A Museum Cost Sharing Problem

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DOI: 10.4236/ajor.2011.12008    4,310 Downloads   8,807 Views   Citations
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ABSTRACT

Ginsburgh and Zang [2] consider a revenue sharing problem for the museum pass program, in which several museums jointly offer museum passes that allow visitors an unlimited access to participating museums in a certain period of time. We consider a cost sharing problem that can be regarded as the dual problem of the above revenue sharing problem. We assume that all museums are public goods and have various (e.g., ser-vice) costs. These costs must be shared by museum visitors. We propose a cost sharing method and provide an axiomatic characterization of the method. We then define a game for the problem and show that the cost sharing method is the Shapley value of the game. We also provide a comparative statics analysis for both the Shapley value of the museum pass game and the Shapley value for the cost sharing game when the number of museums and/or the number of visitors change.

Cite this paper

Y. Wang, "A Museum Cost Sharing Problem," American Journal of Operations Research, Vol. 1 No. 2, 2011, pp. 51-56. doi: 10.4236/ajor.2011.12008.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] V. Ginsburgh and I. Zang, “The Museum Pass Game and Its Value,” Games and Economic Behavior, Vol. 43, No. 2, 2003. pp. 322-325. doi:10.1016/S0899-8256(03)00013-7
[2] L. S. Shapley, “A Value for n-Person Games,” In: H. W. Kuhn and A. W. Tucker, Eds., Contributions to the Theory of Games II, Annals of Mathematics Studies, Princeton University Press, Princeton, Vol. 28, 1953, pp. 307-317.
[3] H. Moulin, “Axiomatic Cost and Surplus Sharing,” In: K. J. Arrow, A. K. Sen and K. Suzumura, Eds., Handbook of Social Choice and Welfare, North-Holland, Amsterdam, Ch.6, 2002, pp. 289-357
[4] H. Moulin and F. Laigret, “Equal-Need Sharing of a Network under Connectivity Constraints,” Games and Economic Behavior, Vol. 72, No. 1, 2011, pp. 314-320. doi:10.1016/j.geb.2010.08.002
[5] J. Aczel, “Function Equations and Their Applications,” Academic Press, New York, 1966.
[6] L. S. Shapley, “Cores of Convex Games,” International Journal of Game Theory, Vol. 1, No. 1, 1971, pp. 11-26. doi:10.1007/BF01753431
[7] C. Trudeau, “Cost Sharing with Multiple Technologies,” Working paper, University of Montreal, Montreal, 2007.

  
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