The social cost problem, rights, and the (non)empty core

• Date: 01 April 2019
• Author: Alain Marciano,Philippe Solal,Stéphane Gonzalez
• DOI: http://doi.org/10.1111/jpet.12334
• Published date: 01 April 2019

Received: 16 October 2017

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Accepted: 11 August 2018

DOI: 10.1111/jpet.12334

ORIGINAL ARTICLE

The social cost problem, rights, and the

(non)empty core

Stéphane Gonzalez

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Alain Marciano

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Philippe Solal

1

1

Groupe d’analyse et de théorie économique,

Université de Saint‐Etienne, Saint‐Etienne,

France

2

Montpellier Recherche en Économie,

Université de Montpellier, Montpellier,

France

Correspondence

Stéphane Gonzalez, Université de

Saint‐Etienne, CNRS, GATE L‐SE UMR 5824,

F‐42023 Saint‐Etienne, France.

Email: stephane.gonzalez@univ-st-etienne.fr

Funding information

Agence Nationale de Recherches, Grant/

Award Numbers: ANR‐11‐IDEX‐0007,

ANR‐10‐LABX‐ll‐0l, ANR‐13‐BSHS1‐0010;

In‐depth UDL 2018; Programme Avenir Lyon

Saint‐Etienne of Université de Lyon

Abstract

We revisit the “Coase theorem”through the lens of a

cooperative game model which takes into account the

assignment of rights among agents involved in a problem

of social cost. We consider the case where one polluter

interactswithmanypotentialvictims.Givenanassign-

ment or a mapping of rights, we represent a social cost

problem by a cooperative game. A solution consists in a

payoff vector. We introduce three properties for a

mapping of rights. First, core compatibility indicates that

the core of the associated cooperative games is none-

mpty. Second, Kaldor‐Hicks core compatibility indicates

that there is a payoff vector in the core where victims are

fully compensated for the damage once the negotiations

are completed. Third, no veto power for a victim says that

novictimhasthepowertovetoanagreementsignedby

the rest of the society. We then demonstrate two main

results. First, core compatibility is satisfied if and only if

the rights are assigned either to the polluter or to the

entire set of victims. Second, there is no mapping of

rights satisfying Kaldor‐Hicks core compatibility and no

veto power for a victim.

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INTRODUCTION

After George Stigler coined the term, and invented its first version (Stigler, 1966, p. 113), the “Coase

theorem”has been reformulated many times, up to the point that it can be said that there does not exist one

but many Coase theorems.

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Despite their differences, these versions can nonetheless be characterized by

J Public Econ Theory. 2019;21:347–365. wileyonlinelibrary.com/journal/jpet © 2018 Wiley Periodicals, Inc.

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See a presentation of the different versions in Medema (2011, 2017) and Medema and Zerbe (2000).

two theses. First, the efficiency thesis according to which in the absence of transaction costs and if property

rights are well defined, agents will always bargain to reach an optimal allocation of resources; second, the

invariance or neutrality thesis according to which the outcome of bargaining is independent of the distribution

of rights. Thus, strictly speaking, it can be said the Coase theorem holds if both theses are verified

simultaneously.

Around these theses, a particularly important literature developed and the theorem was refined in many

directions. Attempts were made to generalize it—in particular because Ronald Coase, in “The Problem of

Social Cost" (1960), reasoned with two agents only—or to demonstrate under whichconditions it is verified—

because of its assumption of zero transaction costs. The models were then developed in terms of competitive

equilibrium (e.g., Chipman & Tian, 2012; Hurwicz, 1995), (perfect) Nash equilibrium of a strategic/bargaining

game (e.g., Anderlini & Felli, 2001, 2006; Ellingsen & Paltseva, 2016; Lee & Sabourian, 2007), of the

nonemptiness of the core of a cooperative game (e.g., Aivazian & Callen, 1981; Aivazian, Callen, &

Lipnowski, 1987; Ambec & Kervinio, 2016; Coase, 1981; Shapley & Shubik, 1969). In this paper, we also adopt

a cooperative approach. Itdiffersfromtheabove‐mentioned works in that we provide necessary and

sufficient conditions under which the assignment of rights between groups of agents leads to a

nonempty core.

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The model

We consider a large class of social cost problems between a finite set of potential victims and only one

polluter; transaction costs are supposed to be equal to zero. The activity of the polluter creates damage that

affects the victims. We propose to describe this damage by nondecreasing functions on the set of activity

levels of the polluter. In a similar manner, the benefit function of the polluter is assumed to be nondecreasing

on his or her set of activity levels. Hence, unsurprisingly, the victims and the polluter have conflicting

interests.

The payoffs that agents may or will receive after these conflicts are solved are obviously shaped by the law that

preexists and frames economic and social interactions. But they are not given by or specified in the law. The law,

general and abstract, applies to the whole set of social cost problems, which means that it specifies how a problem

of social cost, in abstract terms, should be treated—who can negotiate and with whom—but does not say what

should be the payoffs to a specific social cost problem. This is decided by the parties in the negotiation. In other

words, because it shapes interactions between (groups) of agents, the law affects how these (groups) of individuals

will negotiate with each other but does not specify the individual payoffs that will result from the negotiation. Thus,

the law also gives the parties a certain leeway to negotiate a binding agreement to the specific problem of social

cost in which they can be involved.

The negotiation, which takes place between the polluter and the victims, aims at signing a binding

agreement about how much activity the polluter will be allowed to undertake—that is, how much pollution he

is authorized to generate—and how much agents are compensated. For their part, the victims may gather

themselves in coalitions to negotiate with the polluter. And monetary transfers can be freely made within a

coalition.

The possibility or permission granted to any group of agents who want to form a coalition with the purpose a

binding agreement with the polluter corresponds to what we call a right. That right, to be more precise, gives the

possibility to a coalition to select the best contract for itself. Obviously, a large number of coalitions of agents can

have the right to decide the level of production of the polluter, as well as how much compensation its members will

receive. The set of all the possible rights granted to the polluter and victims form what we call a mapping or an

assignment of rights.

In our model, we impose s ome reasonable condition s on the mappings of rights. Firs t, independence:

A mapping of rights is independent from the respective benefi t and damage functions of the indivi duals involved

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GONZALEZ ET AL.