Hamiltonian evolutionary games

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jun 2015Embargo end date: 01 Jan 2014 English Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Journal of Dynamics and Games, volume 2, pages 33-49 (issn: 2164-6066,

Copyright policy )Funded by:FCT | Geometry and Mathematical...

Authors: Alishah, Hassan Najafi; Duarte, Pedro;

doi: 10.3934/jdg.2015.2.33 , 10.48550/arxiv.1404.5900

arXiv: 1404.5900

Hamiltonian evolutionary games

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Abstract

We introduce a class of o.d.e.'s that generalizes to polymatrix games the replicator equations on symmetric and asymmetric games. We also introduce a new class of Poisson structures on the phase space of these systems, and characterize the corresponding subclass of Hamiltonian polymatrix replicator systems. This extends known results for symmetric and asymmetric replicator systems.

23 pages, one figure

Keywords

Dynamic games, Evolutionary games, Poisson Hamiltonian systems, evolutionary games, Dynamical Systems (math.DS), Nonlinear differential equations in abstract spaces, Hamiltonian polymatrix replicator equation, Mathematics - Symplectic Geometry, 91A22, 70G45, Dynamics induced by flows and semiflows, FOS: Mathematics, Symplectic Geometry (math.SG), Mathematics - Dynamical Systems

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