MSc Math Defence: The Replicator Dynamics of Generalized Nash Games

CANDIDATE:   JASON LEQUYER

ABSTRACT:

Generalized Nash Games are a powerful modelling tool, first introduced in the 1950's. They have seen some important developments in the past two decades. Separately, Evolutionary Games were introduced in the 1960's and seek to describe how natural selection can drive phenotypic changes in interacting populations. In this thesis, we show how these two independently formulated models can be linked under a common framework and how this framework can be used to expand each model. At the center of this unified model is the Replicator Equation and the relationship we establish between it and the lesser known Projected Differential Equation. To our knowledge this work is completely original.