The analysis of repeated games through evolution and learning

In this thesis we study the evolution of strategy choices for symmetric, finite, normal games. The second chapter of the dissertation analyzes infinite populations where in each period individuals are randomly and anonymously matched. Individuals are of different types, where a type represents a belief or a strategy choice. After each match individuals are allowed to change types. Thus a stochastic process is defined which describes the evolution of types in the population. The main result in the second chapter is that the evolution of the population can be described through a simpler deterministic system. The third chapter relates the properties of the evolutionary dynamics to standard game theoretic principles. Although individuals act in a purely mechanistic way, in equilibrium, the population as a whole acts like an individual adopting a strategy corresponding to a perfect equilibrium. The fourth chapter analyzes how two learning dynamics for finite normal form games - namely, the Cournot process and fictitious play - can explain experimental data. In doing so the chapter develops econometric techniques that can have a wide application to the analysis of experimental data