Optimal Multi-Object Auctions with Risk Averse Buyers

Kumru, Cagri and Yektas, Hadi (2008): Optimal Multi-Object Auctions with Risk Averse Buyers.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Multi-object Auctions, Optimal Auctions, Multi-dimensional Screening, Risk Averse Buyers, Bundling
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions

References

Armstrong, M. Optimal multi-object auctions, The Review of Economic Studies 67 (2000), 455 - 481. Armstrong, M. and Rochet, J., Multi-dimensional screening: A user's guide, European Economic Review 43 (1999), 959 - 979. Arrow K. J. Essays on the Theory of Risk Bearing, Amsterdam: North-Holland, 1971. Asplund M. Risk-averse firms in oligopoly, International Journal of Industrial Organization 20 (2002), 995 - 1012. Avery, C. and Hendershott, T. Bundling and optimal auctions of multiple products, The Review of Economic Studies 67 (2000), 483 - 497. Border, K. C. Implementation of reduced form auctions: A geometric approach, Econometrica 59 (1991), 1175 - 1187. Cox, J. C., Smith, V. L., and Walker, J. M., Theory and individual behavior of first-price auctions, Journal of Risk and Uncertainty 1 (1988), 61 - 99. J. Cremér and R. P. McLean, Full extraction of the surplus in Bayesian and dominant strategy auctions, Econometrica 56 (1988), 345 - 361. Eső, P. An optimal auction with correlated values and risk aversion, Journal of Economic Theory 125 (2005), 78 - 89. Figueroa N. and Skreta V. Optimal auction design for multiple objects with externalities, mimeo, University of Minnesota. Gal-Or, E. "Sales" and risk-averse consumers, Economica 50 (1983), 477-483. Harris, M. and Raviv, A. Allocation mechanisms and the design of auctions, Econometrica 49 (1981), 1477 - 1499. Kihlstrom, R. E. and Mirman L. J. Constant, increasing and decreasing risk aversion with many commodities, Review of Economic Studies 48 (1981), 271 - 280. Krishna, V. Auction Theory, San Diego, CA: Academic Press, 2002. Kobayashi, B. H. Does economics provide a reliable guide regulating commodity bundling by firms? A survey of the economic literature, Journal of Competition Law and Economics 1 (2005), 707 - 746. Levin J. An optimal auction for complements, Games and Economic Behavior 18 (1997), 176 - 192. Manelli, A. M. and Vincent, D. R. (2004a). Bundling as an optimal mechanism for a multiple-good monopolist, mimeo, Arizona State University and University of Maryland Manelli, A. M. and Vincent, D. R. (2004b). Multi-dimensional mechanism design: Revenue maximization and the multiple good monopolist, mimeo, Arizona State University and University of Maryland Maskin, E. and Riley, J. G. Optimal auctions with risk-averse buyers, Econometrica 52 (1984), 1473 - 1518. Maskin, E. and Riley, J. G. Optimal multi-unit auctions, in The Economics of Missing Markets, Information, and Games (F. Hahn, Ed.), Oxford: Oxford University Press, 1989. Matthews, S. A. Selling to risk-averse buyers with unobservable tastes, Journal of Economic Theory 30 (1983), 370 - 400. Menicucci, D. Optimal two-object auctions with synergies, Review of Economic Design 8 (2003), 143 - 164. Milgrom, P., Putting Auction Theory to Work, Cambridge, United Kingdom: Cambridge University Press, 2004. Myerson, R. B., Optimal auction design, Mathematics of Operations Research 6 (1981), 58 - 73. Pratt, J. Risk aversion in the small and in the large, Econometrica 32 (1964), 122-136. Palfrey, T. R. Bundling decision by a multi-product monopolist with incomplete information, Econometrica 51 (1983), 463-484.