title: The evolution of payoff matrices: providing incentives to cooperate.
abstract: Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.
authors.affiliation: National Institute for Mathematical and Biological Synthesis, 1534 White Avenue, Knoxville, TN 37996, USA. erol@nimbios.org
authors.forename: Erol
authors.initials: E
authors.lastname: Akçay
authors.forename: Joan
authors.initials: J
authors.lastname: Roughgarden
mesh_terms: D000818:Animals; D001522:Behavior, Animal; D005075:Biological Evolution; D003299:Cooperative Behavior; D005716:Game Theory; D009042:Motivation; D011110:Polymorphism, Genetic; D011157:Population Dynamics; D012641:Selection, Genetic