Endogenous Formation of Coalitions

Abstract

THE FORMATION OF COALITIONS is a fundamental problem in game theory. By a is meant a group of (e.g., economic or political agents) which decide to act together, as one unit, relative to the rest of the players. This includes the instances of syndicates, unions, cartels, blocks, political parties, parliamentary coalitions, etc. We would like to emphasize that forming a does not eliminate the individual players as decision makers. In all interactions with the other players, members act as one unit (it may be useful to think of a representative agent taking their place);2 however, this arrangement will continue only as long as each player finds it desirable to act this way. Further bargaining occurs among the members of each on how to divide what they obtained together. Thus, the existence of implies that the interactions among the players will be conducted on two levels: first, among the coalitions, and second, within each coalition. Most of the existing models in economics and game theory assume that the structure is given exogenously; instead, we try here to obtain it as an endogenous outcome of our model. Namely, we want to be able to predict which will in fact form in each given situation.3 Our theory combines two kinds of game theoretic concepts: value and stability. The basic idea is, first, to evaluate the players' prospects in the various structures, and then, based on these values, to find which ones are stable. We will call this value coalition structure value, or for short. The reason we are considering coalition structures (i.e., partitions of the set of players into disjoint coalitions) rather than just coalitions is that, in general, players may find it to their advantage to join forces in some situations, and to act separately in others-all depending on the way the other participants are organized. This implies that both the value and the stability concepts should depend on the entire structure. The CS-value we analyze in this paper was first developed by Owen [7].