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Non-emptiness of the alpha-core

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  • Martins-da-Rocha, Victor Filipe
  • Yannelis, Nicholas C.

Abstract

We prove non-emptiness of the alpha-core for balanced games with non-ordered preferences, extending and generalizing in several aspects the results of Scarf (1971), Border (1984), Florenzano (1989), Yannelis (1991) and Kajii (1992). In particular we answer an open question in Kajii (1992) regarding the applicability of the non-emptiness results to models with infinite dimensional strategy spaces. We provide two models with Knightian and voting preferences for which the results of Scarf (1971) and Kajii (1992) cannot be applied while our non-emptiness result applies.

Suggested Citation

  • Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 716, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  • Handle: RePEc:fgv:epgewp:716
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/89 is not listed on IDEAS
    2. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    3. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, pages 84-92.
    4. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    5. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    6. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    7. Koutsougeras, Leonidas C & Yannelis, Nicholas C, 1993. "Incentive Compatibility and Information Superiority of the Core of an Economy with Differential Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 195-216, April.
    8. Isabelle Lefebvre, 2001. "An alternative proof of the nonemptiness of the private core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(2), pages 275-291.
    9. Holly, Charles, 1994. "An Exchange Economy Can Have an Empty Alpha-Core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 453-461, May.
    10. Florenzano Monique, 1987. "On the non-emptiness of the core of a coalitional production economy without ordered preferences," CEPREMAP Working Papers (Couverture Orange) 8733, CEPREMAP.
    11. 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.
    12. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    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.
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    Cited by:

    1. Uyanık, Metin, 2015. "On the nonemptiness of the α-core of discontinuous games: Transferable and nontransferable utilities," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 213-231.
    2. Graziano, Maria Gabriella & Meo, Claudia & Yannelis, Nicholas C., 2017. "Stable sets for exchange economies with interdependent preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 267-286.
    3. Askoura, Y. & Sbihi, M. & Tikobaini, H., 2013. "The ex ante α-core for normal form games with uncertainty," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 157-162.

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