Issue Eur. Phys. J. B Volume 67, Number 3, February I 2009 Page(s) 345 - 356 Section Interdisciplinary Physics DOI 10.1140/epjb/e2009-00025-7 Published online 24 January 2009

Eur. Phys. J. B 67, 345-356 (2009)
DOI: 10.1140/epjb/e2009-00025-7

Pattern formation, social forces, and diffusion instability in games with success-driven motion

Dirk Helbing

ETH Zurich, UNO D11, Universitätstr. 41, 8092 Zurich, Switzerland

dhelbing@ethz.ch

Received 9 July 2008 / Received in final form 23 December 2008 / Published online 24 January 2009

Abstract
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome and dynamics of spatial games dramatically, in particular as it causes attractive or repulsive interaction forces. These forces act when the spatial distributions of strategies are inhomogeneous. However, even when starting with homogeneous initial conditions, small perturbations can trigger large inhomogeneities by a pattern-formation instability, when certain conditions are fulfilled. Here, these instability conditions are studied for the prisoner's dilemma and the snowdrift game. Furthermore, it is demonstrated that asymmetrical diffusion can drive social, economic, and biological systems into the unstable regime, if these would be stable without diffusion.

PACS
02.50.Le - Decision theory and game theory.
87.23.Ge - Dynamics of social systems.
82.40.Ck - Pattern formation in reactions with diffusion, flow and heat transfer.
87.23.Cc - Population dynamics and ecological pattern formation.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009

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