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Optimal two-object auctions with synergies

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  • Domenico Menicucci

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Abstract

We design the revenue-maximizing auction for two goods when each buyer has bi-dimensional private information and a superadditive utility function (i.e., a synergy is generated if a buyer wins both goods). In this setting the seller is likely to allocate the goods inefficiently with respect to an environ-ment with no synergies. In particular, if the synergy is large then it may occur that a buyer’s valuations for the goods weakly dominate the valuations of another buyer and the latter one receives the bundle. We link this fact, which contrasts with the results for a setting without synergies, to "non-regular" one-good models.

Suggested Citation

  • Domenico Menicucci, 2001. "Optimal two-object auctions with synergies," ICER Working Papers - Applied Mathematics Series 18-2001, ICER - International Centre for Economic Research.
  • Handle: RePEc:icr:wpmath:18-2001
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    References listed on IDEAS

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    Cited by:

    1. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003.
    2. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 471-496, October.
    3. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    4. Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
    5. Elisa Luciano & Elena Vigna, 2005. "A note on stochastic survival probabilities and their calibration," ICER Working Papers - Applied Mathematics Series 1-2005, ICER - International Centre for Economic Research.
    6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean-Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521.
    7. Kumru, Cagri & Yektas, Hadi, 2008. "Optimal Multi-Object Auctions with Risk Averse Buyers," MPRA Paper 7575, University Library of Munich, Germany.
    8. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2004. "Hierarchical mixture modelling with normalized inverse Gaussian priors," ICER Working Papers - Applied Mathematics Series 12-2004, ICER - International Centre for Economic Research.
    9. Hikmet Gunay & Xin Meng, 2012. "Exposure Problem in Multi-unit Auctions," ISER Discussion Paper 0848, Institute of Social and Economic Research, Osaka University.
    10. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    11. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
    12. Elisa Luciano & Elena Vigna, 2005. "Non mean reverting affine processes for stochastic mortality," ICER Working Papers - Applied Mathematics Series 4-2005, ICER - International Centre for Economic Research.
    13. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.
    14. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    15. Lancelot F. James & Antonio Lijoi & Igor Pruenster, 2005. "Bayesian Inference via Classes of Normalized Random Measures," ICER Working Papers - Applied Mathematics Series 5-2005, ICER - International Centre for Economic Research.
    16. Sandro Brusco & Giuseppe Lopomo, 2002. "Collusion via Signalling in Simultaneous Ascending Bid Auctions with Heterogeneous Objects, with and without Complementarities," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 407-436.
    17. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
    18. repec:eee:indorg:v:52:y:2017:i:c:p:165-187 is not listed on IDEAS
    19. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
    20. Fabio Maccheroni & William H. Ruckle, 2001. "BV as a dual space," ICER Working Papers - Applied Mathematics Series 29-2001, ICER - International Centre for Economic Research.
    21. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research.
    22. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.

    More about this item

    Keywords

    Multiple-unit Auctions; Multi-dimensional Screening; Bundling;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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