Dr Tobias Galla, Theoretical Physics Group, The University of Manchester
Abstract: We will review recent statistical mechanics analyses of random replicator equations. Replicators may here refer to interacting species in simple eco-systems, or in the context of evolutionary game theory describe the repetitive interaction of players in so-called matrix games. We will focus on different stable and unstable regimes of the replicator dynamics, their ergodicity properties, and study the connection between fixed points of the replicator equations and the Nash Equilibria of matrix games. We will also present results on the learning dynamics of agents with finite memory, and demonstrate how irregular and potentially chaotic motion may occur in such systems.