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Non-emptiness of the alpha-core

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

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.

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Paper provided by FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 716.

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Date of creation: 06 May 2011
Date of revision:
Handle: RePEc:fgv:epgewp:716
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  1. 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.
  2. 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).
  3. 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 453-61, May.
  4. 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, vol. 116(1), pages 84-92, May.
  5. Jean-Marc Bonnisseau & Vincent Iehle, 2004. "Payoffs-dependent Balancedness and Cores," Game Theory and Information 0403004, EconWPA.
  6. 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.
  7. Luca Rigotti & Chris Shannon=20, 2002. "Uncertainty and Risk in Financial Markets," Game Theory and Information 0201001, EconWPA.
  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. repec:dau:papers:123456789/89 is not listed on IDEAS
  10. 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.
  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. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-42, November.
  13. 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.
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