Some equivalence results for a bargaining set in finite economies

• Published date: 01 June 2018
• Author: Emma Moreno‐García,Javier Hervés‐Estévez
• DOI: http://doi.org/10.1111/ijet.12149
• Date: 01 June 2018

doi: 10.1111/ijet.12149

Some equivalence results for a bargaining set in finite

economies

Javier Herv´

es-Est´

evez∗and Emma Moreno-Garc´

ıa†

We presenta bargaining set for finite economies using Aubin’s (1979) veto and show its coinci-

dence with the set of Walrasianallocations, providing a discrete approach to the characterization

of competitiveequilibria obtained by Mas-Colell (1989) for continuum economies. Wealso study

how the restriction on the formation of coalitions affects the bargaining set. In the last part of

the work, using our equivalence result along with some known characterizations of Walrasian

allocations, we state additional interpretations of the bargaining set.

Key wor ds bargaining set, coalition, core, veto mechanism

JEL classification D51, D11, D00

Accepted 16 January 2017

1 Introduction

Aumann and Maschler (1964) introduced the concept of the bargaining set, containing the core

of a cooperative game. The main idea is to inject a sense of credibility and stability into the veto

mechanism, permitting the implementation of some allocations which otherwise would be formally

blocked, although in a non-credible way. Thus, only objections without counter-objections are

considered as credible or justified, and consequently,blocking an allocation becomes more difficult.

This original concept of the bargaining set was later adapted toatomless economies by Mas-Colell.

Under generality conditions similar to those required in Aumann’s (1964) core-Walras equivalence

theorem, Mas-Colell (1989) showed that the bargaining set and the competitiveallocations coincide

for continuum economies.

In the finite economy framework the core strictly contains the set of Walrasian allocations.

Debreu and Scarf (1963) formalized Edgeworth’s(1881) conjecture showing that the core and the set

of Walrasianallocations become arbitrarily close whenever a finite economy is replicated a sufficiently

large number of times. This result yields the definition of Edgeworth equilibrium1for an economy

with a finite number of agents as an attainable allocation whose r-fold repetition belongs to the core

∗Facultad de Econom´

ıa y Empresa, Universidadde Salamanca, Salamanca, Spain. Email: emmam@usal.es

†Research Group in EconomicAnalysis, Universidad de Vigo, Spain.

Weare especially grateful to Carlos Herv´

es-Beloso for his helpful comments and suggestions. Weare also indebted to Jo˜

ao

Correia da Silva, Marta Faias, and the participants in the European Workshop on General Equilibrium Theory (EWGET

2013, 2014, and 2015), in the V Workshopon Economic Analysis held in Naples in January 2014, and in the UECE Lisbon

Meetings 2014: Game Theory and Applications, where previous versions of this work have been presented. This work

is partially supported by the Research Grants SA072U16 (Junta de Castilla y Le´

on), ECO2016-75712-P (Ministerio de

Econom´

ia y Competitividad) and RGEA-ECOBAS (AGRUP2015/08Xunta de Galicia).

1The concept of Edgeworth equilibrium was defined by Aliprantis et al. (1987); see also Florenzano (1990).

International Journal of Economic Theory 14 (2018) 129–138 © IAET 129

International Journal of Economic Theory