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On monotone strategy equilibria in simultaneous auctions for complementary goods

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  • Gentry, Matthew
  • Komarova, Tatiana
  • Schiraldi, Pasquale
  • Shin, Wiroy
Abstract
We explore existence and properties of equilibrium when N≥2 bidders compete for L≥2 objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for L objects against many local bidders who bid for single objects only. We then consider monotone equilibrium with endogenous tiebreaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that these exist in general. These existence results apply to many auction formats, including first-price, second-price, and all-pay.

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  • Gentry, Matthew & Komarova, Tatiana & Schiraldi, Pasquale & Shin, Wiroy, 2019. "On monotone strategy equilibria in simultaneous auctions for complementary goods," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 109-128.
    • Handle: RePEc:eee:mateco:v:85:y:2019:i:c:p:109-128
    DOI: 10.1016/j.jmateco.2019.08.006
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    1. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    2. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    3. Joachim R. Groeger, 2014. "A Study Of Participation In Dynamic Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1129-1154, November.
    4. Sandro Brusco & Giuseppe Lopomo, 2009. "Simultaneous ascending auctions with complementarities and known budget constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 105-124, January.
    5. Rosenthal, Robert W. & Wang, Ruqu, 1996. "Simultaneous Auctions with Synergies and Common Values," Games and Economic Behavior, Elsevier, vol. 17(1), pages 32-55, November.
    6. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    7. Peter Cramton, 1997. "The FCC Spectrum Auctions: An Early Assessment," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(3), pages 431-495, September.
    8. Hendricks, Kenneth & Porter, Robert H, 1988. "An Empirical Study of an Auction with Asymmetric Information," American Economic Review, American Economic Association, vol. 78(5), pages 865-883, December.
    9. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
    10. Krishna, Vijay & Rosenthal, Robert W., 1996. "Simultaneous Auctions with Synergies," Games and Economic Behavior, Elsevier, vol. 17(1), pages 1-31, November.
    11. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
    12. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    13. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    14. Lawrence M. Ausubel & Peter Cramton, 2004. "Auctioning Many Divisible Goods," Journal of the European Economic Association, MIT Press, vol. 2(2-3), pages 480-493, 04/05.
    15. Jeremy T. Fox & Patrick Bajari, 2013. "Measuring the Efficiency of an FCC Spectrum Auction," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 100-146, February.
    16. Paul Klemperer, 2010. "The Product-Mix Auction: A New Auction Design for Differentiated Goods," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 526-536, 04-05.
    17. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1039-1056.
    18. Susan Athey & Jonathan Levin & Enrique Seira, 2011. "Comparing open and Sealed Bid Auctions: Evidence from Timber Auctions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(1), pages 207-257.
    19. Bikhchandani, Sushil, 1999. "Auctions of Heterogeneous Objects," Games and Economic Behavior, Elsevier, vol. 26(2), pages 193-220, January.
    20. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    21. Meng, Xin & Gunay, Hikmet, 2017. "Exposure problem in multi-unit auctions," International Journal of Industrial Organization, Elsevier, vol. 52(C), pages 165-187.
    22. Goeree, Jacob K. & Lien, Yuanchuan, 2014. "An equilibrium analysis of the simultaneous ascending auction," Journal of Economic Theory, Elsevier, vol. 153(C), pages 506-533.
    23. Szentes, Balazs & Rosenthal, Robert W., 2003. "Three-object two-bidder simultaneous auctions: chopsticks and tetrahedra," Games and Economic Behavior, Elsevier, vol. 44(1), pages 114-133, July.
    24. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    25. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
    26. Sandro Brusco & Giuseppe Lopomo, 2002. "Collusion via Signalling in Simultaneous Ascending Bid Auctions with Heterogeneous Objects, with and without Complementarities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(2), pages 407-436.
    27. Anders Lunander & Sofia Lundberg, 2013. "Bids And Costs In Combinatorial And Noncombinatorial Procurement Auctions—Evidence From Procurement Of Public Cleaning Contracts," Contemporary Economic Policy, Western Economic Association International, vol. 31(4), pages 733-745, October.
    28. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    29. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    30. Ali Hortaçsu & Steven L. Puller, 2008. "Understanding strategic bidding in multi‐unit auctions: a case study of the Texas electricity spot market," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 86-114, March.
    31. Hortaçsu, Ali, 2011. "Recent progress in the empirical analysis of multi-unit auctions," International Journal of Industrial Organization, Elsevier, vol. 29(3), pages 345-349, May.
    32. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    33. Kenneth Hendricks & Joris Pinkse & Robert H. Porter, 2003. "Empirical Implications of Equilibrium Bidding in First-Price, Symmetric, Common Value Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 115-145.
    34. Ali Hortaçsu & David McAdams, 2010. "Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the Turkish Treasury Auction Market," Journal of Political Economy, University of Chicago Press, vol. 118(5), pages 833-865.
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    2. Andrea Canidio & Felix Henneke, 2024. "Combinatorial Auctions without a Numeraire: The Case of Blockchain Trade-Intent Auctions," Papers 2408.12225, arXiv.org.

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    More about this item

    Keywords

    Simultaneous auctions; Complementarities; Synergies; Equilibria existence; Multi-object auctions; Monotone strategies;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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