  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.
