The Power of a Coalition

If certain information is given about the “psychology” of the players who participate in an n-person cooperative game, concerning their bargaining abilities, their moral codes, their roles in the various coalitions and their a priori expectations, then it is possible to define a measure for the power of each coalition which, perhaps, is a better description of the game than the usual characteristic function. The required information, called the standard of fairness of the players is a Thrall partition function which satisfies certain requirements. Its determination is discussed both from an experimental and from a theoretical point of view. In terms of the power, every game becomes a constant-sum game. Applications to the von Neumann and Morgenstern solutions and to the bargaining set are discussed.