March 17, 2010 Wednesday 15:30
Tonguç Rador, Bogazici University
Merger Dynamics in Three Agent Games

Abstract: We present the consequences of mergers in a competitive society where the unit of competition is a struggle to earn a point among three agents of the society. The struggle is decided with a comparison function between the points of the agents. The points are distributed from an infinite pool, that is there is no transfer of points between agents. We first review the general theory of three agent games where mergers are not allowed, that is no alteration of the competition is permitted. This case is exactly soluble giving rise to various interesting social structures in the long time limit. After this review we present our findings on the effects of mergers. We present two flavors of mergers. One where the two lowest ranking players merge against the largest ranking one if the point sum of the former is greater than that of the latter. This case yields stratification of the society in the long run. The other flavor of the mergers we study is representative of a regulatory mechanism where mergers are allowed only within the subset of players with large rate of point gain. We show that exact solutions are possible for the extremely competitive limit; where no-mergers favor (with unit probability) the agent with largest point and mergers favor (with unit probability) the agent in the middle.