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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 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
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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:

    • 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

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