Establishment of Dominance Hierarchies and Cooperation: A Game-Theoretic Perspective

Social interactions among animals can take many forms. While some animals are known to cooperate with each other, others are characterised by dominance hierarchies. This thesis is concerned with the study of these two forms of social organisation amongst animal groups. We model the problem using a game-theoretic framework. We investigate the evolution of animal behaviour under the influence of natural selection and mutation. We study pairwise conflicts between animals from two distinct populations. We model natural selection using a discrete map which increases the proportion of animals that perform better relative to other animals in the population, and model mutations by adding a stochastic element to the discrete map. We begin our analysis with the investigation of dominance hierarchies that can develop in the Hawk–Dove game. We study the different factors that can affect the formation of dominance hierarchies. In order to gain insight into the evolution of cooperation, we generalise our model to incorporate animals that interact with each other repeatedly in one generation. We use this model to investigate the conditions under which cooperation can survive in the populations as a stable long run solution.