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Existence and Optimality of Cost Share Equilibria

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Abstract

We consider pure exchange economies with finitely many private goods including also non-Samuelsonian public goods. For this type of economies, the notion of competitive equilibrium called cost share equilibrium is founded on individual payments for public goods varying according to individual benefits. This situation naturally arises when a level of provision is interpreted as a whole configuration of public policies or when cost share functions are interpreted as voluntary contributions instead of predetermined tax systems (Mas Colell (1980)). We establish the equivalence of cost share equilibria with cooperative and non-cooperative game-theoretic solutions. In particular: 1. we characterize cost share equilibria as those allocations which cannot be improved upon by the society; 2. we characterize cost share equilibria as Nash equilibria of a game with two players. Then we discuss the existence of cost share equilibria in economies with public projects satisfying standard assumptions and provide a condition for the set of cost share equilibria to be non-empty. Our analysis of cooperative solutions is based on contribution schemes which capture the fraction of the total cost of collective goods that each coalition of agents is expected to cover.

Suggested Citation

  • Maria Gabriella Graziano & Marialaura Pesce & Maria Romaniello, 2021. "Existence and Optimality of Cost Share Equilibria," CSEF Working Papers 628, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  • Handle: RePEc:sef:csefwp:628
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    1. 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.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    3. 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.
    4. Mas-Colell, Andreu & Silvestre, Joaquim, 1989. "Cost share equilibria: A Lindahlian approach," Journal of Economic Theory, Elsevier, vol. 47(2), pages 239-256, April.
    5. 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.
    6. Gerard Debreu, 1963. "On a Theorem of Scarf," Review of Economic Studies, Oxford University Press, vol. 30(3), pages 177-180.
    7. Noguchi, Mitsunori, 2000. "A fuzzy core equivalence theorem," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 143-158, August.
    8. 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.
    9. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 203-210, June.
    10. Diamantaras, Dimitrios & Gilles, Robert P, 1996. "The Pure Theory of Public Goods: Efficiency, Dencentralization, and the Core," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 851-860, November.
    11. 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.
    12. Martin Dufwenberg & Paul Heidhues & Georg Kirchsteiger & Frank Riedel & Joel Sobel, 2011. "Other-Regarding Preferences in General Equilibrium," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 613-639.
    13. Achille Basile & Robert P. Gilles & Maria Gabriella Graziano & Marialaura Pesce, 2021. "The Core of economies with collective goods and a social division of labour," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1085-1119, April.
    14. 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.
    15. 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.
    16. Andreu Mas-Colell, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, Oxford University Press, vol. 94(4), pages 625-641.
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    More about this item

    Keywords

    Non-Samuelsonian public goods; Cost share equilibrium; Aubin core; Nash equilibrium.;
    All these keywords.

    JEL classification:

    • D49 - Microeconomics - - Market Structure, Pricing, and Design - - - Other
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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