Asymmetric evolutionary games with non-linear pure strategy payoffs

In this paper, I extend the analytical framework of evolutionary game theory to games with two distinct types of players where the type-specific payoff functions are nonlinear on the right--bi-player-type nonlinear (BNL) evolutionary games. That is, asymmetric games where the payoffs for pairwise interactions are influenced by the ambient frequencies of the pertinent strategies of both types of players. While this paper is motivated by my interest in inter- and intra-gender conflicts of interest in sexual reproduction, BNL games also arise just as naturally in most two-species interactions. Thus, the methodology may provide a novel approach to investigating such classical ecological phenomena as prey-predator/host-parasite interactions and interspecies competition for resources. Finally, given the growing tendency to utilize evolutionary games in economic modeling, a case can be made for the current paper being of interest to traditional game-theoretic modelers in connection with situations such as buyer/seller or employer/employee interaction.