The Evolution of Altruism - Spatial Assortment in the Prisoner's Dilemma

At first glance the existence of altruism in nature seems paradoxical. In displaying an altruistic act, an individual incurs some cost to its own fitness. Natural selection favours the fittest individuals and one would expect that genes promoting altruism would be selected against. This report investigates the mechanisms that facilitates the evolution of altruism. Game theory is widely applied in the study of the evolution of altruism and cooperation. We review game theory concepts which occur regularly in the literature and which are important in the study ofthe evolution of cooperation. The Prisoner's Dilemma game capturesthe essence of altruism and is a model often employed in the theoreticalstudy of cooperation. The best strategy for both players in the single round Prisoner's Dillema (PD) game is to defect, but having repeated rounds can lead to the evolution of cooperation. The mechanism by which cooperation is established in this scenario is known as direct reciprocity. Another mechanism which promotes the evolution of cooperation is the non-random interaction of players, called assortment. A couple of factors could influence the assortment of players, one of which is the spatial distribution of players. A model is constructed in which the players in the PD are placed on a lattice. Each player adopts one of two strategies, pure cooperation or pure defection. The players propagate and die out in proportion to how well they do in playing the PD against their neighbours. The model is used to investigate the spatial dynamics of the players and the level of assortment achieved. A simple movement strategy is introduced, whereby players move if they encounter a defector. The effect of this movement on the assortment is investigated. Our results show that by placing the players in the PD on lattice, enough assortment can be gained to allow the persistence of cooperation. An increase in the dispersal parameter leads to a decline in the success of cooperators and a loss in assortment. This suggests that the best movement strategy for cooperators is to have low dispersal rates, while defectors gain a big benefit from higher dispersal rates