Coalition Formation in Games with Externalities

Abstract

This paper studies an extensive form game of coalition formation with random proposers in games with externalities. It is shown that an agreement will be reached without delay if any set of coalitions profits from merging. Even under this strong condition, the equilibrium coalition structure is not necessarily efficient. There may be multiple equilibria even in the absence of externalities, and symmetric players are not necessarily treated symmetrically in equilibrium. If the grand coalition forms without delay in equilibrium, expected payoffs must be in the core of the characteristic function game that assigns to each coalition its equilibrium payoff. Compared with the rule of order process of Ray and Vohra (Games Econ Behav 26:286–336, 1999), the bargaining procedure with random proposers tends to give a large advantage to the proposer, whereas the bargaining procedure with a rule of order tends to favor the responders. The equilibria of the two procedures cannot be ranked in general in terms of efficiency.

Preface to the Special issue on “Group Formation and Farsightedness”

“…In "Coalition Formation in Games with Externalities", Montero [15] considers partition function games that allow for externalities between coalitions and studies a coalitional bargaining model to determine the coalition structure that will emerge at equilibrium and the division of payoffs among coalition members. It is shown that when the partition function game is positive and fully cohesive, then in any stationary subgame perfect equilibrium of the extensive form game, a coalition structure is formed without delay.…”