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Coincidence of Cooperative Game Theoretic Solutions in the Appointment Problem

Author

Listed:
  • Youngsub Chun

    (Seoul National University)

  • Nari Park

    (Seoul National University)

  • Duygu Yengin

    (School of Economics, University of Adelaide)

Abstract

The fixed-route traveling salesman problem with appointments, simply the appointment problem, is concerned with the following situation. Starting from home, a traveller makes a scheduled visit to a set of sponsors and returns home. If a sponsor in the route cancels her appointment, the traveller returns home and waits for the next appointment. We are interested in finding a way of dividing the total traveling cost among sponsors in the appointment problem by applying solutions developed in the cooperative game theory. We show that the well-known solutions of the cooperative game theory, the Shapley value, the nucleolus (or the prenucleolus), and the t -value, coincide under a mild condition onthe traveling cost.

Suggested Citation

  • Youngsub Chun & Nari Park & Duygu Yengin, 2015. "Coincidence of Cooperative Game Theoretic Solutions in the Appointment Problem," School of Economics and Public Policy Working Papers 2015-09, University of Adelaide, School of Economics and Public Policy.
    • Handle: RePEc:adl:wpaper:2015-09
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    File URL: https://economics.adelaide.edu.au/research/papers/doc/wp2015-09.pdf
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    References listed on IDEAS

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    1. Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2009. "On the coincidence of the prenucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 16-25, January.
    2. Tijs, S.H., 1987. "An axiomatization of the ô-value," Other publications TiSEM 5536ac66-86f3-49fb-9e7d-2, Tilburg University, School of Economics and Management.
    3. A. van den Nouweland & P. Borm & W. van Golstein Brouwers & R. Groot Bruinderink & S. Tijs, 1996. "A Game Theoretic Approach to Problems in Telecommunication," Management Science, INFORMS, vol. 42(2), pages 294-303, February.
    4. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Other publications TiSEM f86cf523-f36d-4652-b774-6, Tilburg University, School of Economics and Management.
    5. Maschler,Michael & Solan,Eilon & Zamir,Shmuel, 2013. "Game Theory," Cambridge Books, Cambridge University Press, number 9781107005488.
    6. Tijs, Stef H., 1987. "An axiomatization of the [tau]-value," Mathematical Social Sciences, Elsevier, vol. 13(2), pages 177-181, April.
    7. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
    8. Potters, J.A.M. & Curiel, I. & Tijs, S.H., 1992. "Traveling salesman games," Other publications TiSEM 0dd4cf3d-25fa-4179-80f6-6, Tilburg University, School of Economics and Management.
    9. Driessen, T.S.H. & Tijs, S.H., 1985. "The t-value, the core and semiconvex games," Other publications TiSEM 016b6b5d-a476-44ca-bd05-7, Tilburg University, School of Economics and Management.
    10. Duygu Yengin, 2012. "Characterizing the Shapley value in fixed-route traveling salesman problems with appointments," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 271-299, May.
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    Citations

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    Cited by:

    1. Rongwu Lu & Xinhua Wang & Hao Yu & Dan Li, 2018. "Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application," Complexity, Hindawi, vol. 2018, pages 1-10, March.
    2. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    3. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    4. Matthias Deceuninck & Stijn Vuyst & Dieter Claeys & Dieter Fiems, 2021. "Appointment games with unobservable and observable schedules," Annals of Operations Research, Springer, vol. 307(1), pages 93-110, December.

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    More about this item

    Keywords

    Fixed-route traveling salesman problem; appointment problem; Shapley value; prenucleolus; nucleolus; t-value; coincidence;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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