Evolutionary Stochastic Games

János Flesch, Thiruvenkatachari Parthasarathy, Frank Thuijsman () and Philippe Uyttendaele

Dynamic Games and Applications, 2013, vol. 3, issue 2, 207-219

Abstract: We extend the notion of Evolutionarily Stable Strategies introduced by Maynard Smith and Price (Nature 246:15–18, 1973 ) for models ruled by a single fitness matrix A, to the framework of stochastic games developed by Lloyd Shapley (Proc. Natl. Acad. Sci. USA 39:1095–1100, 1953 ) where, at discrete stages in time, players play one of finitely many matrix games, while the transitions from one matrix game to the next follow a jointly controlled Markov chain. We show that this extension from a single-state model to a multistate model can be done on the assumption of having an irreducible transition law. In a similar way, we extend the notion of Replicator Dynamics introduced by Taylor and Jonker (Math. Biosci. 40:145–156, 1978 ) to the multistate model. These extensions facilitate the analysis of evolutionary interactions that are richer than the ones that can be handled by the original, single-state, evolutionary game model. Several examples are provided. Copyright Springer Science+Business Media New York 2013

Keywords: Evolutionary games; Stochastic games; Evolutionarily stable strategy; Replicator dynamics (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13235-012-0059-2

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