Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games

• Published date: 01 December 2016
• DOI: http://doi.org/10.1111/jpet.12205
• Author: PHILIPPE SOLAL,MARC DESCHAMPS,SYLVAIN BÉAL
• Date: 01 December 2016

COMPARABLE AXIOMATIZATIONS OF TWO ALLOCATION RULES

FOR COOPERATIVE GAMES WITH TRANSFERABLE UTILITY

AND THEIR SUBCLASS OF DATA GAMES

SYLVAIN B ´

EAL

Univ. Bourgogne Franche-Comt´

e

MARC DESCHAMPS

Univ. Bourgogne Franche-Comt´

e

PHILIPPE SOLAL

Universit´

e de Saint-Etienne

Abstract

The axiom of balanced collective contributions is introduced as a col-

lective variant of the axiom of balanced contributions proposed by My-

erson. It requires the identical average impact of the withdrawal of any

agent from a game on the remaining population. It turns out that the

axiom of balanced collective contributions and the classical axiom of

efficiency characterize the equal allocation of nonseparable costs, an

allocation rule that is extensively used in cost allocation problems and

in accounting. In particular, the equal allocation of nonseparable costs

coincides with the nucleolus on the class of data games within the Euro-

pean REACH legislation. While our result does not hold on data games,

extra axioms enable provision of comparable characterizations of the

equal allocation of nonseparable costs and the Shapley value on this

class of games.

1. Introduction

Cost allocation problems arise in many real-life situations, where individuals, all with

their own motivations, decide to work together. In these situations the problem is to

divide the joint costs, which result from the cooperation among the participants. Such

Sylvain B´

eal, CRESE EA3190, Univ. Bourgogne Franche-Comt´

e, F-25000 Besanc¸on, France

(sylvain.beal@univ-fcomte.fr).

Marc Deschamps, CRESE EA3190, Univ. Bourgogne Franche-Comt´

e, F-25000 Besanc¸on, France

(marc.deschamps@univ-fcomte.fr).

Philippe Solal, Universit´

e de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France

(philippe.solal@univ-st-etienne.fr).

The authors are grateful to Jenny Helstroffer and two anonymous reviewers for valuable com-

ments. Financial support by the National Agency for Research (ANR)—research programs “Dyna-

MITE: Dynamic Matching and Interactions: Theory and Experiments,” contract ANR-13-BSHS1-0010,

and “Damage,” contract ANR-12-JSH1-0001, 2012–2015—and the “Math´

ematiques de la d´

ecision pour

l’ing´

enierie physique et sociale” (MODMAD) project is gratefully acknowledged.

Received April 26, 2016; Accepted April 26, 2016.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (6), 2016, pp. 992–1004.

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