Stochastic evolutionary dynamics in the Volunteer's Dilemma

We study the evolution of cooperation in the Volunteer's Dilemma using the stochastic Moran process, which models a birth/death dynamic on a finite population. Each period one player dies and is replaced by a copy of a player. Players are either matched in pairs or matched in groups to play the Volunteer's Dilemma and their payoffs affect their probabilities of reproduction. This set-up allows to study how selection pressure, initial number of cooperators as well as the size of the groups playing the Volunteer's Dilemma influence the evolution of cooperation. Our main result is that given sufficiently high selection pressure an equilibrium of full cooperation is certain in pairwise interactions but an impossibility in group interactions.