Prisoner’s Dilemma cellular automata revisited: evolution of cooperation underenvironmental pressure

Abstract

We propose an extension of the evolutionary Prisoner’s Dilemma cellular automata, introducedby Nowak and May (1992 Nature 359 826), in which the pressure of the environment is taken intoaccount. This is implemented by requiring that individuals need to collect a minimum scoreUmin, representing indispensable resources (nutrients, energy, money, etc)to prosper in this environment. So the agents, instead of evolving justby adopting the behaviour of the most successful neighbour (who gotUmsn), also take intoaccount if Umsn is above orbelow the threshold Umin. If Umsn<Umin an individual has a probability of adopting the opposite behaviour from the one used by itsmost successful neighbour. This modification allows the evolution of cooperation for payoffsfor which defection was the rule (as happens, for example, when the sucker’s payoff is muchworse than the punishment for mutual defection). We also analyse a more sophisticatedversion of this model in which the selective rule is supplemented with a ‘win-stay,lose-shift’ criterion. The cluster structure is analysed, and for this more complexversion we found power-law scaling for a restricted region in the parameter space.