Noncooperative Foundation of Cooperative Actions: The Generalized Nash Program

We demonstrate how to construct coalition structures with any number of coalitions from noncooperative actions of individual agents. The approach expands the traditional noncooperative game of Nash for the field of noncooperative coalition formation. The suggested game embeds a coalition structure formation mechanism and has two outcomes: an allocation of players over coalitions and payoffs for every player. An individual strategy is a tuple, a coalition structure, and a strategy for it. A player has a set of strategies for every coalition structure. Coalition structures can be described by the Young diagrams. A (social) mechanism transforms a set of all individual strategies into some final one, with explicit allocation of players over coalitions, in a style of folk theorems in a long run. The mechanism has an enforcement power to eliminate conflicts of individual choices. A final coalition structure has a set of individual payoffs. As usual, every game has an equilibrium in mixed strategies, which is different from results of cooperative game theory. The game of Nash is a partial case of the presented model. We demonstrate how to construct a noncooperative stability criteria for the strong Nash equilibrium.