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On the Core of Routing Games

Author

Listed:
  • Jean Derks

    (Department of Mathematics, Faculty of General Sciences, University of Limburg, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

  • Jeroen Kuipers

    (Department of Mathematics, Faculty of General Sciences, University of Limburg, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

Abstract

A repairman makes a round-trip along a set of customers. He starts in his home location, visits each customer exactly once, and returns home. The cost of his trip has to be shared by the customers. A cooperative cost game, called routing game, is associated with this allocation problem, and an {\cal O}(n2) algorithm is given which computes a core element of a routing game if the core is non-empty. The non-emptiness of the core depends on the tour which is traversed by the repairman. Several procedures are given to construct tours which guarantee the non-emptiness of the core.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:26:y:1997:i:2:p:193-205
    Note: Received May 1993 Revised version May 1994
    as

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    Citations

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    Cited by:

    1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    2. Arantza Estévez-Fernández & Peter Borm & Marc Meertens & Hans Reijnierse, 2009. "On the core of routing games with revenues," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 291-304, June.
    3. 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.
    4. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
    5. Duygu Yengin, 2009. "Appointment Games in Fixed-Route Traveling Salesman Problems and the Shapley Value," School of Economics Working Papers 2009-28, University of Adelaide, School of Economics.

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