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Bargaining-equilibrium equivalence

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  • Bhowmik, Anuj
  • Saha, Sandipan

Abstract

The paper tries to answer one of the more nascent questions in the literature on general equilibrium theory by investigating the equivalence between the set of club equilibrium states and the bargaining set for a club economy. Clubs in this framework are treated in a parallel fashion to private goods as articles of choice. Each club membership is composed of three components: (i) the individual's characteristics; (ii) the profile of the club. and (iii) the club project. Thus clubs are identified through their profile and the particular project they undertake. We introduce the bargaining set for such an economy in lieu of Mas-Colell \cite{Mas : 89} and define a two-step veto mechanism. In this paper we establish that non-equilibrium states are those against which there exist a set of agents who agree upon a mutually beneficial trade agreement amongst themselves or in other words there exists a Walrasian objection to such states. In what follows from the literature is that Walrasian objections are justified as well which thereby helps us establish our equivalence.

Suggested Citation

  • Bhowmik, Anuj & Saha, Sandipan, 2023. "Bargaining-equilibrium equivalence," MPRA Paper 117194, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:117194
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    References listed on IDEAS

    as
    1. Engl, Greg & Scotchmer, Suzanne, 1996. "The core and the hedonic core: Equivalence and comparative statics," Journal of Mathematical Economics, Elsevier, vol. 26(2), pages 209-248.
    2. Bhowmik, Anuj & Saha, Sandipan, 2022. "On blocking mechanisms in economies with club goods," MPRA Paper 114928, University Library of Munich, Germany.
    3. Ellickson, Bryan & Grodal, Birgit & Scotchmer, Suzanne & Zame, William R., 2001. "Clubs and the Market: Large Finite Economies," Journal of Economic Theory, Elsevier, vol. 101(1), pages 40-77, November.
    4. Scotchmer, Suzanne, 1996. "Externality pricing in club economies," Ricerche Economiche, Elsevier, vol. 50(4), pages 347-366, December.
    5. Gilles, Robert P. & Scotchmer, Suzanne, 1997. "Decentralization in Replicated Club Economies with Multiple Private Goods," Journal of Economic Theory, Elsevier, vol. 72(2), pages 363-387, February.
    6. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
    7. Robert M. Anderson & Walter Trockel & Lin Zhou, 1997. "Nonconvergence of the Mas-Colell and Zhou Bargaining Sets," Econometrica, Econometric Society, vol. 65(5), pages 1227-1240, September.
    8. Liu, Jiuqiang, 2017. "Equivalence of the Aubin bargaining set and the set of competitive equilibria in a finite coalition production economy," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 55-61.
    9. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    10. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
    11. Jiuqiang Liu & Huihui Zhang, 2016. "Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1095-1109, November.
    12. Anuj Bhowmik & Japneet Kaur, 2022. "Competitive equilibria and robust efficiency with club goods," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2022-014, Indira Gandhi Institute of Development Research, Mumbai, India.
    13. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    14. Scotchmer, Suzanne, 1997. "On price-taking equilibria in club economies with nonanonymous crowding," Journal of Public Economics, Elsevier, vol. 65(1), pages 75-88, July.
    15. Aumann, Robert J., 1973. "Disadvantageous monopolies," Journal of Economic Theory, Elsevier, vol. 6(1), pages 1-11, February.
    16. Scotchmer, Suzanne & Wooders, Myrna Holtz, 1987. "Competitive equilibrium and the core in club economies with anonymous crowding," Journal of Public Economics, Elsevier, vol. 34(2), pages 159-173, November.
    17. Andreu Mas-Colell, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 94(4), pages 625-641.
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    More about this item

    Keywords

    Club goods; Bargaining set; Walrasian objection; Justified objection; Bargaining-Equilibrium equivalence.;
    All these keywords.

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D6 - Microeconomics - - Welfare Economics
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • H4 - Public Economics - - Publicly Provided Goods

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