Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 136-155 |
| Number of pages | 20 |
| Journal | Mathematics of Operations Research |
| Volume | 32 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2007 Feb |
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Keywords
- Assignment model
- Bounded side payments
- Discrete convex analysis
- Marriage model
- Pairwise stability
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Management Science and Operations Research
Cite this
A two-sided discrete-concave market with possibly bounded side payments : An approach by discrete convex analysis. / Fujishige, Satoru; Tamura, Akihisa.
In: Mathematics of Operations Research, Vol. 32, No. 1, 02.2007, p. 136-155.Research output: Contribution to journal › Article
}
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
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 -