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Transferable utility games with uncertainty

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  • Habis, Helga
  • Herings, P. Jean-Jacques

Abstract

We introduce the concept of a TUU-game, a transferable utility game with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TU-games are convex.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 5 (September)
Pages: 2126-2139

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:2126-2139

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Transferable utility games Uncertainty Weak Sequential Core;

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References

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  1. Predtetchinski, Arkadi, 2007. "The strong sequential core for stationary cooperative games," Games and Economic Behavior, Elsevier, vol. 61(1), pages 50-66, October.
  2. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
  3. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
  4. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
  5. Suijs, J.P.M. & Borm, P.E.M. & De Waegenaere, A.M.B. & Tijs, S.H., 1995. "Cooperative games with stochastic payoffs," Discussion Paper 1995-88, Tilburg University, Center for Economic Research.
  6. Predtetchinski A. & Herings P.J.J. & Perea A., 2002. "The Weak Sequential Core for Two-period Economies," Game Theory and Information 0203008, EconWPA.
  7. Helga Habis & P. Jean-Jacques Herings, 2010. "A Note On The Weak Sequential Core Of Dynamic Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 407-416.
  8. Granot, D, et al, 1996. "The Kernel/Nucleolus of a Standard Tree Game," International Journal of Game Theory, Springer, vol. 25(2), pages 219-44.
  9. Bossert,Walter & Derks,Jean & Peters,Hans, 2001. "Efficiency in Uncertain Cooperative Games," Research Memorandum 002, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  10. Laurence Kranich & Andrés Perea & Hans Peters, 2005. "Core Concepts For Dynamic Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 43-61.
  11. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  12. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  13. Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
  14. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer, vol. 18(2), pages 185-87.
  15. Rajiv Vohra, 1997. "Incomplete Information, Incentive Compatibility and the Core," Working Papers 97-11, Brown University, Department of Economics.
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Cited by:
  1. William Thomson, 2013. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update," RCER Working Papers 578, University of Rochester - Center for Economic Research (RCER).
  2. Habis Helga & Herings P. Jean-Jacques, 2011. "Stochastic Bankruptcy Games," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. David Csercsik, 2013. "Competition and cooperation in a PFF game theoretic model of electrical energy trade," IEHAS Discussion Papers 1310, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  4. Habis, Helga, 2012. "Sztochasztikus csődjátékok - avagy hogyan osszunk szét egy bizonytalan méretű tortát?
    [Stochastic bankruptcy games. How can a cake of uncertain dimensions be divided?]
    ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1299-1310.

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