On coalition formation in simple games: A mathematical analysis of Caplow's and Gamson's theories

In this paper, we propose a theory of coalition formation in simple games. The process of coalition formation is modeled as an abstract game. Two solutions of abstract games, the core and the dynamic solution, are used as the predictions of our model. Two classical theories of coalitions in sociology due to Caplow and Gamson are reformulated in a more general and mathematical setting. These theories are then analyzed using the techniques of our theory.