TY - JOUR

T1 - A two-sided discrete-concave market with possibly bounded side payments

T2 - An approach by discrete convex analysis

AU - Fujishige, Satoru

AU - Tamura, Akihisa

N1 - Funding Information:
We sincerely appreciate anonymous reviewers’ efforts and valuable comments. This work was partially supported by the National Science Council, Taiwan, under contract NSC90-2213-E-005-029.

PY - 2007/2

Y1 - 2007/2

N2 - The marriage model due to Gale and Shapley [Gale, D., L. S. Shapley. 1962. College admissions and the stability of marriage. Amer. Math. Monthly 69 9-15] and the assignment model due to Shapley and Shubik [Shapley, L. S., M. Shubik. 1972. The assignment game I: The core. Internat. J. Game Theory 1 111-130] are standard in the theory of two-sided matching markets. We give a common generalization of these models by utilizing discrete-concave functions and considering possibly bounded side payments. We show the existence of a pairwise stable outcome in our model. Our present model is a further natural extension of the model examined in our previous paper [Fujishige, S., A. Tamura. A general two-sided matching market with discrete concave utility functions. Discrete Appl. Math. 154 950-970], and the proof of the existence of a pairwise stable outcome is even simpler than the previous one.

AB - The marriage model due to Gale and Shapley [Gale, D., L. S. Shapley. 1962. College admissions and the stability of marriage. Amer. Math. Monthly 69 9-15] and the assignment model due to Shapley and Shubik [Shapley, L. S., M. Shubik. 1972. The assignment game I: The core. Internat. J. Game Theory 1 111-130] are standard in the theory of two-sided matching markets. We give a common generalization of these models by utilizing discrete-concave functions and considering possibly bounded side payments. We show the existence of a pairwise stable outcome in our model. Our present model is a further natural extension of the model examined in our previous paper [Fujishige, S., A. Tamura. A general two-sided matching market with discrete concave utility functions. Discrete Appl. Math. 154 950-970], and the proof of the existence of a pairwise stable outcome is even simpler than the previous one.

KW - Assignment model

KW - Bounded side payments

KW - Discrete convex analysis

KW - Marriage model

KW - Pairwise stability

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U2 - 10.1287/moor.1070.0227

DO - 10.1287/moor.1070.0227

M3 - Article

AN - SCOPUS:33847304117

VL - 32

SP - 136

EP - 155

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 1

ER -