# On restricted bargaining sets

## Abstract

In this paper we analyze the behavior of bargaining sets in continuum economies when there are restrictions on the formation of coalitions. We provide several characterizations of Vind’s (J Math Econ 21:89–97, 1992) bargaining set in terms of its restricted versions, where not all the coalitions are formed. Moreover, we show that these equivalences do not hold for Mas-Colell’s (J Math Econ 18:129–139, 1989) bargaining set. These findings highlight the different nature of both notions of bargaining sets. Finally, we illustrate the impossibility of extrapolating our results to a more general setting.

## Keywords

Bargaining sets Coalitions Core Veto mechanism## JEL Classification

D51 D11 D00## Notes

### Acknowledgments

This work is partially supported by the Research Grants ECO2012-38860-C02-01 and 02 (Ministerio de Economía y Competitividad), RGEA and 10PXIB300141PR (Xunta de Galicia and FEDER). We are grateful to N. Allouch, J. Correia-da-Silva, M. Faias, G. Graziano, C. Hervés-Beloso, L. Koutsougeras, J. P. Torres-Martínez, the participants in the Simposio de la Asociación Española de Economía, December, 2012, and in the Naples Workshop on Economic Theory, January, 2013. We also thank an associated editor and two anonymous referees for comments and suggestions that indeed helped to improve the final version of this work.

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