Asymptotic Dynamics of Hamiltonian Polymatrix Replicators

TL;DR

This paper investigates the long-term behavior of Hamiltonian polymatrix replicator systems, revealing their Hamiltonian structure and providing insights into their asymptotic dynamics within evolutionary game models.

Contribution

It establishes the Hamiltonian nature of the asymptotic dynamics in Hamiltonian polymatrix replicators, extending previous work on flow analysis on polytopes.

Findings

Asymptotic dynamics are Hamiltonian in nature.

The method captures edge-vertex heteroclinic networks.

Results apply to models in Evolutionary Game Theory.

Abstract

In a previous paper [3] we have studied flows defined on polytopes, presenting a new method to encapsulate its asymptotic dynamics along the edge-vertex heteroclinic network. These results apply to the class of polymatrix replicator systems, which contains several important models in Evolutionary Game Theory. Here we establish the Hamiltonian character of the asymptotic dynamics of Hamiltonian polymatrix replicators.