Hamiltonian Evolutionary Games

TL;DR

This paper introduces a new class of differential equations and Poisson structures to generalize replicator dynamics in polymatrix games, extending existing results for symmetric and asymmetric cases.

Contribution

It develops a generalized framework for Hamiltonian polymatrix replicator systems using novel Poisson structures, broadening the scope of evolutionary game dynamics.

Findings

Introduces a new class of ODEs for polymatrix games.

Defines novel Poisson structures on phase space.

Characterizes Hamiltonian polymatrix replicator systems.

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.