Evolutionary Game Theory

Abstract

This thesis provides an introduction into the basics of Evolutionary Game Theory. Evo- lutionary Game Theory is linked with the concept of natural selection, which deals with selection and mutation. After a small introduction in Game Theory, the definition of an Evolutionary Stable Strategy (ESS) is introduced. An ESS focusses on the concept of mutation, where the payoff is measured by the number of offspring. A point is an ESS if it is a better strategy than a mutant strategy, and it fares better against the mutation than the mutation does against itself. The main result is that an Evolutionary Stable Strategy is always a symmetric Nash equilibrium, but the converse is not true. Then, the concept of the Replicator Dynamic is introduced, which covers the concept of se- lection. The replicator dynamics is an ordinary differential equation, which is used to measure the change in the composition of the population over time. The main result is that a Lyapunov stable stationary state is a symmetric Nash equilibrium. Finally, an economic application of Evolutionary Game Theory is explained, where the replicator dynamic equation is calculated, equilibrium points are found and stability is measured.