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Lindahl Equilibrium as a Collective Choice Rule

Author

Listed:
  • Faruk Gul

    (Princeton University)

  • Wolfgang Pesendorfer

    (Princeton University)

Abstract

A collective choice problem is a finite set of social alternatives and a finite set of economic agents with vNM utility functions. We associate a public goods economy with each collective choice problem and establish the existence and efficiency of (equal income) Lindahl equilibrium allocations. We interpret collective choice problems as cooperative bargaining problems and define a set-valued solution concept, {\it the equitable solution} (ES). We provide axioms that characterize ES and show that ES contains the Nash bargaining solution. Our main result shows that the set of ES payoffs is the same a the set of Lindahl equilibrium payoffs. We consider two applications: in the first, we show that in a large class of matching problems without transfers the set of Lindahl equilibrium payoffs is the same as the set of (equal income) Walrasian equilibrium payoffs. In our second application, we show that in any discrete exchange economy without transfers every Walrasian equilibrium payoff is a Lindahl equilibrium payoff of the corresponding collective choice market. Moreover, for any cooperative bargaining problem, it is possible to define a set of commodities so that the resulting economy's utility possibility set is that bargaining problem {\it and} the resulting economy's set of Walrasian equilibrium payoffs is the same as the set of Lindahl equilibrium payoffs of the corresponding collective choice market.

Suggested Citation

  • Faruk Gul & Wolfgang Pesendorfer, 2020. "Lindahl Equilibrium as a Collective Choice Rule," Papers 2008.09932, arXiv.org, revised Aug 2020.
  • Handle: RePEc:arx:papers:2008.09932
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    References listed on IDEAS

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    1. Andreu Mas-Colell, 1992. "Equilibrium Theory with Possibly Satiated Preferences," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 9, pages 201-213, Palgrave Macmillan.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    4. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    5. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    6. Satoru Fujishige & Zaifu Yang, 2003. "A Note on Kelso and Crawford's Gross Substitutes Condition," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 463-469, August.
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    Cited by:

    1. Sayantan Ghosal & Lukasz Woźny, 2024. "Lindahl meets Condorcet?," Working Papers 2024_08, Business School - Economics, University of Glasgow.
    2. Brandl, Florian & Brandt, Felix & Greger, Matthias & Peters, Dominik & Stricker, Christian & Suksompong, Warut, 2022. "Funding public projects: A case for the Nash product rule," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    3. Florian Brandl & Felix Brandt & Matthias Greger & Dominik Peters & Christian Stricker & Warut Suksompong, 2022. "Funding public projects: A case for the Nash product rule," Post-Print hal-03818329, HAL.

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