players are located on the infinite square lattice and update their strategy in order to maximize their payoff. In the presence of two strategies, and calling a strategy selfish or altruistic depending on a certain ordering of the coefficients of the underlying payoff matrix, a simple analysis of the nonspatial mean-field approximation of this process shows that a strategy is evolutionary stable if and only if it is selfish, making in particular the system bistable when both strategies are selfish. The main objective of this talk is to show that, in contrast with the mean-field approximation, only the most selfish strategy is evolutionary stable for the stochastic process. The main ingredients of the proof are monotonicity results and a coupling between the process properly rescaled in space with bootstrap percolation. This is a joint work with Stephen Evilsizor.
Invited talk Mini-symposium 13
Updated May 14, 2015, by Minus