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On Chinese postman games where residents of each road pay the cost of their road

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  • Granot, Daniel
  • Hamers, Herbert
  • Kuipers, Jeroen
  • Maschler, Michael
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    Abstract

    We study the extended Chinese postman (CP) cooperative game induced by a connected, weighted, undirected graph G, wherein a postman, starting from a post office location, needs to traverse all edges wherein players reside, before returning to the post-office. We characterize the graphs associated with all CP games in which the players on a road pay exactly the cost of the road at each core point, regardless of the number of players residing on the road, the location of the post-office and the edge-weight functions. Here, a road is a maximal path all of whose interior vertices have a degree equal to two in G. For this class of games, the core and nucleolus are Cartesian products of CP games induced by simple cyclic graphs, the core is determined by at most 2n-1 constraints and the nucleolus can be computed in time.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0899825610000308
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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 72 (2011)
    Issue (Month): 2 (June)
    Pages: 427-438

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    Handle: RePEc:eee:gamebe:v:72:y:2011:i:2:p:427-438

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Cooperative games Cost allocation Core Nucleolus Chinese postman;

    References

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    1. Jeroen Kuipers & Ulrich Faigle & Walter Kern, 2001. "On the computation of the nucleolus of a cooperative game," International Journal of Game Theory, Springer, vol. 30(1), pages 79-98.
    2. Hamers, Herbert & Borm, Peter & van de Leensel, Robert & Tijs, Stef, 1999. "Cost allocation in the Chinese postman problem," European Journal of Operational Research, Elsevier, vol. 118(1), pages 153-163, October.
    3. Granot, D. & Hamers, H.J.M. & Tijs, S.H., 1999. "On some balanced, totally balanced and submodular delivery games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-81026, Tilburg University.
    4. Maschler, M & Potters, J A M & Tijs, S H, 1992. "The General Nucleolus and the Reduced Game Property," International Journal of Game Theory, Springer, vol. 21(1), pages 85-106.
    5. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667 Elsevier.
    6. Maschler, M. & Potters, J.A.M. & Tijs, S.H., 1992. "The general nucleolus and the reduced game property," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154217, Tilburg University.
    7. Hamers, Herbert, 1997. "On the concavity of delivery games," European Journal of Operational Research, Elsevier, vol. 99(2), pages 445-458, June.
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