IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v118y2025ics0304406825000345.html

Bargaining-Equilibrium equivalence

Author

Listed:
  • 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 allocations 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 comprises two components: (i) the profile of the club and (ii) the club project. We define a two-step veto mechanism and introduce the bargaining set in line with Aumann et al. (1961) for such an economy. In this paper, we establish that non-club-equilibrium allocations are those against which there exists a set of agents and a price vector at which they agree to trade amongst themselves rather than consume the non-club-equilibrium allocation assigned to them and all other agents (weakly) prefer the non-club-equilibrium allocation to trading at that particular price vector. In other words, there is a Walrasian objection to any non-club equilibrium allocation. We further show that Walrasian objections are also justified, which helps us to establish our equivalence between the set of equilibrium allocations and the bargaining set for an atomless club economy.

Suggested Citation

  • Bhowmik, Anuj & Saha, Sandipan, 2025. "Bargaining-Equilibrium equivalence," Journal of Mathematical Economics, Elsevier, vol. 118(C).
    • Handle: RePEc:eee:mateco:v:118:y:2025:i:c:s0304406825000345
    DOI: 10.1016/j.jmateco.2025.103117

    Download full text from publisher

    As the access to this document is restricted, you may want to for a different version of it.

    References listed on IDEAS

    1. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64(5), pages 416-416.
    2. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    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. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
    5. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
    6. 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.
    7. Bryan Ellickson and Birgit Grodal, Suzanne Scotchmer, and William R. Zame., 1997. "Clubs and the Market: Continuum Economies," Economics Working Papers 97-254, University of California at Berkeley.
    8. Aumann, Robert J., 1973. "Disadvantageous monopolies," Journal of Economic Theory, Elsevier, vol. 6(1), pages 1-11, February.
    9. Scotchmer, Suzanne & Shannon, Chris, 2019. "Verifiability and group formation in markets," Journal of Economic Theory, Elsevier, vol. 183(C), pages 417-477.
    10. 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.
    11. 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.
    12. Hammond, Peter J. & Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "Continuum economies with finite coalitions: Core, equilibria, and widespread externalities," Journal of Economic Theory, Elsevier, vol. 49(1), pages 113-134, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.


    Cited by:

    1. Anuj Bhowmik & Sandipan Saha & Soumi Tikader, 2026. "On fairness and size of coalitions in economies with club goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 55(1), pages 1-40, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bhowmik, Anuj & Saha, Sandipan, 2023. "Bargaining-equilibrium equivalence," MPRA Paper 117194, University Library of Munich, Germany.
    2. Bhowmik, Anuj & Saha, Sandipan, 2023. "Restricted bargaining sets in a club economy," MPRA Paper 119210, University Library of Munich, Germany.
    3. Bhowmik, Anuj & Saha, Sandipan, 2022. "On blocking mechanisms in economies with club goods," MPRA Paper 114928, University Library of Munich, Germany.
    4. John P. Conley & Myrna Holtz Wooders, 1998. "The Tiebout Hypothesis: On the Existence of Pareto Efficient Competitive Equilibrium," Working Papers mwooders-98-06, University of Toronto, Department of Economics.
    5. Allouch, Nizar & Conley, John P. & Wooders, Myrna, 2009. "Anonymous price taking equilibrium in Tiebout economies with a continuum of agents: Existence and characterization," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 492-510, September.
    6. Jaime Luque, 2014. "Wages, local amenities and the rise of the multi-skilled city," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(2), pages 457-467, March.
    7. Japneet Kaur, 2023. "Stable sets in economies with club goods," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2023-011, Indira Gandhi Institute of Development Research, Mumbai, India.
    8. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    9. Nizar Allouch & Myrna Wooders, 2004. "Price Taking Equilibrium in Club Economies with Multiple Memberships and Unbounded Club Sizes," Working Papers 513, Queen Mary University of London, School of Economics and Finance.
    10. Konishi, Hideo, 2008. "Tiebout's tale in spatial economies: Entrepreneurship, self-selection, and efficiency," Regional Science and Urban Economics, Elsevier, vol. 38(5), pages 461-477, September.
    11. Gersbach, Hans & Haller, Hans, 2010. "Club theory and household formation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 715-724, September.
    12. Luque, Jaime, 2013. "Heterogeneous Tiebout communities with private production and anonymous crowding," Regional Science and Urban Economics, Elsevier, vol. 43(1), pages 117-123.
    13. Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, vol. 140(1), pages 246-278, May.
    14. Anuj Bhowmik & Sandipan Saha & Soumi Tikader, 2026. "On fairness and size of coalitions in economies with club goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 55(1), pages 1-40, June.
    15. Hideo Konishi, 2010. "Efficient Mixed Clubs: Nonlinear‐Pricing Equilibria With Entrepreneurial Managers," The Japanese Economic Review, Japanese Economic Association, vol. 61(1), pages 35-63, March.
    16. 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.
    17. Bhowmik, Anuj & Kaur, Japneet, 2023. "Competitive equilibria and robust efficiency with club goods," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    18. Allouch, Nizar & Wooders, Myrna, "undated". "Competitive Pricing in Socially Networked Economies," Economic Research Papers 269413, University of Warwick - Department of Economics.
    19. Dokow, Elad & Luque, Jaime, 2019. "Provision of local public goods in mixed income communities," Journal of Housing Economics, Elsevier, vol. 45(C), pages 1-1.
    20. Bryan Ellickson and Birgit Grodal, Suzanne Scotchmer, and William R. Zame., 1997. "Clubs and the Market: Continuum Economies," Economics Working Papers 97-254, University of California at Berkeley.

    More about this item

    Keywords

    ; ; ; ; ;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D00 - Microeconomics - - General - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:118:y:2025:i:c:s0304406825000345. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.