Hamiltonian evolutionary games

Hassan Najafi  Alishah; Pedro  Duarte

doi:10.3934/jdg.2015.2.33

Article Contents

2015, Volume 2, Issue 1: 33-49. Doi: 10.3934/jdg.2015.2.33

This issue Previous Article Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation Next Article On noncooperative $n$-player principal eigenvalue games

Hamiltonian evolutionary games

Hassan Najafi Alishah^1, and
Pedro Duarte^2,

1.
Departamento de Matemática and CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa
2.
Departamento de Matemática and CMAF, Faculdade de Ciências,Universidade de Lisboa, Campo Grande, Edificio C6, Piso 2, 1749-016 Lisboa

Received: May 2014

Revised: February 2015

Published: January 2015

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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.

Keywords:

Evolutionary games,
Hamiltonian polymatrix replicator equation,
poisson Hamiltonian systems.

Mathematics Subject Classification: Primary: 91A22, 37C10; Secondary: 34G20, 53D17.

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