Bonabeau model on fully occupied site graphs

TL;DR

This paper analyzes the Bonabeau model on fully occupied site graphs, deriving stability bounds for the egalitarian state and introducing a competing model where all fights conclude in finite time.

Contribution

It extends the Bonabeau model to fully occupied graphs and establishes a universal stability bound, also proposing a finite-time fight resolution model.

Findings

Derived a critical stability bound for the egalitarian state.

Proposed a model where all fights end in finite time on all site graphs.

Extended the analysis of the Bonabeau model beyond finite lattices.

Abstract

The Bonabeau model is a competing model where agents fight to maintain or change their positions. Originally studied on a finite lattice, in this model, one agent is randomly selected to move to a neighboring site chosen at random. If the neighboring site is vacant, the agent moves there. However, if the site is occupied, a fight ensues. If the agent wins, they switch places with the other agent; otherwise, they remain in their original position. We investigate the Bonabeau model on fully occupied site graphs and derive a critical bound for the stability of the egalitarian state applicable to all fully occupied connected site graphs. Furthermore, we develop a competing model where all fights end in finite time on all site graphs.