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Payoff-dependent balancedness and cores

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  • Bonnisseau, Jean-Marc
  • Iehle, Vincent

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 parameterized 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

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 61 (2007)
Issue (Month): 1 (October)
Pages: 1-26

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Handle: RePEc:eee:gamebe:v:61:y:2007:i:1:p:1-26

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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Citations

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Cited by:
  1. Vincent Iehlé, 2004. "Transfer Rate Rules and Core Selections in NTU Games," Game Theory and Information 0411001, EconWPA.
  2. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer, vol. 37(2), pages 203-210, June.
  3. 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.
  4. Predtetchinski,Arkadi, 2004. "The Fuzzy Core and the (Π, β)- Balanced Core," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Vincent Iehlé, 2005. "The core-partition of hedonic games," Cahiers de la Maison des Sciences Economiques b05091, Université Panthéon-Sorbonne (Paris 1).
  6. Allouch,Nizar & Predtetchinski,Arkadi, 2005. "On the non-emptiness of the fuzzy core," Research Memorandum 002, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
  8. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
  9. Iehlé, Vincent, 2009. "Sustainability in a Multiproduct and Multiple Agent Contestable Market," Economics Papers from University Paris Dauphine 123456789/84, Paris Dauphine University.
  10. Vincent Iehlé, 2004. "Stable pricing in monopoly and equilibrium-core of cost games," Cahiers de la Maison des Sciences Economiques b05023, Université Panthéon-Sorbonne (Paris 1).

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