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Externalities in economies with endogenous sharing rules

Author

Listed:
  • Philippe Bich

    (Centre d’Economie de la Sorbonne UMR 8174, Université Paris I Panthéon/Sorbonne)

  • Rida Laraki

    (PSL Research University, Lamsade
    Ecole Polytechnique)

Abstract

Endogenous sharing rules were introduced by Simon and Zame (Econometrica 58(4):861–872, 1990) to model payoff indeterminacy in discontinuous games. They prove the existence in every compact strategic game of a mixed Nash equilibrium and an associated sharing rule. We extend their result to economies with externalities (Arrow and Debreu in Econometrica 22(3):265–290, 1954) where, by definition, players are restricted to pure strategies. We also provide a new interpretation of payoff indeterminacy in Simon and Zame’s model in terms of preference incompleteness.

Suggested Citation

  • Philippe Bich & Rida Laraki, 2017. "Externalities in economies with endogenous sharing rules," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 127-137, October.
    • Handle: RePEc:spr:etbull:v:5:y:2017:i:2:d:10.1007_s40505-017-0118-3
    DOI: 10.1007/s40505-017-0118-3
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    References listed on IDEAS

    as
    1. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01396183, HAL.
    2. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    3. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    4. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    5. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    6. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Post-Print hal-01396183, HAL.
    7. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Post-Print halshs-00717135, HAL.
    8. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    9. Bich, Philippe & Laraki, Rida, 2017. "On the existence of approximate equilibria and sharing rule solutions in discontinuous games," Theoretical Economics, Econometric Society, vol. 12(1), January.
    10. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Documents de travail du Centre d'Economie de la Sorbonne 12040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    11. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    12. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    13. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 31-45, September.
    14. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
    15. Guilherme Carmona & Konrad Podczeck, 2016. "Existence of Nash equilibrium in ordinal games with discontinuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 457-478, March.
    16. Philip J. Reny, 2016. "Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 553-569, March.
    17. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
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    More about this item

    Keywords

    Abstract economies; Generalized games; Endogenous sharing rules; Walrasian equilibrium; Incomplete and discontinuous preferences; Better reply security;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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