An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game

TL;DR

This paper examines the replicator dynamics of an asymmetric Hawk-Dove game with four strategies, analyzing equilibrium points, stability, bifurcations, and connecting results to the standard game through theoretical and numerical methods.

Contribution

It provides a comprehensive analysis of the asymmetric Hawk-Dove game, including equilibrium classification, stability conditions, bifurcation analysis, and connections to classical models.

Findings

Identification of all equilibrium points and their stability

Characterization of bifurcations based on game parameters

Numerical simulations illustrating global system behaviors

Abstract

We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detailed account of the local bifurcations that the system exhibits based on choices of the typical Hawk-Dove parameters and . We also give details on the connections between the results found in this work and those of the standard two-strategy Hawk-Dove game. We conclude the paper with some examples of numerical simulations that further illustrate some global behaviours of the system.