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The semireactive bargaining set of a cooperative game

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  • Sudhoelter,P.

    (Institute of Mathematical Economics, Bielefeld University)

  • Potters,J.A.M.

Abstract

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set.

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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 313.

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Date of creation: 1999
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Handle: RePEc:bie:wpaper:313

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References

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  1. Bezalel Peleg & Peter Sudhölter, 1998. "The Positive Prekernel of a Cooperative Game," Working Papers 292, Bielefeld University, Center for Mathematical Economics.
  2. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer, vol. 28(2), pages 229-240.
  3. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  4. Peleg, Bezalel, 1992. "Axiomatizations of the core," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 13, pages 397-412 Elsevier.
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Cited by:
  1. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer, vol. 39(1), pages 163-170, March.
  2. Orshan,G. & Sudhoelter,P., 2001. "The positive core of a cooperative game," Working Papers 326, Bielefeld University, Center for Mathematical Economics.
  3. Morelli, Massimo & Montero, Maria, 2003. "The demand bargaining set: general characterization and application to majority games," Games and Economic Behavior, Elsevier, vol. 42(1), pages 137-155, January.
  4. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer, vol. 16(4), pages 425-440, December.
  5. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.

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