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Asymmetric Auctions: Analytic Solutions to the General Uniform Case

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  • Todd R. Kaplan
  • Shmuel Zamir

Abstract

While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions.

Suggested Citation

  • Todd R. Kaplan & Shmuel Zamir, 2006. "Asymmetric Auctions: Analytic Solutions to the General Uniform Case," Discussion Paper Series dp432, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp432
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    1. Cantillon, Estelle, 2008. "The effect of bidders' asymmetries on expected revenue in auctions," Games and Economic Behavior, Elsevier, vol. 62(1), pages 1-25, January.
    2. Jacob Rubinstein & Elmar Wolfstetter & Michael Landsberger & Shmuel Zamir, 2001. "First-price auctions when the ranking of valuations is common knowledge," Review of Economic Design, Springer;Society for Economic Design, vol. 6(3), pages 461-480.
    3. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    4. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-142, February.
    5. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
    6. Plum, M, 1992. "Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 393-418.
    7. Wolfstetter, Elmar, 1996. " Auctions: An Introduction," Journal of Economic Surveys, Wiley Blackwell, vol. 10(4), pages 367-420, December.
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