We consider evolutionary games on a population whose underlying topology of interactions is determined by a binomial random graph G(n, p). Our focus is on 2-player symmetric games with 2 strategies played between the incident members of such a population. Players update their strategies synchronously: each player selects the strategy that is the best response to the current set of strategies its neighbours play. We show that such a system reduces to generalised majority and minority dynamics. We further show rapid convergence to unanimity for p in a range that depends on a certain characteristic of the payoff matrix. In the presence of a bias among the pure Nash equilibria, we determine a sharp threshold on p above which the largest connected component reaches unanimity with high probability. For p below this critical value, we identify those substructures inside the largest component that block unanimity. (C) 2021 Elsevier Inc. All rights reserved.
Random graphsEvolutionary gamesUnanimityBOOTSTRAP PERCOLATIONINNOVATION DIFFUSIONMAJORITY DYNAMICSTHRESHOLDBEHAVIORGAMES
Durbac, Calina、Fountoulakis, Nikolaos、Chellig, Jordan
NSTL
Elsevier
