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Truth-telling and Nash equilibria in minimum cost spanning tree models

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Listed author(s):
  • Hougaard, Jens Leth
  • Tvede, Mich

Abstract

In this paper we consider the minimum cost spanning tree model. We assume that a central planner aims at implementing a minimum cost spanning tree not knowing the true link costs. The central planner sets up a game where agents announce 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 both in case of full and incomplete information. In particular, we find that the Shapley rule based on 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, and the Proportional rule) are not.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 222 (2012)
Issue (Month): 3 ()
Pages: 566-570

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Handle: RePEc:eee:ejores:v:222:y:2012:i:3:p:566-570
DOI: 10.1016/j.ejor.2012.05.023
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

Keywords: Bayesian Nash equilibrium; Incomplete information; Minimum cost spanning tree; Shapley value; Nash equilibrium; Truth-telling;

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Cited by:

  1. Ruben Juarez & Rajnish Kumar, 2013. "Implementing efficient graphs in connection networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 359-403, October.
  2. Hougaard, Jens Leth & Tvede, Mich, 2015. "Minimum cost connection networks: Truth-telling and implementation," Journal of Economic Theory, Elsevier, vol. 157(C), pages 76-99.
  3. Bergantiños, Gustavo & Martínez, Ricardo, 2014. "Cost allocation in asymmetric trees," European Journal of Operational Research, Elsevier, vol. 237(3), pages 975-987.
  4. Gustavo Bergantiños & Juan Vidal-Puga, 2015. "Characterization of monotonic rules in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 835-868, November.
  5. Jens Leth Hougaard & Mich Tvede, 2011. "Incremental Cost Sharing in Chains and Fixed Trees," MSAP Working Paper Series 02_2011, University of Copenhagen, Department of Food and Resource Economics.

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