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Combinatorial auctions in practice

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  • Palacios-Huerta, Ignacio
  • Parkes, David C.
  • Steinberg, Richard

Abstract

We survey the uses of combinatorial auctions that have been deployed in practice, giving emphasis to their key representational and economic aspects. In addition, we discuss behavioral economics considerations on both the bidder and auctioneer sides of the market, and the interrelated topics of simplicity and trust, highlighting key opportunities for future work.

Suggested Citation

  • Palacios-Huerta, Ignacio & Parkes, David C. & Steinberg, Richard, 2024. "Combinatorial auctions in practice," LSE Research Online Documents on Economics 124108, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:124108
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    1. Manuel Amador & Iván Werning & George-Marios Angeletos, 2006. "Commitment vs. Flexibility," Econometrica, Econometric Society, vol. 74(2), pages 365-396, March.
    2. Benjamin Enke & Thomas W. Graeber, 2021. "Cognitive Uncertainty in Intertemporal Choice," CESifo Working Paper Series 9472, CESifo.
    3. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    4. Alexander Teytelboym & Shengwu Li & Scott Duke Kominers & Mohammad Akbarpour & Piotr Dworczak, 2021. "Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(3), pages 709-750, July.
    5. Bazelon, Coleman, 2009. "Too many goals: Problems with the 700Â MHz auction," Information Economics and Policy, Elsevier, vol. 21(2), pages 115-127, June.
    6. Mochon, Asuncion & Saez, Yago, 2017. "A review of radio spectrum combinatorial clock auctions," Telecommunications Policy, Elsevier, vol. 41(5), pages 303-324.
    7. Rafael Epstein & Lysette Henríquez & Jaime Catalán & Gabriel Y. Weintraub & Cristián Martínez, 2002. "A Combinational Auction Improves School Meals in Chile," Interfaces, INFORMS, vol. 32(6), pages 1-14, December.
    8. Martin Bichler & Pasha Shabalin & Jürgen Wolf, 2013. "Do core-selecting Combinatorial Clock Auctions always lead to high efficiency? An experimental analysis of spectrum auction designs," Experimental Economics, Springer;Economic Science Association, vol. 16(4), pages 511-545, December.
    9. Ernesto Dal Bó & Pedro Dal Bó & Erik Eyster, 2018. "The Demand for Bad Policy when Voters Underappreciate Equilibrium Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 964-998.
    10. Peter Cramton, 2013. "Spectrum Auction Design," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 42(2), pages 161-190, March.
    11. Moreno, R. & Barroso, L.A. & Rudnick, H. & Mocarquer, S. & Bezerra, B., 2010. "Auction approaches of long-term contracts to ensure generation investment in electricity markets: Lessons from the Brazilian and Chilean experiences," Energy Policy, Elsevier, vol. 38(10), pages 5758-5769, October.
    12. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    13. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    14. Paul Klemperer, 2002. "What Really Matters in Auction Design," Journal of Economic Perspectives, American Economic Association, vol. 16(1), pages 169-189, Winter.
    15. Paul Milgrom, 2021. "Auction Research Evolving: Theorems and Market Designs," American Economic Review, American Economic Association, vol. 111(5), pages 1383-1405, May.
    16. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2013. "Salience and Consumer Choice," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 803-843.
    17. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1133-1165.
    18. Abraham Neyman, 1998. "Finitely Repeated Games with Finite Automata," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 513-552, August.
    19. Patrick Bajari & Ali Hortacsu, 2005. "Are Structural Estimates of Auction Models Reasonable? Evidence from Experimental Data," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 703-741, August.
    20. Yossi Sheffi, 2004. "Combinatorial Auctions in the Procurement of Transportation Services," Interfaces, INFORMS, vol. 34(4), pages 245-252, August.
    21. Hal R. Varian & Christopher Harris, 2014. "The VCG Auction in Theory and Practice," American Economic Review, American Economic Association, vol. 104(5), pages 442-445, May.
    22. Peter Cramton & Evan Kwerel & Gregory Rosston & Andrzej Skrzypacz, 2011. "Using Spectrum Auctions to Enhance Competition in Wireless Services," Journal of Law and Economics, University of Chicago Press, vol. 54(S4), pages 167-188.
    23. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2012. "Salience Theory of Choice Under Risk," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1243-1285.
    24. John O. Ledyard & Mark Olson & David Porter & Joseph A. Swanson & David P. Torma, 2002. "The First Use of a Combined-Value Auction for Transportation Services," Interfaces, INFORMS, vol. 32(5), pages 4-12, October.
    25. Tukiainen, Janne, 2008. "Testing for common costs in the City of Helsinki bus transit auctions," International Journal of Industrial Organization, Elsevier, vol. 26(6), pages 1308-1322, November.
    26. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    27. Mark Armstrong & Steffen Huck, 2011. "Behavioral Economics as Applied to Firms: A Primer," Antitrust Chronicle, Competition Policy International, vol. 1.
    28. Terri Kneeland, 2015. "Identifying Higher‐Order Rationality," Econometrica, Econometric Society, vol. 83(5), pages 2065-2079, September.
    29. Kursad Derinkuyu & Fehmi Tanrisever & Nermin Kurt & Gokhan Ceyhan, 2020. "Optimizing Day-Ahead Electricity Market Prices: Increasing the Total Surplus for Energy Exchange Istanbul," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 700-716, July.
    30. David Gill & Victoria Prowse, 2016. "Cognitive Ability, Character Skills, and Learning to Play Equilibrium: A Level-k Analysis," Journal of Political Economy, University of Chicago Press, vol. 124(6), pages 1619-1676.
    31. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    32. Daniel Keniston & Bradley J. Larsen & Shengwu Li & J.J. Prescott & Bernardo S. Silveira & Chuan Yu, 2021. "Fairness in Incomplete Information Bargaining: Theory and Widespread Evidence from the Field," NBER Working Papers 29111, National Bureau of Economic Research, Inc.
    33. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    34. Kagel, John H & Harstad, Ronald M & Levin, Dan, 1987. "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, Econometric Society, vol. 55(6), pages 1275-1304, November.
    35. Ali Hortaçsu & Fernando Luco & Steven L. Puller & Dongni Zhu, 2019. "Does Strategic Ability Affect Efficiency? Evidence from Electricity Markets," American Economic Review, American Economic Association, vol. 109(12), pages 4302-4342, December.
    36. 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.
    37. Gail Hohner & John Rich & Ed Ng & Grant Reid & Andrew J. Davenport & Jayant R. Kalagnanam & Ho Soo Lee & Chae An, 2003. "Combinatorial and Quantity-Discount Procurement Auctions Benefit Mars, Incorporated and Its Suppliers," Interfaces, INFORMS, vol. 33(1), pages 23-35, February.
    38. Eugenio Proto & Aldo Rustichini & Andis Sofianos, 2019. "Intelligence, Personality, and Gains from Cooperation in Repeated Interactions," Journal of Political Economy, University of Chicago Press, vol. 127(3), pages 1351-1390.
    39. Luiz T. A. Maurer & Luiz A. Barroso, 2011. "Electricity Auctions : An Overview of Efficient Practices," World Bank Publications - Books, The World Bank Group, number 2346.
    40. Marcelo Olivares & Gabriel Y. Weintraub & Rafael Epstein & Daniel Yung, 2012. "Combinatorial Auctions for Procurement: An Empirical Study of the Chilean School Meals Auction," Management Science, INFORMS, vol. 58(8), pages 1458-1481, August.
    41. Christian Kroemer & Martin Bichler & Andor Goetzendorff, 2016. "(Un)expected Bidder Behavior in Spectrum Auctions: About Inconsistent Bidding and Its Impact on Efficiency in the Combinatorial Clock Auction," Group Decision and Negotiation, Springer, vol. 25(1), pages 31-63, January.
    42. John H. Kagel & Yuanchuan Lien & Paul Milgrom, 2010. "Ascending Prices and Package Bidding: A Theoretical and Experimental Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 2(3), pages 160-185, August.
    43. Robert L. Graves & Linus Schrage & Jayaram Sankaran, 1993. "An Auction Method for Course Registration," Interfaces, INFORMS, vol. 23(5), pages 81-92, October.
    44. Kagel, John H. & Lien, Yuanchuan & Milgrom, Paul, 2014. "Ascending prices and package bidding: Further experimental analysis," Games and Economic Behavior, Elsevier, vol. 85(C), pages 210-231.
    45. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    46. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 23-46.
    47. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    48. Benjamin Enke, 2020. "What You See Is All There Is," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(3), pages 1363-1398.
    49. 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.
    50. Peter Cramton & Axel Ockenfels, 2017. "The German 4G Spectrum Auction: Design and Behaviour," Economic Journal, Royal Economic Society, vol. 127(605), pages 305-324, October.
    51. Hendricks, Kenneth & Porter, Robert H & Boudreau, Bryan, 1987. "Information, Returns, and Bidding Behavior in OCS Auctions: 1954-1969," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 517-542, June.
    52. Larbi Alaoui & Antonio Penta, 2022. "Cost-Benefit Analysis in Reasoning," Journal of Political Economy, University of Chicago Press, vol. 130(4), pages 881-925.
    53. Tobias Scheffel & Georg Ziegler & Martin Bichler, 2012. "On the impact of package selection in combinatorial auctions: an experimental study in the context of spectrum auction design," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 667-692, December.
    54. Lawrence M. Ausubel & Oleg Baranov, 2017. "A Practical Guide to the Combinatorial Clock Auction," Economic Journal, Royal Economic Society, vol. 127(605), pages 334-350, October.
    55. Salop, Steven C & Scheffman, David T, 1987. "Cost-Raising Strategies," Journal of Industrial Economics, Wiley Blackwell, vol. 36(1), pages 19-34, September.
    56. Heidhues, Paul & Köszegi, Botond, 2018. "Behavioral Industrial Organization," CEPR Discussion Papers 12988, C.E.P.R. Discussion Papers.
    57. Janssen, Maarten & Karamychev, Vladimir, 2016. "Spiteful bidding and gaming in combinatorial clock auctions," Games and Economic Behavior, Elsevier, vol. 100(C), pages 186-207.
    58. Anders Lunander & Sofia Lundberg, 2012. "Combinatorial auctions in public procurement: Experiences from sweden," Journal of Public Procurement, Emerald Group Publishing Limited, vol. 12(1), pages 81-108, March.
    59. Botond Koszegi & Matthew Rabin, 2007. "Reference-Dependent Risk Attitudes," American Economic Review, American Economic Association, vol. 97(4), pages 1047-1073, September.
    60. Benjamin Enke & Thomas Graeber, 2021. "Cognitive Uncertainty in Intertemporal Choice," NBER Working Papers 29577, National Bureau of Economic Research, Inc.
    61. Mohammad Akbarpour & Shengwu Li, 2020. "Credible Auctions: A Trilemma," Econometrica, Econometric Society, vol. 88(2), pages 425-467, March.
    62. Tuomas Sandholm & David Levine & Michael Concordia & Paul Martyn & Rick Hughes & Jim Jacobs & Dennis Begg, 2006. "Changing the Game in Strategic Sourcing at Procter & Gamble: Expressive Competition Enabled by Optimization," Interfaces, INFORMS, vol. 36(1), pages 55-68, February.
    63. Sang Won Kim & Marcelo Olivares & Gabriel Y. Weintraub, 2014. "Measuring the Performance of Large-Scale Combinatorial Auctions: A Structural Estimation Approach," Management Science, INFORMS, vol. 60(5), pages 1180-1201, May.
    64. , K. & ,, 2016. "On the impossibility of core-selecting auctions," Theoretical Economics, Econometric Society, vol. 11(1), January.
    65. Lawrence M. Ausubel & Oleg Baranov, 2017. "A Practical Guide to the Combinatorial Clock Auction," Economic Journal, Royal Economic Society, vol. 127(605), pages 334-350, October.
    66. Janssen, Maarten & Karamychev, Vladimir, 2017. "Raising rivals’ cost in multi-unit auctions," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 473-490.
    67. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-429, February.
    68. Rothkopf, Michael H & Teisberg, Thomas J & Kahn, Edward P, 1990. "Why Are Vickrey Auctions Rare?," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 94-109, February.
    69. Baghestanian, Sascha & Frey, Seth, 2016. "GO figure: Analytic and strategic skills are separable," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 71-80.
    70. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    71. Avi Goldfarb & Mo Xiao, 2011. "Who Thinks about the Competition? Managerial Ability and Strategic Entry in US Local Telephone Markets," American Economic Review, American Economic Association, vol. 101(7), pages 3130-3161, December.
    72. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    73. Bichler, Martin & Goeree, Jacob & Mayer, Stefan & Shabalin, Pasha, 2014. "Spectrum auction design: Simple auctions for complex sales," Telecommunications Policy, Elsevier, vol. 38(7), pages 613-622.
    74. Ball, Michael O. & Berardino, Frank & Hansen, Mark, 2018. "The use of auctions for allocating airport access rights," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PA), pages 186-202.
    75. Milgrom, Paul, 2010. "Simplified mechanisms with an application to sponsored-search auctions," Games and Economic Behavior, Elsevier, vol. 70(1), pages 62-70, September.
    76. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn.
    77. Ali Hortaçsu & David McAdams, 2018. "Empirical Work on Auctions of Multiple Objects," Journal of Economic Literature, American Economic Association, vol. 56(1), pages 157-184, March.
    78. Maarten Janssen & Vladimir Karamychev, 2013. "Gaming in Combinatorial Clock Auctions," Tinbergen Institute Discussion Papers 13-027/VII, Tinbergen Institute, revised 16 Dec 2013.
    79. Simon Loertscher & Leslie M. Marx & Tom Wilkening, 2015. "A Long Way Coming: Designing Centralized Markets with Privately Informed Buyers and Sellers," Journal of Economic Literature, American Economic Association, vol. 53(4), pages 857-897, December.
    80. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-1291, September.
    81. Janssen, Maarten & Kasberger, Bernhard, 2019. "On the clock of the combinatorial clock auction," Theoretical Economics, Econometric Society, vol. 14(4), November.
    82. Jonathan Levin & Andrzej Skrzypacz, 2016. "Properties of the Combinatorial Clock Auction," American Economic Review, American Economic Association, vol. 106(9), pages 2528-2551, September.
    83. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
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    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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