Coalition Formation as a Dynamic Process

Let N be a set of players and X a set of states. Suppose that for each state in X and each coalition S (a nonempty subset of N), a possible set of “coalitional moves” (by S) to some subset of states is given. A mapfrom the current state to a probability distribution over the set of all coalitional moves feasible at that state induces a dynamic process on X. Noting that moves are associated with actions taken by coalitions, we call this a process of coalition formation. Under such a process players receive (additive discounted) utility from the entire path of states. This induces a value for each player in the standard way, as a function of the going state.