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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
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    References listed on IDEAS

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    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, September.
    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.
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    More about this item

    Keywords

    Revealed preferences; infinite models;

    JEL classification:

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

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