Dresden 2009 – wissenschaftliches Programm
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AGSOE: Arbeitsgruppe Physik sozio-ökonomischer Systeme
AGSOE 14: Poster Session
AGSOE 14.1: Poster
Mittwoch, 25. März 2009, 18:10–20:00, P1B
Extinction time of three-strategy cyclic coevolution in finite populations — •Markus Schütt1 and Jens Christian Claussen2,1 — 1Theor. Phys. & Astrophys., CAU Kiel — 2Neuro- und Bioinformatik, U zu Lübeck
In the limit of large populations, coevolutionary dynamics of interacting species (in biology) or strategies (of social individuals) is commonly described by the replicator equations of evolutionary game theory.
In finite populations the microscopic dynamics however is a discrete stochastic process, based on such, fixation and extinction times of strategies can be calculated,
see [1] for an introduction and overview.
In finite populations, the 1/N corrections can be conveniently described by a Fokker-Planck equation
which can lead to counterintuitive effects as a stability reversal (“drift reversal”) in
games between two populations [2].
In [3] we have shown analytically that such a drift reversal also is observed for a Rock-Papers-Scissors (RPS) game within one population, provided that the game is no longer zero-sum:
if the bank looses in the play, biodiversity of strategies is stabilized even in a well-mixed (nonspatial) population.
Here we investigate the extinction time for the non zero-sum RPS game. Its scaling with N changes between
exponential (positive-sum RPS) and polynomial
(zero-sum and negative-sum RPS) scaling, and is
consistent with the results from the drift reversal picture.
[1] Martin Nowak, Evolutionary Dynamics, Harvard (2007).
[2] A Traulsen JC Claussen C Hauert,
PRL 95, 238701 (2005)
[3] JC Claussen A Traulsen PRL 100, 058104 (2008)