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

E. Yanovskaya, R. Brânzei, S.H. Tijs

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages17
Volume2008-102
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-102

Keywords

  • cooperative interval games
  • convex games
  • the constrained egalitarian solution
  • the equal division core
  • consistency

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