Merger dynamics in three agent games

Abstract

The thesis analyses the dynamics of merger in three agent games. The purpose of the study is to nd out how merger a ects the social structure. To begin with the de nition of a game, it is a series of competitions. In these competitions three players are randomly picked and they compete against each other with a given winning probability with respect to their actual points. In competitive games this means that the player with the highest score is favored. In our model, there are two types of competitions with di erent probability sets. First is a competitive game and we de ne the second as merger game. Players act separately in competitive games. In merger games two players combine their points and act as a single player against the third. This would make sense if the players that merge increase their winning chance. The merger is realized by resolving three agent games in terms of two agent mini tournaments. In a microscopic tournament, all players that participate in the microscopic competition will play a two agent game against each other and winning will be determined by the maximum wins in the mini tournament. Winner will gain one point. De ning merger in three agent games doesn't violate the competitive structure of the game. Meanwhile it yields sub-societies among the total hierarchy.