Essays on game theory and stochastic evolution

Evolutionary game theory is a popular framework for modeling the evolution of populations via natural selection. The fitness of a genetic or cultural trait often depends on the composition of the population as a whole and cannot be determined by looking at just the individual ("player") possessing the trait. This frequency-dependent fitness is quite naturally modeled using game theory since a player's trait can be encoded by a strategy and their fitness can be computed using the payoffs from a sequence of interactions with other players. However, there is often a distinct trade-off between the biological relevance of a game and the ease with which one can analyze an evolutionary process defined by a game. The goal of this thesis is to broaden the scope of some evolutionary games by removing restrictive assumptions in several cases. Specifically, we consider multiplayer games; asymmetric games; games with a continuous range of strategies (rather than just finitely many); and alternating games. Moreover, we study the symmetries of an evolutionary process and how they are influenced by the environment and individual-level interactions. Finally, we present a mathematical framework that encompasses many of the standard stochastic evolutionary processes and provides a setting in which to study further extensions of stochastic models based on natural selection.Science, Faculty ofMathematics, Department ofGraduat