Eur. Phys. J. B 83, 289-299 (2011)
https://doi.org/10.1140/epjb/e2011-20326-4

Merger dynamics in three-agent games

¹ Boğaziçi University, Department of Physics Bebek 34342, İstanbul, Turkey
² İzmir Institute of Technology, Department of Physics Urla 35430, İzmir, Turkey
³ İş Bankası, İş Kuleler, Kule 1 Levent 34330, İstanbul, Turkey

Corresponding author: ^a tonguc.rador@boun.edu.tr

Received: 27 April 2011
Revised: 21 July 2011
Published online: 12 September 2011

Abstract

We present the effect of mergers, a term which we use to mean a temporary alliance, 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.