Formation of coalition structures as a non-cooperative game
We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative simultaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and has two outcomes: an allocation of players over coalitions and a payoff for every player. Coalition structures of a game are described by Young diagrams. They serve to enumerate coalition structures and allocations of players over them. For every coalition structure a player has a set of finite strategies. A player chooses a coalition structure and a strategy. A (social) mechanism eliminates conflicts in individual choices and produces final coalition structures. Every final coalition structure is a non-cooperative game. Mixed equilibrium always exists and consists of a mixed strategy profile, payoffs and equilibrium coalition structures. We use a maximum coalition size to parametrize the family of the games. The non-cooperative game of Nash is a partial case of the model. The result is different from the Shapley value, a strong Nash, coalition-proof equilibria, core solutions, and other equilibrium concepts. We supply few non-cooperative coalition structure stability criteria.