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Multiple-trial conflicts and stochastic evolutionary game dynamics

Part of: Game theory Markov processes

Published online by Cambridge University Press:  01 July 2016

Lorens A. Imhof
Lorens A. Imhof*
Affiliation:
Bonn University
*
∗ Postal address: Statistische Abteilung und Hausdorff-Zentrum für Mathematik, Universität Bonn, Adenauerallee 24-42, 53113 Bonn, Germany. Email address: limhof@uni-bonn.de
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Abstract

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We consider stochastic replicator processes for games that are composed of finitely many trials. Several general results on the relation between Nash equilibria and the long-run behaviour of the stochastic processes are proved. In particular, a sufficient condition is given for almost sure convergence to a state where everyone plays in every trial a strict Nash equilibrium. The results are applied to multiple-trial conflicts based on wars of attrition and on sperm competition games with fair raffles, respectively.

Keywords

Nash equilibriumrandom strategystochastic differential equationstochastic replicator dynamicswar of attrition

MSC classification

Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary: 91A22: Evolutionary games 92D25: Population dynamics (general)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 4 , December 2008 , pp. 1174 - 1197
Copyright
Copyright © Applied Probability Trust 2008 

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