Regensburg 2007 – scientific programme

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 7: Economic Models and Evolutionary Game Theory I

AKSOE 7.4: Talk

Tuesday, March 27, 2007, 11:45–12:15, H8

Agents under pressure: Altrusim before the transition to extinction — •Konstantin Klemm — Bioinformatics, Leipzig University, H"artelstr. 16-18, D-04107 Leipzig

We study the evolution of altruism in spatially extended populations at the survival-extinction transition. At contrast with earlier spatial models, e.g. [Nowak and May, Nature (1992)], we consider variations in the population density by allowing lattice sites to be empty. As the selective pressure p, defined as the death rate of agents in the absence of cooperating neighbors, approaches the critical value p_c from below, the dominance of defectors becomes unstable at a value p_u < p_c. Cooperators can invade and become dominant. This effect — cooperation before extinction — is observed whenever the total benefit is larger than the cost incurred by the altruistic act. For a sufficiently large benefit-cost ratio, the increase in the number of cooperators is larger than the decrease in the number of defectors as p rises from p_u to p_c. Thus the overall population density increases as a function of the pressure. These properties of the phase diagram are derived analytically using pair approximation.