Dresden 2011 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 19: Economic Models and Evolutionary Game Theory II (with BP, DY)
SOE 19.2: Talk
Thursday, March 17, 2011, 14:15–14:30, GÖR 226
When does stochastic learning in game theory fixate ? — John Realpe-Gomez1, Bartosz Szczesny2, Luca Dall'Asta3, and •Tobias Galla4 — 1Politecnico di Torino, Corso Duca degli Abbruzzi 24, 10129 Torino, Italy — 2University of Leeds, Department of Applied Mathematics, School of Mathematics, Leeds LS2 9JT, UK — 3The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy — 4University of Manchester, School of Physics and Astronomy, Manchester M13 9PL, UK
Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can occur in stochastic learning of a fixed set of players interacting repeatedly in a given game. We study in detail the mechanisms behind these absorption phenomena, in particular we present analytical predictions for the resulting fixation times and provide a detailed comparison with fixation in evolutionary dynamics. Specific examples are discussed, including simple two-player games, but also multi-player games defined on networks, resulting in more complicated interaction structures. In the final part of the talk I will discuss an imitation dynamics leading to absorption at fixed points in the interior of strategy space, a phenomenon not usually observed in standard models of evolutionary dynamics.