The Hawk-Dove game in phenotypically homogeneous and heterogeneous populations of finite dimension

The Hawk-Dove game played between individuals in populations of finite dimension is analyzed by means of a stochastic model. We take into account both cases when all individuals in the population are either phenotypically homogeneous or heterogeneous. A strategy in the model is a gene representing the probability of playing the Hawk strategy. Individual interactions at the microscopic level are described by a genetic algorithm where evolution results from the interplay among selection, mutation, drift and cross-over of genes. We show that the behavioral patterns observed at the macroscopic level can be reproduced as the emergent result of individual interactions governed by the rules of the Hawk-Dove game at the microscopic level. We study how the results of the genetic algorithm compare with those obtained in evolutionary game theory, finding that, although genes continuously change both their presence and frequency in the population over time, the population average behavior always achieves stationarity and, when this happens, the final average strategy played in the population oscillates around the evolutionarily stable strategy in the homogeneous population case or the neutrally stable set in the heterogeneous population case.