Essays in evolutionary game theory

This dissertation focuses on Evolutionary Game Theory. Chapter 1 provides a brief description of evolutionary game theory, discusses the motivations behind this approach to game theory, and also summarizes the other three chapters.;In Chapter 2, co-authored with William H. Sandholm and Emin Dokumaci, we introduce a new evolutionary dynamic called the projection dynamic. The projection dynamic maps each population game to a new vector field: namely, the set of feasible directions of motion of the population. We investigate the geometric underpinnings of the projection dynamic, describe its basic game-theoretic properties, and establish a number of close connections between the projection dynamic and the replicator dynamic.;In Chapter 3, we examine whether price dispersion is an equilibrium phenomenon or a cyclical phenomenon. We develop a finite strategy model of price dispersion based on Burdett and Judd (1983). Using perturbed best response dynamics, we conclude that dispersed price equilibria are evolutionarily unstable leading us to interpret price dispersion as a cyclical process. For a particular case of the model, we prove the existence of a Shapley polygon. In Chapter 4, we define the logit dynamic in the space of probability measures for a game with a compact and continuous strategy set. The original Burdett and Judd (1983) model of price dispersion comes under this framework. We then show that if the payoff functions of the game satisfy Lipschitz continuity under the strong topology in the space of signed measures, the logit dynamic admits a unique solution in the space of probability measures. As a corollary, we obtain that the logit is well defined in the Burdett and Judd model.