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Payoff-dependent balancedness and cores (revised version)

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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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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  1. Iehlé, Vincent, 2004. "Transfer Rate Rules and Core Selections in NTU Games," Economics Papers from University Paris Dauphine 123456789/86, Paris Dauphine University.
  2. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2007. "Socially structured games," Other publications TiSEM c2546c5b-249a-44a8-b917-7, Tilburg University, School of Economics and Management.
  3. Roberto Serrano & Ken-Ichi Shimomura, 2005. "A Comparison Of The Average Prekernel And The Prekernel," Economics Working Papers we055827, Universidad Carlos III, Departamento de Economía.
  4. Reny, Philip J. & Holtz Wooders, Myrna, 1998. "An extension of the KKMS theorem," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 125-134, March.
  5. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
  6. Greenberg, Joseph, 1994. "Coalition structures," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 37, pages 1305-1337 Elsevier.
  7. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
  8. Herings P. Jean-Jacques & Predtetchinski Arkadi, 2002. "A Necessary and Sufficient Condition for Non--emptiness of the Core of a Non--transferable Utility Game," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. 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.
  10. Vohra, Rajiv, 1988. "On the existence of equilibria in economies with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 179-192, April.
  11. repec:oup:restud:v:41:y:1974:i:3:p:429-36 is not listed on IDEAS
  12. 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.
  13. FORGES, Françoise & MERTENS, Jean-François & VOHRA, Rajiv, 2001. "The ex ante incentive compatible core in the absence of wealth effects," CORE Discussion Papers 2001001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Ichiishi, Tatsuro & Quinzii, Martine, 1983. "Decentralization for the Core of a Production Economy with Increasing Returns," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 397-412, June.
  15. Ichiishi, Tatsuro & Idzik, Adam, 1996. "Bayesian Cooperative Choice of Strategies," International Journal of Game Theory, Springer, vol. 25(4), pages 455-73.
  16. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  17. Kajii, Atsushi, 1992. "A generalization of Scarf's theorem: An [alpha]-core existence theorem without transitivity or completeness," Journal of Economic Theory, Elsevier, vol. 56(1), pages 194-205, February.
  18. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-77, March.
  19. Jean-Marc Bonnisseau, 1997. "Existence of Equilibria in Economies with Externalities and Nonconvexities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00176205, HAL.
  20. Yakar Kannai & Myrna H. Wooders, 1996. "A Further Extension of the KKMS Theorem," Center for Mathematical Economics Working Papers 251, Center for Mathematical Economics, Bielefeld University.
  21. Ichiishi,Tatsuro, 1993. "The Cooperative Nature of the Firm," Cambridge Books, Cambridge University Press, number 9780521414449.
  22. Roy Radner & Tatsuro Ichiishi, 1999. "A profit-center game with incomplete information," Review of Economic Design, Springer, vol. 4(4), pages 307-343.
  23. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "The Partnered Core of an Economy and the Partnered Competitive Equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 143-152, August.
  24. Orshan, Gooni & Zarzuelo, Jose M., 2000. "The Bilateral Consistent Prekernel for NTU Games," Games and Economic Behavior, Elsevier, vol. 32(1), pages 67-84, July.
  25. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer, vol. 1(1), pages 108-16, January.
  26. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-42, November.
  27. Reny, Philip J. & Holtz Wooders, Myrna, 1996. "The Partnered Core of a Game without Side Payments," Journal of Economic Theory, Elsevier, vol. 70(2), pages 298-311, August.
  28. repec:ebl:ecbull:v:3:y:2004:i:42:p:1-10 is not listed on IDEAS
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