On the existence of population-monotonic solutions on the domain of quasi-convex games

Toru Hokari; Seigo Uchida

doi:10.1016/j.orl.2016.12.008

On the existence of population-monotonic solutions on the domain of quasi-convex games

Toru Hokari, Seigo Uchida

Department of Economic

Research output: Contribution to journal › Article › peer-review

Abstract

On the domain of convex games, the Shapley value and the Dutta–Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.

Original language	English
Pages (from-to)	90-92
Number of pages	3
Journal	Operations Research Letters
Volume	45
Issue number	1
DOIs	https://doi.org/10.1016/j.orl.2016.12.008
Publication status	Published - 2017 Jan 1

Keywords

Dutta–Ray solution
Population-monotonicity
Quasi-convex games
Shapely value
TU-games

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2016.12.008

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abstract = "On the domain of convex games, the Shapley value and the Dutta–Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.",

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N2 - On the domain of convex games, the Shapley value and the Dutta–Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.

AB - On the domain of convex games, the Shapley value and the Dutta–Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.

KW - Dutta–Ray solution

KW - Population-monotonicity

KW - Quasi-convex games

KW - Shapely value

KW - TU-games

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JO - Operations Research Letters

JF - Operations Research Letters

IS - 1

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On the existence of population-monotonic solutions on the domain of quasi-convex games

Abstract

Keywords

ASJC Scopus subject areas

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