Pattern formation,social forces,and diffusion instability in games with success-driven motion |
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Authors: | Dirk Helbing |
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Institution: | 1.ETH Zurich, UNO D11, Universit?tstr. 41,Zurich,Switzerland |
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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. |
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Keywords: | PACS" target="_blank">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 |
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