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On bidding with securities: Risk aversion and positive dependence

Author

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  • Abhishek, Vineet
  • Hajek, Bruce
  • Williams, Steven R.

Abstract

DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk aversion. However, it does not hold if affiliation is relaxed to a less restrictive form of positive dependence, namely first order stochastic dominance (FOSD). We define the relative strong steepness of families of securities and show that it provides a necessary and sufficient condition for comparing two families in the FOSD case. All results extend to the English auction.

Suggested Citation

  • Abhishek, Vineet & Hajek, Bruce & Williams, Steven R., 2015. "On bidding with securities: Risk aversion and positive dependence," Games and Economic Behavior, Elsevier, vol. 90(C), pages 66-80.
    • Handle: RePEc:eee:gamebe:v:90:y:2015:i:c:p:66-80
    DOI: 10.1016/j.geb.2015.02.004
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    References listed on IDEAS

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    1. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    2. Peter M. DeMarzo & Ilan Kremer & Andrzej Skrzypacz, 2005. "Bidding with Securities: Auctions and Security Design," American Economic Review, American Economic Association, vol. 95(4), pages 936-959, September.
    3. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    4. Byoung Jun & Elmar Wolfstetter, 2014. "Security bid auctions for agency contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 18(4), pages 289-319, December.
    5. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    6. Shimon Kogan & John Morgan, 2010. "Securities Auctions under Moral Hazard: An Experimental Study," Review of Finance, European Finance Association, vol. 14(3), pages 477-520.
    7. Ohlin, Jan, 1969. "On a class of measures of dispersion with application to optimal reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 5(2), pages 249-266, May.
    8. Yeon-Koo Che & Jinwoo Kim, 2010. "Bidding with Securities: Comment," American Economic Review, American Economic Association, vol. 100(4), pages 1929-1935, September.
    9. Luciano De Castro, 2010. "Affiliation, Equilibrium Existence and Revenue Ranking of Auctions," Discussion Papers 1530, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Abhishek, Vineet & Hajek, Bruce & Williams, Steven R., 2013. "Auctions with a profit sharing contract," Games and Economic Behavior, Elsevier, vol. 77(1), pages 247-270.
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    Cited by:

    1. Liu, Tingjun, 2016. "Optimal equity auctions with heterogeneous bidders," Journal of Economic Theory, Elsevier, vol. 166(C), pages 94-123.
    2. Andrés Fioriti & Allan Hernandez-Chanto, 2022. "Leveling the Playing Field for Risk-Averse Agents in Security-Bid Auctions," Management Science, INFORMS, vol. 68(7), pages 5441-5463, July.
    3. Diego Carrasco-Novoa & Allan Hernández-Chanto, 2022. "Competing Sellers in Security-Bid Auctions under Risk-Averse Bidders," Discussion Papers Series 655, School of Economics, University of Queensland, Australia.
    4. Zalzadeh, Saeed & Pellerey, Franco, 2016. "A positive dependence notion based on componentwise unimodality of copulas," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 51-57.
    5. Takeharu Sogo & Dan Bernhardt & Tingjun Liu, 2016. "Endogenous Entry to Security-Bid Auctions," American Economic Review, American Economic Association, vol. 106(11), pages 3577-3589, November.

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    More about this item

    Keywords

    Security bidding; Auction; Positive dependence; Risk aversion;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G00 - Financial Economics - - General - - - General

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