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Optimal auction with a general distribution: Virtual valuation without densities

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  • Monteiro, Paulo Klinger
  • Svaiter, Benar Fux

Abstract

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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    1. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    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.
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    5. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    6. , & ,, 2007. "A non-differentiable approach to revenue equivalence," Theoretical Economics, Econometric Society, vol. 2(4), December.
    7. Page Jr., Frank H., 1998. "Existence of optimal auctions in general environments," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 389-418, May.
    8. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    9. 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.
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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. Christian Ewerhart, 2013. "Regular type distributions in mechanism design and $$\rho $$ -concavity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 591-603, August.
    6. Yi-Chun Chen & Xiangqian Yang, 2020. "Information Design in Optimal Auctions," Papers 2010.08990, arXiv.org, revised Oct 2022.
    7. Chen, Yi-Chun & Yang, Xiangqian, 2023. "Information design in optimal auctions," Journal of Economic Theory, Elsevier, vol. 212(C).
    8. 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.
    9. Monteiro, Paulo Klinger, 2015. "A note on the continuity of the optimal auction," Economics Letters, Elsevier, vol. 137(C), pages 127-130.
    10. Kotowski, Maciej H., 2018. "On asymmetric reserve prices," Theoretical Economics, Econometric Society, vol. 13(1), January.
    11. Yang, Kai Hao & Zentefis, Alexander K., 2023. "Regulating oligopolistic competition," Journal of Economic Theory, Elsevier, vol. 212(C).
    12. Maslov, Alexander & Noiset, Luc & Schwartz, Jesse A., 2022. "A closer look at two conjectures about irregular marginal revenue," Economics Letters, Elsevier, vol. 218(C).

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