Darwinian dynamics and the evolution of cooperation

Background/Question/Methods The evolution of cooperation can be analyzed using evolutionary game theory. Here we use Darwinian dynamics formulated in terms of G-functions to examine the evolution of cooperation for a family of cost-benefit games. The term Darwinian dynamics is used to describe the combination of population dynamics plus the dynamics of strategies (heritable phenotypes) that result from natural selection. The G-function method is a game theoretic approach that allows one to determine the fitness of any focal individual in a population of individual with the same evolutionary potential. A cost-benefit game is one that involves shared costs and benefits with a continuum of strategies available from non-cooperation to complete cooperation. Results/Conclusions Darwinian dynamics produce ESS solutions of complete cooperation, partial cooperation, non-cooperation, and coexistence between complete cooperation and non-cooperation. Cooperation emerges from an interplay between the nonlinearities in the cost and benefit functions. For instance, when benefits increase at a decelerating rate and costs increase at an accelerating rate with the degree of cooperation then the ESS has an intermediate level of cooperation. Darwinian dynamics can also produce non-ESS points such as a convergent stable minimum, convergent unstable minimum and convergent unstable maximum. The emergence of cooperative behavior in this game represents enlightened self interest whereas non-cooperative solutions illustrate the tragedy of the commons. Games having either a stable maximum or stable minimum have the property that small changes in model parameter values result in correspondingly small changes in the degree of cooperation. However with unstable maximum or unstable minimum small changes parameter values can result in a switch from non-cooperation to complete cooperation (and vice-versa). Knowing the nature of these solutions will help to identify when human or animal societies have the potential for cooperation and whether or not it is robust or fragile.