THE REPLICATOR DYNAMICS OF GENERALIZED NASH GAMES

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. The dynamics of Evolutionary Games are frequently studied using the Replicator Equation, however there is no general theory about how to derive these kinds of dynamics for more complex games, such as Generalized Nash Games. In this paper we extend and generalize the Replicator Equation by using an analogy with the Projected Dynamical System, and show how this extension can be used to derive a Replicator Equation for a wide range of problems. We also show how this extension enables us to to consider the dynamics of a new type of Evolutionary Games where we add shared inter-species contraints.