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Seoul Journal of Economics - Vol. 20 , No. 2
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Seoul Journal of Economics - Vol. 20, No. 2, pp. 223-237
Abbreviation: SJE
ISSN: 1225-0279 (Print)
Print publication date 31 May 2007
Received 09 Oct 2006 Revised 27 Feb 2007

On the Coincidence of the Shapley Value and the Nucleolus in Queueing Problems
Youngsub Chun ; Toru Hokari
Professor, School of Economics, Seoul National University, Seoul 151-746, Korea, Tel: +82-2-880-6382 (ychun@snu.ac.kr)
Associate Professor, Institute of Social Sciences, University of Tsukuba, 1-1-1 Ten’no-dai, Tsukuba, Ibaraki 305-8571, Japan

Funding Information ▼

JEL Classification: C71, D63, D71

Abstract

Given a group of agents to be served in a facility, the queueing problem is concerned with finding the order to serve agents and the (positive or negative) monetary compensations they should receive. As shown in Maniquet (2003), the minimal transfer rule coincides with the Shapley value of the game obtained by defining the worth of each coalition to be the minimum total waiting cost incurred by its members under the assumption that they are served before the non-coalitional members. Here, we show that it coincides with the nucleolus of the same game. Thereby, we establish the coincidence of the Shapley value and the nucleolus for queueing problems. We also investigate the relations between the minimal transfer rule and other rules discussed in the literature.

Keywords: Queueing problems, Minimal transfer rule, Shapley value, Nucleolus, Coincidence
Acknowledgments

We are grateful to William Thomson, Yukihiko Funaki, René van den Brink, Eun Jeong Heo, and a referee for their comments. Chun acknowledges the support from the Advanced Strategy Program (ASP) of the Institute of Economic Research, Seoul National University, and Hokari from the Ministry of Education, Culture, Sports, Science, and Technology in Japan under grant No. 15730089 and 18730125.

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