A Strategic Implementation of the Shapley Value for the Nested Cost‐Sharing Problem

• Author: CHUN‐HSIEN YEH,YOUNGSUB CHUN,CHENG‐CHENG HU
• DOI: http://doi.org/10.1111/jpet.12190
• Published date: 01 February 2017
• Date: 01 February 2017

ASTRATEGIC IMPLEMENTATION OF THE SHAPLEY VALUE

FOR THE NESTED COST-SHARING PROBLEM

YOUNGSUB CHUN

Seoul National University

CHENG-CHENG HU

National Cheng Kung University

CHUN-HSIEN YEH

Academia Sinica

Abstract

When agents have different needs for a public facility but serving a

given agent allows serving all agents with smaller needs than his with-

out any extra cost, how should the agents divide the cost of the facil-

ity among themselves? We provide a strategic implementation of the

Shapley value for this class of cost-sharing problems. We introduce a

three-stage extensive form game that respects individual rationality and

show that there is one and only one subgame-perfect equilibrium out-

come of the game. Moreover,it is the allocation assigned by the Shapley

value.

1. Introduction

When a (public) facility is shared by agents having different needs for it but serving a

given agent allows serving any agent with smaller need than his without any extra cost,

how should the agents divide the cost of the facility among themselves?1This nested

cost-sharing problem can be applied to a number of real life situations. An example is

1This class of cost-sharing problems was initiated by Littlechild and Owen (1973). For a comprehensive

survey of the literature, see Thomson (2004).

Youngsub Chun, Department of Economics, Seoul National University, Seoul 151-746, Korea

(ychun@snu.ac.kr). Cheng-Cheng Hu, Department of Economics, National Cheng Kung University,

Tainan 70101, Taiwan (hucc@mail.ncku.edu.tw). Corresponding author: Chun-Hsien Yeh, Institute of

Economics, Academia Sinica, Taipei 115, Taiwan (chyeh@econ.sinica.edu.tw).

We would like to thank William Thomson, Hans Peters, Christopher Chambers, Cheng-Zhong Qin,

Walter Trockel, Tomas Sj¨

ostr¨

om, Yuan Ju, and David Perez-Castrillo for their comments. In particular,

we would like to thank the associate editor in charge and two referees for their helpful suggestions and

comments. Chun’s work was supported by the National Research Foundation of Korea Grant funded by

the Korean Government (NRF-2013S1A3A2055391). Yeh acknowledges financial support from Career

Development Award of Academia Sinica, Taiwan(AS-99-CDA-H01) and the grant of Ministry of Science

and Technology, Taiwan (NSC-102-2410-H-001-010-MY3). Hu acknowledges financial support from the

grant of Ministry of Science and Technology, Taiwan (NSC-102-2410-H-006-002-MY2).

Received September 28, 2014; Accepted November 22, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 19 (1), 2017, pp. 219–233.

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