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A Note on a Two-Sided Discrete-Concave Market with Possibly Bounded Salaries

Author

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  • Rashid Farooq

    (School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan)

  • Ayesha Mahmood

    (School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan)

Abstract

This paper deals with a many-to-many matching model with discrete-concave value functions and possibly bounded salaries. We extend the model of Fujishige and Tamura [(2007) Math. Oper. Res. 32, 136–155] by generalizing the payoff functions. We introduce weighted income and payments. To find a pairwise strictly stable outcome in our model, we propose an algorithm. We give a new method to modify salary vector in each iteration of the algorithm.

Suggested Citation

  • Rashid Farooq & Ayesha Mahmood, 2017. "A Note on a Two-Sided Discrete-Concave Market with Possibly Bounded Salaries," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-21, September.
    • Handle: RePEc:wsi:igtrxx:v:19:y:2017:i:03:n:s0219198917500177
    DOI: 10.1142/S0219198917500177
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    References listed on IDEAS

    as
    1. Satoru Fujishige & Akihisa Tamura, 2007. "A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 136-155, February.
    2. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    3. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    4. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    5. Péter Biró & Flip Klijn, 2013. "Matching With Couples: A Multidisciplinary Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-18.
    6. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    7. Kazuo Murota & Yu Yokoi, 2015. "On the Lattice Structure of Stable Allocations in a Two-Sided Discrete-Concave Market," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 460-473, February.
    8. Kazuo Murota & Akiyoshi Shioura, 1999. "M-Convex Function on Generalized Polymatroid," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 95-105, February.
    9. Sotomayor, Marilda, 2000. "Existence of stable outcomes and the lattice property for a unified matching market," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 119-132, March.
    10. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    11. David Gale, 2001. "The Two-Sided Matching Problem: Origin, Development And Current Issues," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 237-252.
    12. Satoru Fujishige & Zaifu Yang, 2003. "A Note on Kelso and Crawford's Gross Substitutes Condition," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 463-469, August.
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