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Characterizations of equilibrium allocations in an economy with public goods and infinitely many commodities

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  • Anuj Bhowmik

Abstract

This paper examines the characterizations of equilibrium in economies with public projects. Public goods, as discussed by Mas-Colell (1980), are modeled as elements of an abstract set lacking a unified ordering structure. We introduce the concepts of cost share equilibrium for such economies, where the private commodity space is a (possibly nonseparable) Banach lattice. Within this framework, we present two distinct characterizations of cost share equilibria via the veto power of the grand coalition in economies featuring finitely many agents. The first characterization involves allocations that are Aubin non-dominated, while the second establishes that an allocation is a cost share equilibrium if and only if it cannot be dominated by the grand coalition, where domination is considered under specific perturbations of initial endowments.

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  • Anuj Bhowmik, 2025. "Characterizations of equilibrium allocations in an economy with public goods and infinitely many commodities," Papers 2509.24437, arXiv.org.
    • Handle: RePEc:arx:papers:2509.24437
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    References listed on IDEAS

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    1. De Simone, Anna & Graziano, Maria Gabriella, 2004. "The pure theory of public goods: the case of many commodities," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 847-868, November.
    2. Bhowmik, Anuj & Graziano, Maria Gabriella, 2015. "On Vind’s theorem for an economy with atoms and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 26-36.
    3. Dimitrios Diamantaras & Robert P. Gilles, 1997. "Linear cost sharing in economies with non-Samuelsonian public goods: Core equivalence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 121-139.
    4. Tourky, Rabee & Yannelis, Nicholas C., 2001. "Markets with Many More Agents than Commodities: Aumann's "Hidden" Assumption," Journal of Economic Theory, Elsevier, vol. 101(1), pages 189-221, November.
    5. Achille Basile & Anna Simone & Maria Graziano, 2005. "Coalitional economies with public projects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 127-139, October.
    6. Achille Basile & Maria Gabriella Graziano & Marialaura Pesce, 2016. "Oligopoly And Cost Sharing In Economies With Public Goods," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 487-506, May.
    7. 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.
    8. Maria Graziano & Maria Romaniello, 2012. "Linear cost share equilibria and the veto power of the grand coalition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 269-303, February.
    9. Achille Basile & Maria Gabriella Graziano & Marialaura Pesce, 2016. "Oligopoly And Cost Sharing In Economies With Public Goods," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(2), pages 487-506, May.
    10. Diamantaras, Dimitrios & Gilles, Robert P & Scotchmer, Suzanne, 1996. "Decentralization of Pareto Optima in Economies with Public Projects, Nonessential Private Goods and Convex Costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 555-564, October.
    11. Maria Gabriella Graziano, 2007. "Economies With Public Projects: Efficiency And Decentralization," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 1037-1063, August.
    12. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
    13. Podczeck, Konrad & Yannelis, Nicholas C., 2008. "Equilibrium theory with asymmetric information and with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 141(1), pages 152-183, July.
    14. Robert P. Gilles & Suzanne Scotchmer & Dimitrios Diamantaras, 1996. "Decentralization of Pareto optima in economies with public projects, nonessential private goods and convex costs (☆)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 555-564.
    15. Konrad Podczeck, 2003. "Core and Walrasian equilibria when agents' characteristics are extremely dispersed," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 699-725, November.
    16. 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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