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Characterizing the Shapley value in fixed-route traveling salesman problems with appointments

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  • Duygu Yengin

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Abstract

Starting from her home, a service provider visits several customers, following a predetermined route, and returns home after all customers are visited. The problem is to ?nd a fair allocation of the total cost of this tour among the customers served. A transferable-utility cooperative game can be associated with this cost allocation problem. We intro- duce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We characterize the Shapley Value in this class using a property which requires that sponsors do not bene?t from mergers, or splitting into a set of sponsors.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:41:y:2012:i:2:p:271-299
    DOI: 10.1007/s00182-011-0285-7
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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    2. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    3. Derks, J. & Tijs, S.H., 2000. "On merge properties of the Shapley value," Other publications TiSEM f9a2d218-87e0-4dc7-af3f-a, Tilburg University, School of Economics and Management.
    4. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    5. Chun, Youngsub, 2006. "A pessimistic approach to the queueing problem," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 171-181, March.
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    7. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
    8. Jean Derks & Jeroen Kuipers, 1997. "On the Core of Routing Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(2), pages 193-205.
    9. Youngsub Chun, 2011. "Consistency and monotonicity in sequencing problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 29-41, February.
    10. 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.
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    Cited by:

    1. Youngsub Chun & Nari Park & Duygu Yengin, 2016. "Coincidence of cooperative game theoretic solutions in the appointment problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 699-708, August.

    More about this item

    Keywords

    Fixed-route traveling salesman games; Routing games; Appointment games; The Shapley value; The core; Transferable-utility games; Merging and splitting proofness; Networks; Cost allocation; C71;

    JEL classification:

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

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