A heterogeneous evolutionary stable population under assortative matching: Exploring the diversity of preferences

Recent studies have shown that a population acting not only upon self-interest but also exhibiting some morality preference has an evolutionary advantage. Specifically, in the setting of a symmetric fitness game, a resident population is evolutionary stable against all types of mutants if it has the utility function of Homo-moralis, with a morality equal to the assortativity. In this paper, we extend the scope of analysis allowing for the presence of a diversity of preferences in the population. Establishing a Payoff Equality condition, we prove the possibility of co-existence of two residents in the population. We then introduce a tripartite assortment function and study the conditions for the evolutionary stability of this diverse population. In the case of a constant assortment function, we show the existence of an evolutionary stable and heterogeneous resident population.