Merger Dynamics in Three-Agent Games

TL;DR

This paper analyzes how mergers influence the dynamics of three-agent competitive models, providing an analytical solution in the fully competitive limit and revealing stratified, self-similar score distributions.

Contribution

It introduces a merger mechanism into three-agent models using a single competitiveness parameter and derives an analytical solution for the fully competitive case.

Findings

Score distribution is stratified and self-similar in the fully competitive limit.

Mergers increase agents' winning probabilities by combining forces.

Analytical solution characterizes the impact of mergers on dynamics.

Abstract

We present the effect of mergers in the dynamics of the three-agent model studied by Ben-Naim, Kahng and Kim and by Rador and Mungan. Mergers are possible in three-agent games because two agents can combine forces against the third player and thus increase their probability to win a competition. We implement mergers in this three-agent model via resolving merger and no-merger units of competition in terms of a two-agent unit. This way one needs only a single parameter which we have called the competitiveness parameter. We have presented an analytical solution in the fully competitive limit. In this limit the score distribution of agents is stratified and self-similar.