Evolutionary aspects of spatial Prisoner’s Dilemma in a population modeled by continuous probabilistic cellular automata and genetic algorithm.

How cooperation arises in some situations has been studying in areas like biology, economics and psychology. Here, we attempt to confront genetic algorithm and spatial Prisoner’s Dilemma in a population to add an evolutionary point of view in this context. Instead of using genetic algorithm to maximize a function, their processes are used in population in order to select best fit individuals and produce a new generation using genetic operators and mutation. Interactions will be modeled by Prisoner’s Dilemma (PD) with two players and two actions game, setting either a game against the field or a population game. Individual chromosomes contain the information of the probability of cooperation for the players. Moreover, individuals characteristics like lifetime, amount of life and caused death (last two related to games payoff) are used to evaluate an individual success and to formalize this evaluation, eleven fitness functions are used. Population is modeled by Continuous Probabilistic Cellular Automata (CPCA) and Ordinary Differential Equations (ODE), and a relation between two approaches is explored. The objective of this paper is to analyze numerically how parameters of Prisoner’s Dilemma game and genetic algorithm influence in the evolution of cooperation in a population.