Economic Theory

, Volume 44, Issue 2, pp 293–306 | Cite as

Decentralized pricing in minimum cost spanning trees

  • Jens Leth Hougaard
  • Hervé Moulin
  • Lars Peter Østerdal
Research Article

Abstract

In the minimum cost spanning tree model we consider decentralized pricing rules, i.e., rules that cover at least the efficient cost while the price charged to each user only depends upon his own connection costs. We define a canonical pricing rule and provide two axiomatic characterizations. First, the canonical pricing rule is the smallest among those that improve upon the Stand Alone bound, and are either superadditive or piece-wise linear in connection costs. Our second, direct characterization relies on two simple properties highlighting the special role of the source cost.

Keywords

Pricing rules Minimum cost spanning trees Canonical pricing rule Stand-alone cost Decentralization 

JEL Classification

C71 D60 

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References

  1. Aarts H., Driessen T.: The irreducible core of a minimum cost spanning tree game. ZOR Methods Models Oper Res 38, 163–174 (1993)CrossRefGoogle Scholar
  2. Bergantinos G., Vidal-Puga J.J.: A fair rule in minimum cost spanning tree problems. J Econ Theory 137, 326–352 (2007)CrossRefGoogle Scholar
  3. Bird C.G.: On cost allocation for a spanning tree: a game theoretic approach. Networks 6, 335–350 (1976)CrossRefGoogle Scholar
  4. Bogomolnaia A., Moulin H.: A new solution to the random assignment problem. J Econ Theory 100, 295–328 (2001)CrossRefGoogle Scholar
  5. Bogomolnaia, A., Moulin, H.: Sharing the cost of a minimal cost spanning tree: beyond the Folk solution, mimeo, Rice University (2008)Google Scholar
  6. Brânzei R., Moretti S., Norde H., Tijs S.: The P-value for cost sharing in minimum cost spanning tree situations. Theory Dec 56, 47–61 (2004)CrossRefGoogle Scholar
  7. Brams S.J., Taylor A.D.: Fair Division: from Cake-cutting to Dispute Resolution. Cambridge University Press, Cambridge (1996)Google Scholar
  8. Bollobas B.: Random Graphs. 2nd edn. Cambridge University Press, Cambridge (2001)Google Scholar
  9. Claus A., Kleitman D.J.: Cost allocation for a spanning tree. Networks 3, 289–304 (1973)CrossRefGoogle Scholar
  10. Demko S., Hill T.P.: Equitable distribution of indivisible objects. Math Soc Sci 16, 145–158 (1988)CrossRefGoogle Scholar
  11. Dubins, L.F.: Group decision devices, American Math Monthly, May, 350–356 (1977)Google Scholar
  12. Dutta B., Kar A.: Cost monotonicity, consistency, and minimum cost spanning tree games. Games Econ Behav 48, 223–248 (2004)CrossRefGoogle Scholar
  13. Feltkamp, T., Tijs, S., Muto, S.: On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems, mimeo University of Tilburg, CentER DP 94106 (1994)Google Scholar
  14. Kruskal J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7, 48–50 (1956)CrossRefGoogle Scholar
  15. Moulin H.: Characterizations of the pivotal mechanism. J Pub Econ 31, 53–78 (1986)CrossRefGoogle Scholar
  16. Moulin H.: Uniform externalities: two axioms for fair allocation. J Pub Econ 43, 305–326 (1990)CrossRefGoogle Scholar
  17. Moulin H.: Welfare bounds in the cooperative production problem. Games Econ Behav 4, 373–401 (1992)CrossRefGoogle Scholar
  18. Moulin H., Shenker S.: Strategyproof sharing of submodular costs: budget balance versus efficiency. Econ Theory 18, 511–533 (2001)CrossRefGoogle Scholar
  19. Norde H., Moretti S., Tijs S.: Minimum cost spanning tree games and population monotonic allocation schemes. Euro J Oper Res 154, 84–97 (2001)CrossRefGoogle Scholar
  20. Prim R.C.: Shortest connection networks and some generalizations. Bell Sys Tech J 36, 1389–1401 (1957)Google Scholar
  21. Sharkey W.W.: The Theory of Natural Monopoly. Cambridge University Press, Cambridge (1982)CrossRefGoogle Scholar
  22. Sharkey W.W. et al.: Network models in economics. In: Ball, (eds) Handbooks in Operations Research and Management Science, pp. 713–765. Elsevier, New York (1995)Google Scholar
  23. Steinhaus H.: The problem of fair division. Econometrica 16, 101–104 (1948)Google Scholar
  24. Thomson W.: Maximin Strategies and elicitation of preferences. In: Laffont, J.J. Aggregation and Revelation of Preferences, Studies in Public economics, North-Holland, Amsterdam (1979)Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Jens Leth Hougaard
    • 1
  • Hervé Moulin
    • 2
  • Lars Peter Østerdal
    • 3
  1. 1.Department of Food and Resource EconomicsUniversity of CopenhagenFrederiksberg C.Denmark
  2. 2.Department of EconomicsRice UniversityHoustonUSA
  3. 3.Department of EconomicsUniversity of CopenhagenCopenhagen K.Denmark

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