Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games

E. Yanovskaya, R. Brânzei, S.H. Tijs

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

Abstract

This chapter 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
Title of host publicationCollective Decision Making
Subtitle of host publicationViews from Social Choice and Game Theory
EditorsA. van Deemen, A. Rusinowska
Place of PublicationHeidelberg
PublisherSpringer Verlag
Pages249-266
Number of pages304
ISBN (Print)9783642028649
Publication statusPublished - 2010

Publication series

NameTheory and Decision Library C

Fingerprint

Monotonicity
Half line
Game
Interval
Classical Solution
Person

Cite this

Yanovskaya, E., Brânzei, R., & Tijs, S. H. (2010). Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games. In A. van Deemen, & A. Rusinowska (Eds.), Collective Decision Making: Views from Social Choice and Game Theory (pp. 249-266). (Theory and Decision Library C). Heidelberg: Springer Verlag.
Yanovskaya, E. ; Brânzei, R. ; Tijs, S.H. / Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games. Collective Decision Making: Views from Social Choice and Game Theory. editor / A. van Deemen ; A. Rusinowska. Heidelberg : Springer Verlag, 2010. pp. 249-266 (Theory and Decision Library C).
@inbook{70978b41c8bf456f8569ea13a1d8943a,
title = "Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games",
abstract = "This chapter 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.",
author = "E. Yanovskaya and R. Br{\^a}nzei and S.H. Tijs",
note = "Appeared earlier as CentER Discussion Paper 2008-102 Pagination: 304",
year = "2010",
language = "English",
isbn = "9783642028649",
series = "Theory and Decision Library C",
publisher = "Springer Verlag",
pages = "249--266",
editor = "{van Deemen}, A. and A. Rusinowska",
booktitle = "Collective Decision Making",
address = "Germany",

}

Yanovskaya, E, Brânzei, R & Tijs, SH 2010, Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games. in A van Deemen & A Rusinowska (eds), Collective Decision Making: Views from Social Choice and Game Theory. Theory and Decision Library C, Springer Verlag, Heidelberg, pp. 249-266.

Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games. / Yanovskaya, E.; Brânzei, R.; Tijs, S.H.

Collective Decision Making: Views from Social Choice and Game Theory. ed. / A. van Deemen; A. Rusinowska. Heidelberg : Springer Verlag, 2010. p. 249-266 (Theory and Decision Library C).

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

TY - CHAP

T1 - Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games

AU - Yanovskaya, E.

AU - Brânzei, R.

AU - Tijs, S.H.

N1 - Appeared earlier as CentER Discussion Paper 2008-102 Pagination: 304

PY - 2010

Y1 - 2010

N2 - This chapter 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.

AB - This chapter 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.

M3 - Chapter

SN - 9783642028649

T3 - Theory and Decision Library C

SP - 249

EP - 266

BT - Collective Decision Making

A2 - van Deemen, A.

A2 - Rusinowska, A.

PB - Springer Verlag

CY - Heidelberg

ER -

Yanovskaya E, Brânzei R, Tijs SH. Monotonicity properties of interval solutions and the Dutta-Ray solution for convex interval games. In van Deemen A, Rusinowska A, editors, Collective Decision Making: Views from Social Choice and Game Theory. Heidelberg: Springer Verlag. 2010. p. 249-266. (Theory and Decision Library C).