Conformist Transmission and the Evolution of Cooperation

We study the effects of conformist transmission on the evolutionary dynamics of the Prisoner’s Dilemma, the Snowdrift and the Stag Hunt games in both well-mixed and spatially structured populations. The addition of conformism introduces a transformation of the payoff matrix that favours the stability of pure equilibria and reduces the basin of attraction of risk dominant equilibria. When both conformism and local interactions are present, the system can exhibit higher levels of cooperation than those obtained in the absence of any of the two mechanisms. Introduction and Related Work Evolutionary game theory (Hofbauer and Sigmund, 1998; Gintis, 2000) is the theory of evolutionary dynamics when selection is frequency-dependent, i.e. when the success of an individual is conditioned not only by the strategy she holds but also by the strategies held by other individuals in the population. Although originally developed as an application of game theory to the study of genetic evolution (Maynard Smith, 1982), evolutionary game theory has also been used to investigate cultural evolutionary processes, that is the way ideas or beliefs spread through a population of individuals capable of imitation. In cultural evolutionary game-theoretic models, ideas are transmitted via biased imitation. Most of these models posit that the only important psychological bias underlying imitation is prestige or payoff-based bias, defined as the predisposition to imitate successful individuals. Under the assumption of a very large and well-mixed population, payoff-based biased transmission can be shown to generate a famous differential equation, named the replicator dynamics (Taylor and Jonker, 1978; Gintis, 2000). In the context of evolutionary game theory, the equilibrium points and other characteristics of the dynamics of different games are studied in order to better understand the involved evolutionary processes. The Prisoner’s Dilemma (PD), Snowdrift1 (SD) and the Stag Hunt (SH) are among the most studied two-person, Also known as Hawks-Doves or Chicken. symmetric games in the literature. They are used for investigating under which circumstances altruistic traits can become fixed in a population of “selfish” individuals. In social dilemmas of cooperation, individuals’ behaviours are of two types: cooperative and non-cooperative. Cooperators are willing to engage in cooperative tasks, while noncooperators (usually called defectors) prefer not to. The success resulting from the interaction of cooperators and defectors is given by the payoff matrix: