IDEAS home Printed from https://ideas.repec.org/p/nuf/econwp/1510.html
   My bibliography  Save this paper

Understanding Preferences: “Demand Types”, and the Existence of Equilibrium with Indivisibilities

Author

Listed:
  • Elizabeth Baldwin

    (London School of Economics)

  • Paul Klemperer

    (Nuffield College, Oxford University)

Abstract

We propose new techniques for understanding agents’ valuations. Our classification into “demand types”, incorporates existing definitions (such as substitutes, complements, “strong substitutes”, etc.), and permits additional distinctions. We obtain an easy-to-check necessary and sufficient condition for the existence of a competitive equilibrium for indivisible goods. Our condition generalises many existing results, and provides new insights: contrary to much popular belief, there are more classes of purelycomplements preferences than classes of purely-substitutes preferences for which competitive equilibrium always exists. Our techniques are also powerful when equilibrium cannot be guaranteed from the “demand type”. For a specific set of individual valuations, we often can check for equilibrium existence by simply counting the number of intersection points of the geometric objects we study! Our methods also have applications to matching, and to the Product-Mix Auction, introduced by the Bank of England in response to the financial crisis.

Suggested Citation

  • Elizabeth Baldwin & Paul Klemperer, 2015. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium with Indivisibilities," Economics Papers 2015-W10, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:1510
    as

    Download full text from publisher

    File URL: https://www.nuffield.ox.ac.uk/economics/papers/2015/demandtypes.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966-1005.
    2. John J. Bartholdi & James B. Orlin & H. Donald Ratliff, 1980. "Cyclic Scheduling via Integer Programs with Circular Ones," Operations Research, INFORMS, vol. 28(5), pages 1074-1085, October.
    3. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
    4. Michael Richter & Ariel Rubinstein, 2015. "Back to Fundamentals: Equilibrium in Abstract Economies," American Economic Review, American Economic Association, vol. 105(8), pages 2570-2594, August.
    5. Teytelboym, Alexander, 2014. "Gross substitutes and complements: A simple generalization," Economics Letters, Elsevier, vol. 123(2), pages 135-138.
    6. Danilov, Vladimir I. & Koshevoy, Gleb A. & Lang, Christine, 2008. "Equilibria with indivisible goods and package-utilities," Papers 08-30, Sonderforschungsbreich 504.
    7. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, January.
    8. 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.
    9. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    10. Manzini, Paola & Mariotti, Marco & Ulku, Levent, 2015. "Stochastic Complementarity," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-60, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," SciencePo Working papers Main hal-03588302, HAL.
    12. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    13. Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, May.
    14. McKelvey, Richard D. & McLennan, Andrew, 1997. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 411-425, February.
    15. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    16. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    17. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    18. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    19. Ngoc Mai Tran & Josephine Yu, 2015. "Product-Mix Auctions and Tropical Geometry," Papers 1505.05737, arXiv.org, revised Oct 2017.
    20. Ning Sun & Zaifu Yang, 2014. "An Efficient and Incentive Compatible Dynamic Auction for Multiple Complements," Journal of Political Economy, University of Chicago Press, vol. 122(2), pages 422-466.
    21. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    22. Danilov, Vladimir & Koshevoy, Gleb & Murota, Kazuo, 2001. "Discrete convexity and equilibria in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 251-273, May.
    23. Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
    24. Thanh Nguyen & Rakesh Vohra, 2014. "Near Feasible Stable Matchings with Complementarities," PIER Working Paper Archive 14-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    25. Frost, Tarkus & Govier, Nick & Horn, Tom, 2015. "Innovations in the Bank’s provision of liquidity insurance via Indexed Long-Term Repo (ILTR) operations," Bank of England Quarterly Bulletin, Bank of England, vol. 55(2), pages 181-188.
    26. 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.
    27. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    28. , M. & , Glen & White, Alexander, 2013. "Walrasian equilibrium in large, quasi-linear markets," Theoretical Economics, Econometric Society, vol. 8(2), May.
    29. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
    30. Danilov, V. & Koshevoy, G. & Lang, C., 2013. "Equilibria in Markets with Indivisible Goods," Journal of the New Economic Association, New Economic Association, vol. 18(2), pages 10-34.
    31. Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    32. Jacob K. Goeree & Alexey Kushnir, 2011. "A geometric approach to mechanism design," ECON - Working Papers 056, Department of Economics - University of Zurich, revised Jun 2013.
    33. Kazuo Murota & Akiyoshi Shioura, 1999. "M-Convex Function on Generalized Polymatroid," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 95-105, February.
    Full references (including those not matched with items on IDEAS)

    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. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    2. Satoru Fujishige & Zaifu Yang, 2020. "A Universal Dynamic Auction for Unimodular Demand Types: An Efficient Auction Design for Various Kinds of Indivisible Commodities," Discussion Papers 20/08, Department of Economics, University of York.
    3. Elizabeth Baldwin & Omer Edhan & Ravi Jagadeesan & Paul Klemperer & Alexander Teytelboym, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," Papers 2006.16939, arXiv.org.
    4. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.
    5. 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.
    6. Satoru Fujishige & Zaifu Yang, 2015. "Decentralised Random Competitive Dynamic Market Processes," Discussion Papers 15/27, Department of Economics, University of York.
    7. Akiyoshi Shioura & Zaifu Yang, 2013. "Equilibrium, Auction, Multiple Substitutes and Complements," Discussion Papers 13/17, Department of Economics, University of York.
    8. Jagadeesan, Ravi & Kominers, Scott Duke & Rheingans-Yoo, Ross, 2018. "Strategy-proofness of worker-optimal matching with continuously transferable utility," Games and Economic Behavior, Elsevier, vol. 108(C), pages 287-294.
    9. Satoru Fujishige & Zaifu Yang, 2017. "On a spontaneous decentralized market process," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 2(1), pages 1-37, December.
    10. Ravi Jagadeesan & Scott Duke Kominers & Ross Rheingans-Yoo, 2020. "Lone wolves in competitive equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 215-228, August.
    11. Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    12. Ozan Candogan & Markos Epitropou & Rakesh V. Vohra, 2021. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Operations Research, INFORMS, vol. 69(1), pages 114-147, January.
    13. 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.
    14. Yang, Yi-You, 2013. "Competitive equilibrium with indivisible objects," MPRA Paper 74662, University Library of Munich, Germany, revised 19 Oct 2016.
    15. Chao Huang, 2021. "Unidirectional substitutes and complements," Papers 2108.12572, arXiv.org.
    16. Eric Balkanski & Renato Paes Leme, 2020. "On the Construction of Substitutes," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 272-291, February.
    17. Saeed Alaei & Kamal Jain & Azarakhsh Malekian, 2016. "Competitive Equilibria in Two-Sided Matching Markets with General Utility Functions," Operations Research, INFORMS, vol. 64(3), pages 638-645, June.
    18. Kazuo Murota & Akiyoshi Shioura & Zaifu Yang, 2014. "Time Bounds for Iterative Auctions: A Unified Approach by Discrete Convex Analysis," Discussion Papers 14/27, Department of Economics, University of York.
    19. Jim Ingebretsen Carlson, 2020. "A speedy auction using approximated bidders’ preferences," Annals of Operations Research, Springer, vol. 288(1), pages 65-93, May.
    20. Sun, Ning & Yang, Zaifu, 2016. "An Efficient and Strategy-Proof Double-Track Auction for Substitutes and Complements," Center for Mathematical Economics Working Papers 523, Center for Mathematical Economics, Bielefeld University.

    More about this item

    Keywords

    consumer theory; equilibrium existence; general equilibrium; competitive equilibrium; duality; indivisible goods; geometry; tropical geometry; convex geometry; auction; product mix auction; product-mix auction; substitute; complement; demand type; matching;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:nuf:econwp:1510. 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: Maxine Collett (email available below). General contact details of provider: https://www.nuffield.ox.ac.uk/economics/ .

    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.