IDEAS home Printed from https://ideas.repec.org/a/inm/orisre/v29y2018i4p1024-1043.html
   My bibliography  Save this article

A Matter of Equality: Linear Pricing in Combinatorial Exchanges

Author

Listed:
  • Martin Bichler

    (Department of Informatics, Technical University of Munich, 80333 Munich, Germany)

  • Vladimir Fux

    (Department of Informatics, Technical University of Munich, 80333 Munich, Germany)

  • Jacob Goeree

    (Department of Economics, University of New South Wales, Kensington, New South Wales 2052, Australia)

Abstract

Combinatorial exchanges that allow for package offers to address nonconvexities in demand or supply typically employ linear and anonymous prices because they are simple, tractable, and fair. Despite their prevalence, linear anonymous prices do not necessarily correspond to Walrasian competitive equilibrium prices in such settings, and their impact is not well understood. This paper is the first to analyze the effect of different pricing rules on the efficiency of combinatorial exchanges, using both analytic methods and numerical experiments. Our analysis is motivated by a combinatorial fishery-rights exchange designed to reform the fishing industry in New South Wales (NSW), Australia. We find that when linearity and anonymity are required for only one side of the market, the average efficiency loss is negligible. In contrast, with a single linear price vector for both sides, the efficiency loss is substantial, especially when the market is small. In a formal model, we show that efficiency losses decrease when the number of buyers grows or the size of the submitted packages decreases. Besides the reform of the NSW fishing industry, our results have important implications for other cap-and-trade programs as well as other industries where demand or cost complementarities play a role.

Suggested Citation

  • Martin Bichler & Vladimir Fux & Jacob Goeree, 2018. "A Matter of Equality: Linear Pricing in Combinatorial Exchanges," Information Systems Research, INFORMS, vol. 29(4), pages 1024-1043, December.
    • Handle: RePEc:inm:orisre:v:29:y:2018:i:4:p:1024-1043
    DOI: 10.1287/isre.2017.0766
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/isre.2017.0766
    Download Restriction: no
    File URL: https://libkey.io/10.1287/isre.2017.0766?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Nicholas Georgescu-Roegen, 1979. "Methods in Economic Science," Journal of Economic Issues, Taylor & Francis Journals, vol. 13(2), pages 317-328, June.
    2. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-438, March.
    3. Iftekhar, M.S. & Tisdell, J.G., 2012. "Comparison of simultaneous and combinatorial auction designs in fisheries quota market," Marine Policy, Elsevier, vol. 36(2), pages 446-453.
    4. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    5. Ioannis Petrakis & Georg Ziegler & Martin Bichler, 2013. "Ascending Combinatorial Auctions with Allocation Constraints: On Game Theoretical and Computational Properties of Generic Pricing Rules," Information Systems Research, INFORMS, vol. 24(3), pages 768-786, September.
    6. Gediminas Adomavicius & Alok Gupta, 2005. "Toward Comprehensive Real-Time Bidder Support in Iterative Combinatorial Auctions," Information Systems Research, INFORMS, vol. 16(2), pages 169-185, June.
    7. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
    8. Meeus, Leonardo & Verhaegen, Karolien & Belmans, Ronnie, 2009. "Block order restrictions in combinatorial electric energy auctions," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1202-1206, August.
    9. M. J. Farrell, 1959. "The Convexity Assumption in the Theory of Competitive Markets," Journal of Political Economy, University of Chicago Press, vol. 67(4), pages 377-377.
    10. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    11. Gediminas Adomavicius & Shawn P. Curley & Alok Gupta & Pallab Sanyal, 2012. "Effect of Information Feedback on Bidder Behavior in Continuous Combinatorial Auctions," Management Science, INFORMS, vol. 58(4), pages 811-830, April.
    12. WOLSEY, Laurence A., 1981. "Integer programming duality: price functions and sensitivity analysis," LIDAM Reprints CORE 431, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Green, Jerry & Laffont, Jean-Jacques, 1977. "On the revelation of preferences for public goods," Journal of Public Economics, Elsevier, vol. 8(1), pages 79-93, August.
    14. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-127, January.
    15. Martin Bichler & Pasha Shabalin & Alexander Pikovsky, 2009. "A Computational Analysis of Linear Price Iterative Combinatorial Auction Formats," Information Systems Research, INFORMS, vol. 20(1), pages 33-59, March.
    16. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    17. , M. & , Glen & White, Alexander, 2013. "Walrasian equilibrium in large, quasi-linear markets," Theoretical Economics, Econometric Society, vol. 8(2), May.
    18. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    19. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-1063, September.
    20. Tobias Scheffel & Alexander Pikovsky & Martin Bichler & Kemal Guler, 2011. "An Experimental Comparison of Linear and Nonlinear Price Combinatorial Auctions," Information Systems Research, INFORMS, vol. 22(2), pages 346-368, June.
    21. 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.
    22. Wolfgang Ketter & John Collins & Maria Gini & Alok Gupta & Paul Schrater, 2012. "Real-Time Tactical and Strategic Sales Management for Intelligent Agents Guided by Economic Regimes," Information Systems Research, INFORMS, vol. 23(4), pages 1263-1283, December.
    23. Xia, Mu & Koehler, Gary J. & Whinston, Andrew B., 2004. "Pricing combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 154(1), pages 251-270, April.
    24. Timothy N. Cason & Karthik N. Kannan & Ralph Siebert, 2011. "An Experimental Study of Information Revelation Policies in Sequential Auctions," Management Science, INFORMS, vol. 57(4), pages 667-688, April.
    25. Innes, James & Thébaud, Olivier & Norman-López, Ana & Richard Little, L. & Kung, John, 2014. "Evidence of package trading in a mature multi-species ITQ market," Marine Policy, Elsevier, vol. 46(C), pages 68-71.
    26. VAN VYVE, Mathieu, 2011. "Linear prices for non-convex electricity markets: models and algorithms," LIDAM Discussion Papers CORE 2011050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    27. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    28. Christoph Brunner & Jacob K. Goeree & Charles A. Holt & John O. Ledyard, 2010. "An Experimental Test of Flexible Combinatorial Spectrum Auction Formats," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 39-57, February.
    29. O'Neill, Richard P. & Sotkiewicz, Paul M. & Hobbs, Benjamin F. & Rothkopf, Michael H. & Stewart, William R., 2005. "Efficient market-clearing prices in markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 269-285, July.
    30. Zhiling Guo & Gary J. Koehler & Andrew B. Whinston, 2012. "A Computational Analysis of Bundle Trading Markets Design for Distributed Resource Allocation," Information Systems Research, INFORMS, vol. 23(3-part-1), pages 823-843, September.
    31. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mete Şeref Ahunbay & Martin Bichler & Johannes Knörr, 2023. "Challenges in Designing Electricity Spot Markets," NBER Chapters, in: New Directions in Market Design, National Bureau of Economic Research, Inc.
    2. Ahunbay, Mete Şeref & Bichler, Martin & Dobos, Teodora & Knörr, Johannes, 2024. "Solving large-scale electricity market pricing problems in polynomial time," European Journal of Operational Research, Elsevier, vol. 318(2), pages 605-617.
    3. Martin Bichler & Johannes Knörr & Felipe Maldonado, 2023. "Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response," Information Systems Research, INFORMS, vol. 34(2), pages 652-675, June.
    4. Jacob K Goeree, 2023. "Yquilibrium: A Theory for (Non-) Convex Economies," Papers 2305.06256, arXiv.org.
    5. Martin Bichler & Douglas Ferrell & Vladimir Fux & Jacob K. Goeree, 2019. "Designing Environmental Markets for Trading Catch Shares," Interfaces, INFORMS, vol. 49(5), pages 324-337, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Martin Bichler & Pasha Shabalin & Georg Ziegler, 2013. "Efficiency with Linear Prices? A Game-Theoretical and Computational Analysis of the Combinatorial Clock Auction," Information Systems Research, INFORMS, vol. 24(2), pages 394-417, June.
    2. Martin Bichler & Johannes Knörr & Felipe Maldonado, 2023. "Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response," Information Systems Research, INFORMS, vol. 34(2), pages 652-675, June.
    3. Zhiling Guo & Gary J. Koehler & Andrew B. Whinston, 2012. "A Computational Analysis of Bundle Trading Markets Design for Distributed Resource Allocation," Information Systems Research, INFORMS, vol. 23(3-part-1), pages 823-843, September.
    4. Andor Goetzendorff & Martin Bichler & Pasha Shabalin & Robert W. Day, 2015. "Compact Bid Languages and Core Pricing in Large Multi-item Auctions," Management Science, INFORMS, vol. 61(7), pages 1684-1703, July.
    5. Ioannis Petrakis & Georg Ziegler & Martin Bichler, 2013. "Ascending Combinatorial Auctions with Allocation Constraints: On Game Theoretical and Computational Properties of Generic Pricing Rules," Information Systems Research, INFORMS, vol. 24(3), pages 768-786, September.
    6. Gediminas Adomavicius & Alok Gupta & Mochen Yang, 2022. "Bidder Support in Multi-item Multi-unit Continuous Combinatorial Auctions: A Unifying Theoretical Framework," Information Systems Research, INFORMS, vol. 33(4), pages 1174-1195, December.
    7. Dirk Briskorn & Kurt Jørnsten & Jenny Nossack, 2016. "Pricing combinatorial auctions by a set of linear price vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1043-1070, October.
    8. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    9. Jinpeng Ma & Qiongling Li, 2016. "Convergence of price processes under two dynamic double auctions," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 1-44, December.
    10. , K. & ,, 2016. "On the impossibility of core-selecting auctions," Theoretical Economics, Econometric Society, vol. 11(1), January.
    11. Pallab Sanyal, 2016. "Characteristics and Economic Consequences of Jump Bids in Combinatorial Auctions," Information Systems Research, INFORMS, vol. 27(2), pages 347-364, June.
    12. Jawad Abrache & Teodor Crainic & Michel Gendreau & Monia Rekik, 2007. "Combinatorial auctions," Annals of Operations Research, Springer, vol. 153(1), pages 131-164, September.
    13. Bart Vangerven & Dries R. Goossens & Frits C. R. Spieksma, 2021. "Using Feedback to Mitigate Coordination and Threshold Problems in Iterative Combinatorial Auctions," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 63(2), pages 113-127, April.
    14. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.
    15. Wellman, Michael P. & Walsh, William E. & Wurman, Peter R. & MacKie-Mason, Jeffrey K., 2001. "Auction Protocols for Decentralized Scheduling," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 271-303, April.
    16. Xiaojing Xu & Jinpeng Ma & Xiaoping Xie, 2019. "Price Convergence under a Probabilistic Double Auction," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1113-1155, October.
    17. Martin Bichler & Douglas Ferrell & Vladimir Fux & Jacob K. Goeree, 2019. "Designing Environmental Markets for Trading Catch Shares," Interfaces, INFORMS, vol. 49(5), pages 324-337, September.
    18. Gediminas Adomavicius & Shawn P. Curley & Alok Gupta & Pallab Sanyal, 2012. "Effect of Information Feedback on Bidder Behavior in Continuous Combinatorial Auctions," Management Science, INFORMS, vol. 58(4), pages 811-830, April.
    19. Paul Milgrom, 2006. "Package Auctions and Package Exchanges: the 2004 Fisher-Schultz Lecture," Levine's Bibliography 321307000000000131, UCLA Department of Economics.
    20. Mishra, Debasis & Parkes, David C., 2007. "Ascending price Vickrey auctions for general valuations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 335-366, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orisre:v:29:y:2018:i:4:p:1024-1043. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.