Bargaining ability,the utility of playing a game,and models of coalition formation

A utility function for playing a given position in a game is developed as a natural extension of the utility function which defines the rewards available in the game. This function is determined by a player's opinion of his bargaining ability. A characterization of such utilities is obtained which generalizes previous results that the Shapley value and Banzhaf-Coleman index are both cardinal utility functions which reflect different bargaining abilities. The approach taken here is related to models of coalition formation.