Formation of Coalition Structures As a Non-Cooperative Game

NRU Higher School of Economics , 2017. No. WP BRP 157/EC/2017.

Levando D. V.

The paper defines a family of nested non-cooperative simultaneous finite games to study coalition structure formation with intra and inter-coalition externalities. The novelties of the paper are: a definition of every games embeds a coalition structure formation mechanism. Every game has two outcomes - an allocation of players over coalitions and a payoff profile for every player. The family is parametrized by a maximum coalition size in every coalition structure (a partition) in a game. For every partition a player has a partition-specific set of strategies.  The mechanism portions a set of strategies of the game (a Cartesian product) into partition-specific strategy domains, what makes every partition to be itself a non-cooperative game with partition-specific payoffs for every player. Payoffs are assigned separately for every partition and are independent from the mechanism. 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 paper demonstrate some applications of the proposed toolkit: for non-cooperative fundamentals of cooperation in a coalition, Bayesian game, stochastic games and construction of a non-cooperative criterion of coalition structure stability.

Keywords: Non-Cooperative Games, некооперативные игры, cooperative games, кооперативные игры, Stochastic games, mixed strategies equilibrium, coalition structures, Bayesian games, non-cooperative criterion for coalition structure stability, равновесие по Нэпу, Байесовские игры, стохастические игры, некооперативный критерий стабильности