Homophily and the evolution of cooperation in the Volunteer’s Dilemma: A computational study on dynamic graphs

We study the evolution of cooperation in the Volunteer’s Dilemma using the stochastic Moran process on dynamic graphs, which models a birth–death dynamic on structured finite populations. According to the Moran process, in each period one player is selected to reproduce, where the probability of being selected is proportional to payoff-related fitness levels, and a copy of this player is substituted for a player who is randomly selected to die. The interaction of the players is embedded in a network structure which determines the overlapping groups within which the Volunteer’s Dilemma is played. Networks vary to the extent they exhibit homophily, i.e., they vary in the extent to which the interacting groups primarily encompass either cooperators or defectors instead of a mix of both types of players. By varying the degree of homophily in the network, we thus can study the question if and to what extent assortment of strategies favors the evolution of cooperation in the Volunteer’s Dilemma. Our results show that a surprisingly high extent of homophily is required to ensure the evolution of cooperation in the Volunteer’s Dilemma when modeled as a stochastic process in pure strategies. Other parameters, such as selection pressure or the number of initial cooperators, have a comparatively small effect on the fixation of cooperation in the population.