Allocating joint costs by means of the nucleolus

Abstract

This paper presents a sufficient condition for the nucleolus to coincide with the SCRB method vector and for nonemptiness of the core. It also studies the reasonableness and the monotonicity of the nucleolus under this condition. Finally it analyses the class of games satisfying the condition and compares it with the classes of convex games, subconvex games and the class Q of Driessen and Tijs.

Empirical Study on Fair Allocation of Joint Project by Cooperative Game Theory-A Case of Local Bus Transportation Service in Japan-

“…Among them, we focus on the unique allocation concepts based on the core such as nucleolus (Schmeidler, 1969). It is known that the allocations by nucleolus and practical allocation method such as SCRB and Egalitarian Non-Separable Cost method (ENSC) may coincide (Nakayama, 1976;Legros, 1986;Driessen and Funaki, 1991). Therefore, it is likely that the concepts of nucleolus and its variants are acceptable in real joint projects including the allocating of costs for local bus transportation services by several municipalities.…”

“…Since their seminal studies, several variants and extensions have been developed (see the reviews by Krus and Bronisz, 2000;Monderer and Samet, 2002) and applied to the allocation of costs in joint projects (Young, 1985, Young, 1994. The relationships between these concepts and practical cost allocation methods such as the Separable Cost Remaining Benefit method (SCRB) have also been investigated (Nakayama, 1976;Legros, 1986;Driessen and Funaki, 1991). The results of these studies have helped to clarify the theoretical concept of fairness as held by practical allocation methods.…”

Collinearity between the Shapley value and the egalitarian division rules for cooperative games

“…The ENSC-value and the CIS-value are well known concepts in the game theoretic literature (cf. [2], [3], [4], [6], [7], [9], [11], [14]). The ENAC-value has been introduced by Driessen and Funaki (1993a), who presented three motivations for the study of this value 9 The formula (2.12) for the ENAC-value, which is the sum of the egalitarian division of the overall profits and some part of the difference between two average worth with respect to (n-2)-person In the next sections, we shall provide two types of sufficient conditions on the game so that the one-point solutions according to the Shapley value, the ENSC-value (or ENAC-value) and the CIS-value are collinear (i.e., lie on the same line).…”

Coincidence of and collinearity between game theoretic solutions

“…In the following three subsections we first review the conditions, as mentioned in Funaki (1986), Legros (1986) and Driessen (1983;1985;1988, page 73) respectively, and secondly, we reformulate their conditions in terms of the gap function. Subsection3.1.…”