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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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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 41 (2012)
Issue (Month): 2 (May)
Pages: 271-299

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Handle: RePEc:spr:jogath:v:41:y:2012:i:2:p:271-299

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Related research

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;

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  1. Potters, J.A.M. & Curiel, I. & Tijs, S.H., 1992. "Traveling salesman games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154221, Tilburg University.
  2. Jean Derks & Jeroen Kuipers, 1997. "On the Core of Routing Games," International Journal of Game Theory, Springer, vol. 26(2), pages 193-205.
  3. MANIQUET, François, . "A characterization of the Shapley value in queueing problems," CORE Discussion Papers RP -1662, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  5. Chun, Youngsub, 2006. "A pessimistic approach to the queueing problem," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 171-181, March.
  6. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
  7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  8. Youngsub Chun, 2011. "Consistency and monotonicity in sequencing problems," International Journal of Game Theory, Springer, vol. 40(1), pages 29-41, February.
  9. Derks, J. & Tijs, S.H., 2000. "On merge properties of the Shapley value," Open Access publications from Tilburg University urn:nbn:nl:ui:12-86382, Tilburg University.
  10. 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.
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