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Payoff-dependent balancedness and cores (revised version)

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  • Jean-Marc Bonnisseau

    ()

  • Vincent Iehlé

    ()

Abstract

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.

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Bibliographic Info

Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 678.07.

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Length: 34
Date of creation: 22 Jan 2007
Date of revision:
Handle: RePEc:aub:autbar:678.07

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Keywords: balancedness; cooperative game; core; parametrized game;

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References

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  2. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Liu, Jiuqiang & Liu, Xiaodong, 2013. "A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 150-156.
  2. Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," Economics Working Papers (Ensaios Economicos da EPGE) 716, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  3. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, Elsevier, vol. 54(2), pages 176-185, September.

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