Critical transition induced by neighbourhood size in evolutionary spatial games

Abstract

We consider an evolutionary two-strategy two-player game where individual strategies evolve by imitation of players with large payoffs, and affected by noise. In a well-mixed population, the system approaches a mixed state with a part of the population in each strategy. On the other hand, when the population is distributed along a one-dimensional array and interactions are limited to a small neighbourhood of each player, the system falls in an absorbing state with a pure dominant strategy. We characterize the transition between these two regimes as a function of the neighbourhood size, providing evidence that it belongs to the universality class of directed percolation. Critical exponents are numerically evaluated, and the dependence of the critical point on the payoff and noise parameters is analyzed.