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Optimal Mechanism for Selling Two Goods

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Abstract

We solve for the optimal mechanism for selling two goods when the buyer’s demand characteristics are unobservable. In the case of substitutable goods, the seller has an incentive to offer lotteries over goods in order to charge the buyers with large differences in the valuations a higher price for obtaining their desired good with certainty. However, the seller also has a countervailing incentive to make the allocation of the goods among the participating buyers more efficient in order to increase the overall demand. In the case when the buyer can consume both goods, the seller has an incentive to underprovide one of the goods in order to charge the buyers with large valuations a higher price for the bundle of both goods. As in the case of substitutable goods, the seller also has a countervailing incentive to lower the price of the bundle in order to increase the overall demand.

Suggested Citation

  • Gregory Pavlov, 2010. "Optimal Mechanism for Selling Two Goods," UWO Department of Economics Working Papers 20103, University of Western Ontario, Department of Economics.
  • Handle: RePEc:uwo:uwowop:20103
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    References listed on IDEAS

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    1. Nicolas Gruyer, 2009. "Optimal auctions when a seller is bound to sell to collusive bidders," Post-Print hal-01021568, HAL.
    2. Nicolas Gruyer, 2009. "OPTIMAL AUCTIONS WHEN A SELLER IS BOUND TO SELL TO COLLUSIVE BIDDERS -super-," Journal of Industrial Economics, Wiley Blackwell, vol. 57(4), pages 835-850, December.
    3. Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, vol. 137(1), pages 153-185, November.
    4. Pavlov Gregory, 2011. "A Property of Solutions to Linear Monopoly Problems," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-18, February.
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    8. Gregory Pavlov, 2006. "Optimal Mechanism for Selling Substitutes," Boston University - Department of Economics - Working Papers Series WP2006-014, Boston University - Department of Economics.
    9. R. Preston McAfee & John McMillan & Michael D. Whinston, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 371-383.
    10. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
    11. William James Adams & Janet L. Yellen, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, Oxford University Press, vol. 90(3), pages 475-498.
    12. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in economics and econometrics: the eighth world congress," ULB Institutional Repository 2013/9557, ULB -- Universite Libre de Bruxelles.
    13. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
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    Cited by:

    1. Hurkens, Sjaak & Jeon, Doh-Shin & Menicucci, Domenico, 2013. "Dominance and Competitive Bundling," TSE Working Papers 13-423, Toulouse School of Economics (TSE).
    2. Reny, Philip J. & Hart, Sergiu, 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    3. Menicucci, Domenico & Hurkens, Sjaak & Jeon, Doh-Shin, 2015. "On the optimality of pure bundling for a monopolist," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 33-42.
    4. Antonio Rosato, 2016. "Selling substitute goods to loss-averse consumers: limited availability, bargains, and rip-offs," RAND Journal of Economics, RAND Corporation, vol. 47(3), pages 709-733, August.
    5. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    6. Pavlov Gregory, 2011. "A Property of Solutions to Linear Monopoly Problems," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-18, February.
    7. repec:eee:jetheo:v:172:y:2017:i:c:p:313-347 is not listed on IDEAS
    8. Tang, Pingzhong & Wang, Zihe, 2017. "Optimal mechanisms with simple menus," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 54-70.
    9. Rochet, Jean-Charles & Thanassoulis, John, 2017. "Intertemporal Price Discrimination with Multiple Products," CEPR Discussion Papers 12034, C.E.P.R. Discussion Papers.
    10. Armstrong, Mark, 2013. "A more general theory of commodity bundling," Journal of Economic Theory, Elsevier, vol. 148(2), pages 448-472.
    11. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    12. Cai, Yang & Daskalakis, Constantinos, 2015. "Extreme value theorems for optimal multidimensional pricing," Games and Economic Behavior, Elsevier, vol. 92(C), pages 266-305.
    13. repec:eee:jetheo:v:173:y:2018:i:c:p:95-117 is not listed on IDEAS

    More about this item

    Keywords

    Multidimensional screening; Price discrimination; Optimal selling strategies; Mechanism design;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

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