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Appointment Games in Fixed-Route Traveling Salesman Problems and the Shapley Value

Author

Listed:
  • Duygu Yengin

    (School of Economics, University of Adelaide)

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 find 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 introduce a new class of games, which we refer as the fixed-route traveling salesman games with appointments. We study the Shapley Value in this class and show that it is in the core. Our first characterization of the Shapley value involves a property which requires that sponsors do not benefit from mergers, or splitting into a set of sponsors. Our second theorem involves a property which requires that the cost shares of two sponsors who get connected are equally effected. We also show that except for our second theorem, none of our results for appointment games extend to the class of routing games (Potters et al, 1992).

Suggested Citation

  • Duygu Yengin, 2009. "Appointment Games in Fixed-Route Traveling Salesman Problems and the Shapley Value," School of Economics and Public Policy Working Papers 2009-28, University of Adelaide, School of Economics and Public Policy.
    • Handle: RePEc:adl:wpaper:2009-28
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    File URL: https://media.adelaide.edu.au/economics/papers/doc/wp2009-28.pdf
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    References listed on IDEAS

    as
    1. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 763-774, November.
    2. Biung-Ghi Ju, 2003. "Manipulation via merging and splitting in claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 205-215, October.
    3. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    4. Jean Derks & Stef Tijs, 2000. "On Merge Properties Of The Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 249-257.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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