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Bargaining Foundation for Ratio Equilibrium in Public Good Economies

Author

Listed:
  • Anne Van den Nouweland

    (University of Oregon [Eugene])

  • Agnieszka Rusinowska

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

Abstract

We provide a bargaining foundation for the concept of ratio equilibrium in public good economies. We define a bargaining game of alternating offers in which players bargain to determine their cost shares of public good production and a level of public good. We study the stationary subgame perfect equilibrium without delay of the bargaining game. We demonstrate that when the players are perfectly patient, they are indifferent between the equilibrium offers of all players. We also show that every stationary subgame perfect equilibrium without delay in which the ratios offered by all players are the same leads to a ratio equilibrium. In addition, we demonstrate that all equilibrium ratios are offered by the players at some stationary subgame perfect equilibrium without delay. We use these results to discuss the case when the assumption of perfectly patient players is relaxed and the cost of delay vanishes.

Suggested Citation

  • Anne Van den Nouweland & Agnieszka Rusinowska, 2018. "Bargaining Foundation for Ratio Equilibrium in Public Good Economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01720001, HAL.
  • Handle: RePEc:hal:cesptp:halshs-01720001
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01720001
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    References listed on IDEAS

    as
    1. Kaneko, Mamoru, 1977. "The Ratio Equilibria and the Core of the Voting Game G(N, W) in a Public Goods Economy," Econometrica, Econometric Society, vol. 45(7), pages 1589-1594, October.
    2. Julio Dávila & Jan Eeckhout & César Martinelli, 2009. "Bargaining over Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(6), pages 927-945, December.
    3. Dávila, J. & Eeckhout, J., 2008. "Competitive bargaining equilibrium," Journal of Economic Theory, Elsevier, vol. 139(1), pages 269-294, March.
    4. Chae, Suchan & Yang, Jeong-Ae, 1988. "The unique perfect equilibrium of an n-person bargaining game," Economics Letters, Elsevier, vol. 28(3), pages 221-223.
    5. Foley, Duncan K, 1970. "Lindahl's Solution and the Core of an Economy with Public Goods," Econometrica, Econometric Society, vol. 38(1), pages 66-72, January.
    6. Anne van den Nouweland & Myrna H. Wooders & S. Tijs, 2002. "Axiomatization of ratio equilibria in public good economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 627-636.
    7. repec:hal:journl:halshs-00633592 is not listed on IDEAS
    8. Kaneko, Mamoru, 1977. "The ratio equilibrium and a voting game in a public goods economy," Journal of Economic Theory, Elsevier, vol. 16(2), pages 123-136, December.
    9. repec:eee:matsoc:v:89:y:2017:i:c:p:50-60 is not listed on IDEAS
    10. Guoqiang Tian, 1989. "Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 613-621.
    11. van den Nouweland, Anne & Wooders, Myrna, 2011. "Share equilibrium in local public good economies," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 376-381.
    12. Luis Corchon & Simon Wilkie, 1996. "Double implementation of the ratio correspondence by a market mechanism," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 325-337, December.
    13. Yang, Jeong-Ae, 1992. "Another n-person bargaining game with a unique perfect equilibrium," Economics Letters, Elsevier, vol. 38(3), pages 275-277, March.
    14. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
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