Hamiltonian evolutionary games. (English) Zbl 1334.91017
Summary: 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.
MSC:
| 91A22 | Evolutionary games |
| 91A25 | Dynamic games |
| 37C10 | Dynamics induced by flows and semiflows |
| 34G20 | Nonlinear differential equations in abstract spaces |
Keywords:
evolutionary games; Hamiltonian polymatrix replicator equation; Poisson Hamiltonian systemsReferences:
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