On the core of routing games (original) (raw)

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 anO(n 2) 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.

Access this article

Log in via an institution

Subscribe and save

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. Aarts H, Solymosi T (1984) AnO(n 4) algorithm to determine the nucleolus of a routing game with non-empty core. Working paper, University of Twente, The Netherlands
    Google Scholar
  2. Aumann RJ, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the talmuds. Journal of Economic Theory 36: 195–213
    Google Scholar
  3. Curiel IJ, Pederzoli G, Tijs SH (1989) Sequencing games. European Journal of Operational Research 40: 344–351
    Google Scholar
  4. Derks JJM, Gilles R, Kuipers J (1994) Coalition formation with limited communication. Working paper, RE Maastricht, The Netherlands
  5. Fishburn PC, Pollack HO (1983) Fixed route cost allocation. American Mathematical Monthly 90: 366–378
    Google Scholar
  6. Fonlupt J, Naddef D (1992) The traveling salesman problem in graphs with some excluded minors. Mathematical Programming 53: 147–172
    Google Scholar
  7. Granot D, Huberman G (1981) Minimum cost spanning tree games. Mathematical Programming 21: 1–18
    Google Scholar
  8. Kuipers J (1994) Combinatorial methods in cooperative game theory. PhD Thesis, Maastricht
  9. Kuipers J (1991) A note on the 5-person traveling salesman game. Zeitschrift fur Operations Research 21: 339–351
    Google Scholar
  10. Maschler M, Peleg B, Shapley ES (1979) Geometric properties of the kernel, nucleolus, and related solution concepts. Methods of Operations Research 4: 303–338
    Google Scholar
  11. Owen G (1975) On the core of linear production games. Mathematical Programming 9: 358–370
    Google Scholar
  12. Papadimitriou CH, Steiglitz K (1982) Combinatorial optimization: Algorithms and complexity. Prentice-Hall
  13. Potters JAM, Curiel IJ, Tijs SH (1992) Traveling salesman games. Mathematical Programming 53: 199–211
    Google Scholar
  14. Shapley LS, Shubik M (1971) The assignment game_i_: the core. International Journal of Game Theory 1: 111–130
    Google Scholar
  15. Tamir A (1989) On the core of a traveling salesman cost allocation game. Operation Research Eetters 8: 31–34
    Google Scholar

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of General Sciences, University of Limburg, P.O. Box 616, 6200, MD Maastricht, The Netherlands
    Jean Derks & Jeroen Kuipers

Authors

  1. Jean Derks
  2. Jeroen Kuipers

Rights and permissions

About this article

Cite this article

Derks, J., Kuipers, J. On the core of routing games.Int J Game Theory 26, 193–205 (1997). https://doi.org/10.1007/BF01295848

Download citation

Keywords