  The paper defines a non-cooperative simultaneous finite game to study
coalition structure formation with intra and inter-coalition externalities. The
novelty of the game is that the game definition embeds a \textit{coalition
structure formation mechanism}. This mechanism portions a set of strategies of
the game into partition-specific strategy domains, what makes every partition
to be a non-cooperative game with partition-specific payoffs for every player.
The mechanism includes a maximum coalition size, a set of eligible partitions
with coalitions sizes no greater than this number (which also serves as a
restriction for a maximum number of deviators) and a coalition structure
formation rule. The paper defines a family of nested non-cooperative games
parametrized by a size of a maximum coalition size. Every game in the family
has an equilibrium in mixed strategies. The equilibrium can generate more than
one coalition and encompasses intra and inter group externalities, what makes
it different from the Shapley value. Presence of individual payoff allocation
makes it different from a strong Nash, coalition-proof equilibrium, and some
other equilibrium concepts. The accompanying papers demonstrate applications of
the proposed toolkit.
