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Monotonicity Problems of Interval Solutions and the Dutta-Ray Solution for Convex Interval Games

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  • Yanovskaya, E.
  • Brânzei, R.
  • Tijs, S.H.

    (Tilburg University, Center for Economic Research)

Abstract

This paper examines several monotonicity properties of value-type interval solutions on the class of convex interval games and focuses on the Dutta-Ray (DR) solution for such games. Well known properties for the classical DR solution are extended to the interval setting. In particular, it is proved that the interval DR solution of a convex interval game belongs to the interval core of that game and Lorenz dominates each other interval core element. Consistency properties of the interval DR solution in the sense of Davis-Maschler and of Hart-Mas-Colell are verified. An axiomatic characterization of the interval DR solution on the class of convex interval games with the help of bilateral Hart-Mas-Colell consistency and the constrained egalitarianism for two-person interval games is given.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-102.

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Date of creation: 2008
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Handle: RePEc:dgr:kubcen:2008102

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Web page: http://center.uvt.nl

Related research

Keywords: cooperative interval games; convex games; the constrained egalitarian solution; the equal division core; consistency;

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  1. Borm, P.E.M. & Tijs, S.H. & Timmer, J.B., 2005. "Convexity in stochastic cooperative situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-167605, Tilburg University.
  2. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer, vol. 19(2), pages 153-69.
  3. Suijs, Jeroen & Borm, Peter & De Waegenaere, Anja & Tijs, Stef, 1999. "Cooperative games with stochastic payoffs," European Journal of Operational Research, Elsevier, vol. 113(1), pages 193-205, February.
  4. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
  5. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer, vol. 29(1), pages 133-137.
  6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  7. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
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