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Optimal Multi-Object Auctions with Risk Averse Buyers

Author

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  • Kumru, Cagri
  • Yektas, Hadi

Abstract

We analyze the optimal auction of multiple non-identical objects when buyers are risk averse. We show that the auction formats that yield the maximum revenue in the risk neutral case are no longer optimal. In particular, selling the goods independently does not maximize the seller's revenue. We observe that seller's incentive for bundling arises solely due to the risk aversion of the buyers. The optimal auction which remains weakly efficient has the following properties: The seller perfectly insures all buyers against the risk of losing the object(s) for which they have high valuation. While the buyers who have high valuation for both objects are compensated if they do not win either object, the buyers who have low valuation for both objects incur a positive payment to the seller in the same event.

Suggested Citation

  • Kumru, Cagri & Yektas, Hadi, 2008. "Optimal Multi-Object Auctions with Risk Averse Buyers," MPRA Paper 7575, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7575
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    File URL: https://mpra.ub.uni-muenchen.de/7575/1/MPRA_paper_7575.pdf
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    References listed on IDEAS

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    1. Richard E. Kihlstrom & Leonard J. Mirman, 1981. "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," Review of Economic Studies, Oxford University Press, vol. 48(2), pages 271-280.
    2. Eso, Peter, 2005. "An optimal auction with correlated values and risk aversion," Journal of Economic Theory, Elsevier, vol. 125(1), pages 78-89, November.
    3. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    4. Mark Armstrong, 2000. "Optimal Multi-Object Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 455-481.
    5. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    6. Asplund, Marcus, 2002. "Risk-averse firms in oligopoly," International Journal of Industrial Organization, Elsevier, vol. 20(7), pages 995-1012, September.
    7. Levin, Jonathan, 1997. "An Optimal Auction for Complements," Games and Economic Behavior, Elsevier, vol. 18(2), pages 176-192, February.
    8. Vasiliki Skreta & Nicolas Figueroa, 2004. "Optimal Auction Design For Multiple Objects with Externalities," Econometric Society 2004 Latin American Meetings 287, Econometric Society.
    9. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
    10. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 143-164, October.
    11. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, April.
    12. Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-1499, November.
    13. Christopher Avery & Terrence Hendershott, 2000. "Bundling and Optimal Auctions of Multiple Products," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 483-497.
    14. Cox, James C & Smith, Vernon L & Walker, James M, 1988. "Theory and Individual Behavior of First-Price Auctions," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 61-99, March.
    15. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
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    More about this item

    Keywords

    Multi-object Auctions; Optimal Auctions; Multi-dimensional Screening; Risk Averse Buyers; Bundling;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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