VON NEUMANN-MORGENSTERN SOLUTIONS TO COOPERATIVE GAMES WITHOUT SIDE PAYMENTS

Abstract

The use of side payments in the classical theory of ^-person games involves three restrictive assumptions. First, there must be a common medium of exchange (such as money) in which the side payments may be effected; next, the side payments must be physically and legally feasible; and finally, it is assumed that utility is "unrestrictedly transferable," i.e. that each player's utility for money is a linear function of the amount of money. These assumptions severely limit the applicability of the classical theory; in particular, the last assumption has been characterized by Luce and Raiffa [2, p. 233] as being "exceedingly restrictive—for many purposes it renders nperson theory next to useless." It is the purpose of this paper to present the outline of a theory that parallels the classical theory, but makes no use of side payments.* Our definitions are related to those given in [2, p. 234] and in [3], but whereas the previous work went no further than proposing definitions, the theory outlined here contains results which generalize a considerable portion of the classical theory. I t thus demonstrates that the restrictive side payment assumption is not necessary for the development of a theory based on the ideas of von Neumann and Morgenstern. Only a general description of the theory and statements of the more important theorems will be included here; details and proofs will be published elsewhere.