Game theory, chaos and noise
I will discuss the learning dynamics of a small set of players whointeract repeatedly in a given game, and who learn from past experience adapting to their opponents' actions. Such dynamics lead to to modified replicator equations in a deterministic limit, corresponding to an infinite number of observations made between adaption events. If only a finite number of moves of the opposing players are sampled between adaption steps, the learning dynamics becomes stochastic, similar to noise corrections observed in evolutionary systems in finite populations. I will here discuss the effects of memory-loss and of noise on the learning of agents for some simple two-player games, and show that the combination of both may affect the attractors considerably. Memory-loss may promote co-operation in social dilemmas, and the agents fail to retrieve the Nash equilibrium. In cyclic games, memory-loss drives the system towards stability in deterministic learning, but fixed points may be removed if sampling is stochastic, resulting in coherent random cycling.
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..