Journal of Dynamics and Games (JDG)

Hamiltonian evolutionary games

Pages: 33 - 49, Volume 2, Issue 1, January 2015      doi:10.3934/jdg.2015.2.33

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Hassan Najafi Alishah - Departamento de Matemática and CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal (email)
Pedro Duarte - Departamento de Matemática and CMAF, Faculdade de Ciências,Universidade de Lisboa, Campo Grande, Edi ficio C6, Piso 2, 1749-016 Lisboa, Portugal (email)

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.

Received: May 2014;      Revised: February 2015;      Available Online: June 2015.