On exploring the genetic algorithm for modeling the evolution of cooperation in a population

• A population is modeled via cellular automata and ordinary differential equations.
• Individuals compete for benefits according to prisoner’s dilemma game.
• Individual have a strategy in its genotype, and the phenotype is the action chosen.
• Genetic algorithm rules the individual reproduction.
• The evolution of cooperation depends on the fitness function adopted.

In this paper, we propose a genetic algorithm approximation for modeling a population which individuals compete with each other based on prisoner’s dilemma game. Players act according to their genome, which gives them a strategy (phenotype); in our case, a probability for cooperation. The most successful players will produce more offspring and that depends directly of the strategy adopted. As individuals die, the newborns parents will be those fittest individuals in a certain spatial region. Four different fitness functions are tested to investigate the influence in the evolution of cooperation. Individuals live in a lattice modeled by probabilistic cellular automata and play the game with some of their neighborhoods. In spite of players homogeneously distributed over the space, a mean-field approximation is presented in terms of ordinary differential equations.