Random mobility and the evolution of cooperation in spatial N-player iterated Prisoner’s Dilemma games

We study the effects of random mobility on the evolution of cooperation in a spatial version of the N-player Iterated Prisoner’s Dilemma game, where individuals are located on a two-dimensional regular lattice with periodic boundary conditions. The probability that an individual moves from its current location is based on the amount of time it has occupied a given position and the relative fitness values of the individual occupying the destination position. Our results show that random movement can promote cooperative behaviour in N-player games. In some circumstances, random mobility enhances system-wide cooperation levels when compared to the static model. However, the outcome is strictly dependent on the cost-to-benefit ratio and the range of movement. An analysis of the population dynamics suggests that the convergence rate of the model (i.e., the time for the population to reach an equilibrium state) is faster with mobility in place. Our findings help to further understand the relationship between mobility and evolving game-playing strategies in spatially structured populations, especially when efficient collective actions matter.