Positive and negative selective assortment in pairwise interactions

In populations subject to evolutionary processes, the assortment of players with different genes or strategies can have a large impact on players payoffs and on the expected evolution of each strategy in the population. Here we consider assortment generated by a process of partner choice known as selective assortment. Under selective assortment, players looking for a mate can observe the strategies of a sample of potential mates or co-players, and select one of them to interact with. This selection mechanism can generate positive assortment (if there is a preference for players using the same strategy), or negative assortment. We study the impact of selective assortment in the evolution and in the equilibria of a population, providing results for different games under different evolutionary dynamics (including the replicator dynamics).