Regensburg 2010 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 11: Evolutionary Game Theory II (joint SOE, BP)

BP 11.1: Vortrag

Dienstag, 23. März 2010, 11:15–11:30, H44

Evolutionary dynamics, intrinsic noise and cycles of co-operation — •Alex Bladon, Tobias Galla, and Alan J McKane — Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom

The puzzle of how co-operation emerges in evolving populations subject to natural selection is unsolved, and the dynamic interaction of co-operation and defection is a current topic of wide interest in game theory. Periodic cycles between co-operation, defection and retaliation have been reported in numerical simulations of the iterated prisoner's dilemma in small populations of evolving agents [PNAS, 102, 31, 10797-10800, 2005]. Using tools from statistical mechanics and non-linear dynamics we here provide an analytical underpinning of these numerical observations and show that such cycles are the signature of amplified coherent oscillations sustained by demographic noise. We derive effective Langevin equations describing these oscillations and compute their power spectra analytically in the limit of large, but finite populations and in excellent agreement with numerical simulations. Our analytical theory reveals that the amplitude of these stochastic oscillations is, to a large degree, set by the inverse real part of the relevant eigenvalue of the deterministic dynamics, and that it can hence become singular near a Hopf bifurcation. Macroscopic oscillations are then observed even at large system sizes. Our analysis extends to cases in which errors of the 'trembling hand' type are considered, and where the strategy space includes a win-stay, lose-shift action.