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Optimal auction with a general distribution: Virtual valuation without densities


  • Monteiro, Paulo Klinger
  • Svaiter, Benar Fux


We characterize the optimal auction in an independent private values framework for a completely general distribution of valuations. We do this introducing a new concept: the generalized virtual valuation. To show the wider applicability of this concept we present two examples showing how to extend the classical models of Mussa and Rosen and Baron and Myerson for arbitrary distributions.

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  • Monteiro, Paulo Klinger & Svaiter, Benar Fux, 2010. "Optimal auction with a general distribution: Virtual valuation without densities," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 21-31, January.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:21-31

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    References listed on IDEAS

    1. Page Jr., Frank H., 1998. "Existence of optimal auctions in general environments," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 389-418, May.
    2. Baron, David P & Myerson, Roger B, 1982. "Regulating a Monopolist with Unknown Costs," Econometrica, Econometric Society, vol. 50(4), pages 911-930, July.
    3. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    4. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    5. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    6. Subir Bose & Arup Daripa, 2009. "Optimal sale across venues and auctions with a buy-now option," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 137-168, January.
    7. Che, Yeon-Koo & Gale, Ian, 2006. "Revenue comparisons for auctions when bidders have arbitrary types," Theoretical Economics, Econometric Society, vol. 1(1), pages 95-118, March.
    8. Olszewski, Wojciech & Chung, Kim-Sau, 2007. "A non-differentiable approach to revenue equivalence," Theoretical Economics, Econometric Society, vol. 2(4), December.
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    Cited by:

    1. Paulo Monteiro, 2009. "Abstract types and distributions in independent private value auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 497-507, September.
    2. Monteiro, Paulo Klinger & Page, Frank H. & Svaiter, Benar fux, 2013. "Optimal auctions with multidimensional types and the desirability of exclusion," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 106-110.
    3. Skreta, Vasiliki, 2015. "Optimal auction design under non-commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 854-890.
    4. Bougheas, Spiros & Worrall, Tim, 2012. "Cost padding in regulated monopolies," International Journal of Industrial Organization, Elsevier, vol. 30(4), pages 331-341.
    5. L. Elisa Celis & Gregory Lewis & Markus Mobius & Hamid Nazerzadeh, 2011. "Buy-it-now or Take-a-chance: A New Pricing Mechanism for Online Advertising," Working Papers 11-21, NET Institute, revised Nov 2011.
    6. Monteiro, Paulo Klinger, 2015. "A note on the continuity of the optimal auction," Economics Letters, Elsevier, vol. 137(C), pages 127-130.


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