The Generalized Nucleolus as a Solution of a Cost Allocation Problem

It has recently become clear that ideas and methods from the theory of cooperative games can be used quite successfully to solve cost allocation problems. Among the extensive literature (see Loughlin, 1977) dealing with this subject we shall concentrate on an article based on work carried out at IIASA (Young et al., 1980). The authors of this article used game theory principles of rationality to solve the problem of sharing the cost of a joint municipal water supply system among the group of Swedish municipalities participating in the project. In Section 1 we introduce the notion of the generalized nucleolus. The nucleolus and all its known mcdifications are special cases of our definition. Section 2 describes a method for calculating the nucleolus that can be readily implemented on a computer, and Section 3 puts forward an analytical criterion for testing the results. In Section 4 we describe some applications of the method to linear-fractional excess functions and convex games, and a number of formulas for three-person games are also given. Section 5 contains numerical results for seven modifications of the nucleolus for the six-person game discussed in Young et al. (1980)