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Strategyproof Nash Equilibria in Minimum Cost Spanning Tree Models

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  • Jens Leth Hougaard

    ()
    (Department of Food and Resource Economics, University of Copenhagen)

  • Mich Tvede

    ()
    (Department of Economics, University of Copenhagen)

Abstract

In this paper we consider the Minimum Cost Spanning Tree model. We assume that a central planner aims at implementing the minimum cost spanning tree not knowing the true link costs. The central planner sets up a game where agents announce the link costs, a tree is chosen and costs are allocated according to the rules of the game. We characterize ways of allocating costs such that true announcements constitute Nash equilibria. In particular, we nd that the Shapley rule with respect to the irreducible cost matrix is consistent with truthful announcements while a series of other well-known rules (such as the Bird-rule, Serial Equal Split, the Proportional rule etc.) are not.

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Bibliographic Info

Paper provided by University of Copenhagen, Department of Food and Resource Economics in its series MSAP Working Paper Series with number 01_2010.

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Length: 20 pages
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:foi:msapwp:01_2010

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Web page: http://www.msap.life.ku.dk/
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Related research

Keywords: Minimum cost spanning tree; Strategyproof Implementation; Nash equilibrium; Shapley value;

References

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  1. Jens Leth Hougaard & Hervé Moulin & Lars Peter Østerdal, 2008. "Decentralized Pricing in Minimum Cost Spanning Trees," Discussion Papers 08-24, University of Copenhagen. Department of Economics.
  2. Bergantiños, Gustavo & Vidal-Puga, Juan, 2009. "Additivity in minimum cost spanning tree problems," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 38-42, January.
  3. Ruben Juarez & Rajnish Kumar, 2010. "Implementing Efficient Graphs in Connection Networks," Working Papers 201022, University of Hawaii at Manoa, Department of Economics.
  4. Schmeidler David & Tauman Yair, 1994. "Incentive-Compatible Cost-Allocation Schemes," Journal of Economic Theory, Elsevier, vol. 63(2), pages 189-207, August.
  5. Peyton Young, H., 1998. "Cost allocation, demand revelation, and core implementation," Mathematical Social Sciences, Elsevier, vol. 36(3), pages 213-228, December.
  6. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
  7. Bergantiños, Gustavo & Vidal-Puga, Juan, 2010. "Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms," European Journal of Operational Research, Elsevier, vol. 201(3), pages 811-820, March.
  8. Sanjeev Goyal, 2007. "Introduction to Connections: An Introduction to the Economics of Networks
    [Connections: An Introduction to the Economics of Networks]
    ," Introductory Chapters, Princeton University Press.
  9. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-38, March.
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