Computing the constrained game function CGF(S) for n-person cooperative transferable utility normal form games

Abstract

This is the third in a series of articles dealing with computational programs for cooperative n-person game theory models. An APL computer program is described for calculating the constrained game function CGF(S) introduced by Charnes and his colleagues (Charnes, 1953). The constrained game function forms an important extension of the von Neumann-Morgenstern characteristic function. It indexes the expected value of coalitions when constraints prevent the free implementation of every distinguishable strategy choice alternative. This modelling approach could materially improve the descriptive accuracy of game theory analysis—especially in application settings where it is seldom reasonable to assume that coalitions have free and equal access to every apparent strategy alternative.