Berlin 2008 – wissenschaftliches Programm

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SYDN: Symposium Game theory in dynamical systems

SYDN 1: Game theory in dynamical systems

SYDN 1.2: Vortrag

Freitag, 29. Februar 2008, 10:50–11:05, H 0105

Learning to play random games: effects of memory-loss and mutation — •Tobias Galla — The University of Manchester, School of Physics and Astronomy, Schuster Building, Manchester M13 9PL, UK

The dynamics of players with finite memory capacities learning to play a two-person game can be described by the so-called Sato-Crutchfield equations, a modification of the standard replicator dynamics. In this talk we will present a statistical mechanics analysis of such dynamics in the context of games with large random payoff matrices. Our main tool are here generating functionals drawn from spin glass physics, and a subsequent fixed point and stability analysis. A transition is found between a stable ergodic fixed point phase at large memory loss rate, and an unstable, potentially chaotic phase at slow memory-loss. We will also discuss the influence of copying errors in the reproduction process, as modelled by random replicator-mutator equations.