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Analytical solution of $k$th price auction

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  • Martin Mihelich
  • Yan Shu

Abstract

We provide an exact analytical solution of the Nash equilibrium for the $k$th price auction by using inverse of distribution functions. As applications, we identify the unique symmetric equilibrium where the valuations have polynomial distribution, fat tail distribution and exponential distributions.

Suggested Citation

  • Martin Mihelich & Yan Shu, 2019. "Analytical solution of $k$th price auction," Papers 1911.04865, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1911.04865
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    References listed on IDEAS

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    1. Eric Maskin, 2004. "The Unity of Auction Theory: Paul Milgrom's Masterclass," Economics Working Papers 0044, Institute for Advanced Study, School of Social Science.
    2. Gadi Fibich & Arieh Gavious, 2010. "Large auctions with risk-averse bidders," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 359-390, July.
    3. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    4. Eric Maskin, 2004. "The Unity of Auction Theory: Milgrom's Masterclass," Journal of Economic Literature, American Economic Association, vol. 42(4), pages 1102-1115, December.
    5. Nawar, Abdel-Hameed & Sen, Debapriya, 2018. "kth price auctions and Catalan numbers," Economics Letters, Elsevier, vol. 172(C), pages 69-73.
    6. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    7. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    8. Robert B. Wilson, 2021. "Strategic Analysis of Auctions," Econometrica, Econometric Society, vol. 89(2), pages 555-561, March.
    9. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
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