Long-Run Analysis of the Stochastic Replicator Dynamics in the Presence\n of Random Jumps

2012/06/02 by Andrew Vlasic, Vlasic, Andrew
Biochemistry, Genetics and Molecular Biology · Social Sciences · Mathematics · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1206.0344

Abstract

A further generalization of the stochastic replicator dynamic derived by\nFudenberg and Harris citeFH92 is considered. In particular, a Poissonian\nintegral is introduced to the fitness to simulate the affects of anomalous\nevents. For the two strategy population, an estimation of the long run behavior\nof the dynamic is derived. For the population with many strategies, conditions\nfor stability to pure strict Nash equilibria, extinction of dominated pure\nstrategies, and recurrence in a neighborhood of an internal evolutionary stable\nstrategy are derived. This extends the results given by Imhof citeI05.\n

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