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Traveling salesman games

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In this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited. We introduce two types of cooperative games—fixed-route traveling salesman games and traveling salesman games—as a tool to attack this problem. Under very mild conditions we prove that fixed-route traveling salesman games have non-empty cores if the fixed route is a solution of the classical traveling salesman problem. Core elements provide us with fair cost allocations. A traveling salesman game may have an empty core, even if the cost matrix satisfies the triangle inequality. In this paper we introduce a class of matrices defining TS-games with non-empty cores.

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  1. O.N. Bondareva, “Some applications of linear programming methods to the theory of cooperative games,”Problemy Kibernetiki 10 (1963) 119–129. [In Russian.]

    Google Scholar 

  2. D. Granot and G. Huberman, “Minimum cost spanning tree games,”Mathematical Programming 21 (1981) 1–18.

    Google Scholar 

  3. P.C. Fishburn and H.O. Pollak, “Fixed route cost allocation,”American Mathematical Monthly 90 (1983) 366–378.

    Google Scholar 

  4. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, eds.,The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Wiley, New York, 1985).

    Google Scholar 

  5. W.F. Lucas, “Applications of cooperative games to equitable allocations,” in:Game Theory and its Applications, Proceedings of Symposia in Applied Mathematics, Vol. 24, AMS Short Course (American Mathematical Society, Providence, RI, 1981).

    Google Scholar 

  6. G. Owen, “On the core of linear production games,”Mathematical Programming 9 (1975) 358–379.

    Google Scholar 

  7. G. Owen,Game Theory (Academic Press, New York, 1982).

    Google Scholar 

  8. J.A.M. Potters, “A class of traveling salesman games,” to appear in:Methods of Operations Research.

  9. A. Schrijver,Theory of Linear and Integer Programming (Wiley, New York, 1986) Chapter 19.

    Google Scholar 

  10. L.S. Shapley, “On balanced sets and cores,”Naval Research Logistics Quarterly 14 (1979) 453–460.

    Google Scholar 

  11. L.S. Shapley, “Discussant's comment,” in: S. Moriarty, ed.,Joint Cost Allocation (Oklahoma University Press, Norman, OK, 1981) pp. 131–136.

    Google Scholar 

  12. A. Tamir, “On the core of a traveling salesman cost allocation game,”Operations Research Letters 8 (1988) 31–34.

    Google Scholar 

  13. S.H. Tijs and T.H.S. Driessen, “Game theory and cost allocation problems,”Management Science 32 (1986) 1015–1028.

    Google Scholar 

  14. H.P. Young, “Methods and principles of cost allocation,” in: H.P. Young, ed.,Cost Allocation: Methods, Principles and Applications (North-Holland, New York, 1985) pp. 3–29.

    Google Scholar 

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Potters, J.A.M., Curiel, I.J. & Tijs, S.H. Traveling salesman games. Mathematical Programming 53, 199–211 (1992).

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