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Relationships between centrality measures and VCG mechanism

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  • Alessandro Avenali

    ()
    (Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza")

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    Abstract

    In this work we show that some recent centrality measures in network analysis are exactly an application of the principles underlying the Vickrey-Clarke-Groves (VCG) mechanism. We then present specific examples of completely different frameworks which highlights how these centrality measures ˆ la VCG can indeed provide valuable information to fairly assess the importance of the analyzed network elements. However, by taking inspiration from the relevant literature on the VCG auction design, we verify that in general cases centrality measures ˆ la VCG can determine a poor estimate of the actual significance of some network elements; therefore, we provide a general approach to effectively improve such estimates, based on applying the VCG rule to suitable groups of elements of the network.

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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/report/2014-05.pdf
    File Function: First version, 2014
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    Bibliographic Info

    Paper provided by Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza" in its series DIAG Technical Reports with number 2014-05.

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    Date of creation: 2014
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    Handle: RePEc:aeg:report:2014-05

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    Keywords: Network analysis; centrality measures; VCG mechanism; externalities;

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    1. Avenali, Alessandro, 2009. "Exploring the VCG mechanism in combinatorial auctions: The threshold revenue and the threshold-price rule," European Journal of Operational Research, Elsevier, vol. 199(1), pages 262-275, November.
    2. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
    3. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
    4. Gómez, Daniel & Figueira, José Rui & Eusébio, Augusto, 2013. "Modeling centrality measures in social network analysis using bi-criteria network flow optimization problems," European Journal of Operational Research, Elsevier, vol. 226(2), pages 354-365.
    5. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    6. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, October.
    7. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    8. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
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