Monotonic Stable Solutions for Minimum Coloring Games

CentER Discussion Paper No. 2011-016

20 Pages Posted: 19 Feb 2011

See all articles by Herbert Hamers

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Sylvia Miquel

University of Lleida - Department of Mathematics

Henk Norde

Tilburg University - Center For Economic Research; Tilburg University - Department of Econometrics & Operations Research

Date Written: February 17, 2011

Abstract

For the class of minimum coloring games (introduced by Deng et al. (1999)) we investigate the existence of population monotonic allocation schemes (introduced by Sprumont (1990)). We show that a minimum coloring game on a graph G has a population monotonic allocation scheme if and only if G is (P4, 2K2)-free (or, equivalently, if its complement graph G is quasi-threshold). Moreover, we provide a procedure that for these graphs always selects an integer population monotonic allocation scheme.

Keywords: Minimum Coloring Game, Population Monotonic Allocation Scheme

JEL Classification: C71

Suggested Citation

Hamers, Herbert and Miquel, Sylvia and Norde, Henk W., Monotonic Stable Solutions for Minimum Coloring Games (February 17, 2011). CentER Discussion Paper No. 2011-016, Available at SSRN: https://ssrn.com/abstract=1763813 or http://dx.doi.org/10.2139/ssrn.1763813

Herbert Hamers (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Sylvia Miquel

University of Lleida - Department of Mathematics ( email )

Carrer Jaume II
69 Campus Cappont
Lleida, Catalunya E-25001
Spain

Henk W. Norde

Tilburg University - Center For Economic Research ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 3245 (Phone)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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