IDEAS home Printed from https://ideas.repec.org/a/the/publsh/5878.html
   My bibliography  Save this article

To infinity and beyond: a general framework for scaling economic theories

Author

Listed:
  • Gonczarowski, Yannai A.

    (Department of Economics and Department of Computer Science, Harvard University)

  • Kominers, Scott Duke

    (Entrepreneurial Management Unit, Harvard Business School; Department of Economics and Center of Mathematical Sciences and Applications, Harvard University; and a16z crypto)

  • Shorrer, Ran I.

    (Department of Econonics, Penn State University)

Abstract

Many economic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness assumptions. Our sufficient conditions are on the theorem statement only, and not on its proof. This results in short proofs, and even allows us to use the same argument to scale similar theorems that were proven using distinctly different tools. We demonstrate the versatility of our approach via an array of examples from revealed-preference theory.

Suggested Citation

  • Gonczarowski, Yannai A. & Kominers, Scott Duke & Shorrer, Ran I., 0. "To infinity and beyond: a general framework for scaling economic theories," Theoretical Economics, Econometric Society.
  • Handle: RePEc:the:publsh:5878
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5878/39867/1
    File Function: Working paper version. Paper will be copyedited and typeset before publication.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. de Clippel, Geoffroy & Rozen, Kareen, 2021. "Bounded rationality and limited datasets," Theoretical Economics, Econometric Society, vol. 16(2), May.
    2. Fishburn, Peter C., 1984. "Comment on the Kannai-Peleg impossibility theorem for extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 176-179, February.
    3. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    4. Matias D. Cattaneo & Xinwei Ma & Yusufcan Masatlioglu & Elchin Suleymanov, 2020. "A Random Attention Model," Journal of Political Economy, University of Chicago Press, vol. 128(7), pages 2796-2836.
    5. Aumann, Robert J, 1975. "Values of Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 43(4), pages 611-646, July.
    6. Andrew Caplin & Mark Dean & John Leahy, 2022. "Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy," Journal of Political Economy, University of Chicago Press, vol. 130(6), pages 1676-1715.
    7. Christopher P. Chambers & Federico Echenique & Eran Shmaya, 2014. "The Axiomatic Structure of Empirical Content," American Economic Review, American Economic Association, vol. 104(8), pages 2303-2319, August.
    8. Andrew Caplin & Mark Dean, 2015. "Revealed Preference, Rational Inattention, and Costly Information Acquisition," American Economic Review, American Economic Association, vol. 105(7), pages 2183-2203, July.
    9. de Oliveira, Henrique & Denti, Tommaso & Mihm, Maximilian & Ozbek, Kemal, 2017. "Rationally inattentive preferences and hidden information costs," Theoretical Economics, Econometric Society, vol. 12(2), May.
    10. Apartsin, Yevgenia & Kannai, Yakar, 2006. "Demand properties of concavifiable preferences," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 36-55, December.
    11. Kannai, Yakar, 2004. "When is individual demand concavifiable?," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 59-69, February.
    12. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    13. Philip J. Reny, 2015. "A Characterization of Rationalizable Consumer Behavior," Econometrica, Econometric Society, vol. 83, pages 175-192, January.
    14. Joseph Halpern, 2009. "A nonstandard characterization of sequential equilibrium, perfect equilibrium, and proper equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 37-49, March.
    15. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804.
    16. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    17. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
    18. Ziv Hellman & Yehuda John Levy, 2019. "Measurable Selection for Purely Atomic Games," Econometrica, Econometric Society, vol. 87(2), pages 593-629, March.
    19. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    20. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    21. Holzman, Ron, 1984. "An extension of Fishburn's theorem on extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 192-196, February.
    22. Reny, Philip J., 2013. "A simple proof of the nonconcavifiability of functions with linear not-all-parallel contour sets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 506-508.
    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. Mikhail Freer & César Martinelli, 2023. "An algebraic approach to revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 717-742, April.
    2. Tsakas, Elias, 2018. "Robust scoring rules," Research Memorandum 023, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. Yannai A. Gonczarowski & Scott Duke Kominers & Ran I. Shorrer, 2019. "To Infinity and Beyond: A General Framework for Scaling Economic Theories," Papers 1906.10333, arXiv.org, revised Apr 2023.
    4. Chambers, Christopher P. & Yenmez, M. Bumin, 2018. "A simple characterization of responsive choice," Games and Economic Behavior, Elsevier, vol. 111(C), pages 217-221.
    5. Gorno, Leandro, 2019. "Revealed preference and identification," Journal of Economic Theory, Elsevier, vol. 183(C), pages 698-739.
    6. Philippe Jehiel & Jakub Steiner, 2020. "Selective Sampling with Information-Storage Constraints [On interim rationality, belief formation and learning in decision problems with bounded memory]," The Economic Journal, Royal Economic Society, vol. 130(630), pages 1753-1781.
    7. Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2023. "Rational Inattention: A Review," Journal of Economic Literature, American Economic Association, vol. 61(1), pages 226-273, March.
    8. Hébert, Benjamin & Woodford, Michael, 2023. "Rational inattention when decisions take time," Journal of Economic Theory, Elsevier, vol. 208(C).
    9. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, April.
    10. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    11. Isaac Baley & Laura Veldkamp, 2021. "Bayesian learning," Economics Working Papers 1797, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Chambers, Christopher P. & Liu, Ce & Rehbeck, John, 2020. "Costly information acquisition," Journal of Economic Theory, Elsevier, vol. 186(C).
    13. Monte, Daniel & Linhares, Luis Henrique, 2023. "Stealth Startups, Clauses, and Add-ons: A Model of Strategic Obfuscation," MPRA Paper 115926, University Library of Munich, Germany.
    14. Xavier Gabaix, 2017. "Behavioral Inattention," NBER Working Papers 24096, National Bureau of Economic Research, Inc.
    15. Benjamin Hébert & Michael Woodford, 2017. "Rational Inattention and Sequential Information Sampling," NBER Working Papers 23787, National Bureau of Economic Research, Inc.
    16. Duffy, Sean & Gussman, Steven & Smith, John, 2021. "Visual judgments of length in the economics laboratory: Are there brains in stochastic choice?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 93(C).
    17. John Quah & Hiroki Nishimura & Efe A. Ok, 2013. "A Unified Approach to Revealed Preference Theory: The Case of Rational Choice," Economics Series Working Papers 686, University of Oxford, Department of Economics.
    18. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2018. "The Cost of Information: The Case of Constant Marginal Costs," Papers 1812.04211, arXiv.org, revised Feb 2023.
    19. Frank Huettner & Tamer Boyacı & Yalçın Akçay, 2019. "Consumer Choice Under Limited Attention When Alternatives Have Different Information Costs," Operations Research, INFORMS, vol. 67(3), pages 671-699, May.
    20. Andrew Caplin & Dániel CsabaQuantCo & John Leahy & Oded Nov, 2020. "Rational Inattention, Competitive Supply, and Psychometrics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(3), pages 1681-1724.

    More about this item

    Keywords

    Revealed preferences; infinite models;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D00 - Microeconomics - - General - - - General

    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:the:publsh:5878. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    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.