The paper defines a family of nested non-cooperative simultaneous finite games to study coalition structure formation with intra and inter-coalition externalities. Every game has two outcomes - an allocation of players over coalitions and a payoff profile for every player. Every game in the family has an equilibrium in mixed strategies. The equilibrium can generate more than one coalition with a presence of intra and inter group externalities. These properties make it different from the Shapley value, strong Nash, coalition-proof equilibrium, core, kernel, nucleolus. The paper demonstrates some applications: non-cooperative cooperation, Bayesian game, stochastic games and construction of a non-cooperative criterion of coalition structure stability for studying focal points. An example demonstrates that a payoff profile in the Prisoners' Dilemma is non-informative to deduce a cooperation of players.