Kinetic and Related Models (KRM)

On a continuous mixed strategies model for evolutionary game theory

Pages: 187 - 213, Volume 4, Issue 1, March 2011      doi:10.3934/krm.2011.4.187

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Astridh Boccabella - Dipartimento di Scienze di Base e Applicate per l’Ingegneria (SBAI), Università degli Studi “Sapienza” di Roma, Italy (email)
Roberto Natalini - Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, c/o Dip. di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1; I-00133 Roma, Italy (email)
Lorenzo Pareschi - Dipartimento di Matematica & CMCS, Università degli Studi di Ferrara, Italy (email)

Abstract: We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical properties of the model and global estimates. The asymptotic behavior and the stability of solutions in the case of two strategies is analyzed in details. Numerical schemes for two and three strategies which are able to capture the correct equilibrium states are also proposed together with several numerical examples.

Keywords:  Continuous mixed strategies, Replicator dynamics, Evolutionary Game Theory, Kinetic equations, Numerical methods.
Mathematics Subject Classification:  35Q91, 65R20, 45G10.

Received: October 2010;      Revised: November 2010;      Available Online: January 2011.