IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v113y2024ics030440682400065x.html
   My bibliography  Save this article

From local utility to neural networks

Author

Listed:
  • Ke, Shaowei
  • Zhao, Chen

Abstract

We introduce and analyze two preference-based notions of local linearity in the spirit of Machina (1982). We show how the weaker among the two extends Machina’s local utility analysis, and that the stronger among the two characterizes continuous finite piecewise linear (CFPL) utility functions. We introduce a representation of the decision maker’s preference called the neural-network utility representation that is equivalent to the CFPL representation, in which the decision maker evaluates an alternative through a neural network.

Suggested Citation

  • Ke, Shaowei & Zhao, Chen, 2024. "From local utility to neural networks," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    • Handle: RePEc:eee:mateco:v:113:y:2024:i:c:s030440682400065x
    DOI: 10.1016/j.jmateco.2024.103003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440682400065X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2024.103003?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    2. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    3. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    4. Chen, Xiaolu & Weng, Tongfeng & Li, Chunzi & Yang, Huijie, 2022. "Equivalence of machine learning models in modeling chaos," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    5. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    6. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    7. Ulrich Schmidt, 2001. "Lottery Dependent Utility: a Reexamination," Theory and Decision, Springer, vol. 50(1), pages 35-58, February.
    8. Andrew Caplin & Daniel J. Martin & Philip Marx, 2022. "Modeling Machine Learning: A Cognitive Economic Approach," NBER Working Papers 30600, National Bureau of Economic Research, Inc.
    9. Andrew Ellis & Yusufcan Masatlioglu, 2022. "Choice with Endogenous Categorization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 240-278.
    10. Drew Fudenberg & Annie Liang, 2019. "Predicting and Understanding Initial Play," American Economic Review, American Economic Association, vol. 109(12), pages 4112-4141, December.
    11. Amos Tversky & Daniel Kahneman, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 1039-1061.
    12. Richard H. R. Hahnloser & Rahul Sarpeshkar & Misha A. Mahowald & Rodney J. Douglas & H. Sebastian Seung, 2000. "Correction: Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit," Nature, Nature, vol. 408(6815), pages 1012-1012, December.
    13. Andrew Caplin & Daniel Martin & Philip Marx, 2022. "Calibrating for Class Weights by Modeling Machine Learning," Papers 2205.04613, arXiv.org, revised Jul 2022.
    14. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.
    15. Faruk Gul & Paulo Natenzon & Wolfgang Pesendorfer, 2014. "Random Choice as Behavioral Optimization," Econometrica, Econometric Society, vol. 82, pages 1873-1912, September.
    16. Hong, Chew Soo & Nishimura, Naoko, 1992. "Differentiability, comparative statics, and non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 56(2), pages 294-312, April.
    17. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    18. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    19. Castagnoli, Erio & Maccheroni, Fabio, 2000. "Restricting independence to convex cones," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 215-223, October.
    20. Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
    21. Harless, David W., 1992. "Predictions about indifference curves inside the unit triangle : A test of variants of expected utility theory," Journal of Economic Behavior & Organization, Elsevier, vol. 18(3), pages 391-414, August.
    22. Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva, 2022. "Caution and Reference Effects," PIER Working Paper Archive 22-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    23. Richard H. R. Hahnloser & Rahul Sarpeshkar & Misha A. Mahowald & Rodney J. Douglas & H. Sebastian Seung, 2000. "Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit," Nature, Nature, vol. 405(6789), pages 947-951, June.
    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. Ke, Shaowei & Wu, Brian & Zhao, Chen, 2024. "Learning from a black box," Journal of Economic Theory, Elsevier, vol. 221(C).

    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. Jürgen Eichberger & David Kelsey, 2014. "Optimism And Pessimism In Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(2), pages 483-505, May.
    2. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2022. "Objective rationality foundations for (dynamic) α-MEU," Journal of Economic Theory, Elsevier, vol. 200(C).
    3. Ghirardato, Paolo & Pennesi, Daniele, 2020. "A general theory of subjective mixtures," Journal of Economic Theory, Elsevier, vol. 188(C).
    4. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2019. "Boolean Representations of Preferences under Ambiguity," Rationality and Competition Discussion Paper Series 173, CRC TRR 190 Rationality and Competition.
    5. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2019. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2180, Cowles Foundation for Research in Economics, Yale University.
    6. Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo, 2014. "Perceived Ambiguity and Relevant Measures," Econometrica, Econometric Society, vol. 82(5), pages 1945-1978, September.
    7. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    8. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2020. "Objective rationality foundations for (dynamic) alpha-MEU," Cowles Foundation Discussion Papers 2244R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2021.
    9. Juan Sebastián Lleras & Evan Piermont & Richard Svoboda, 2019. "Asymmetric gain–loss reference dependence and attitudes toward uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 669-699, October.
    10. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    11. Hartmann, Lorenz, 2023. "Strength of preference over complementary pairs axiomatizes alpha-MEU preferences," Journal of Economic Theory, Elsevier, vol. 213(C).
    12. Ludwig, Alexander & Zimper, Alexander, 2006. "Investment behavior under ambiguity: The case of pessimistic decision makers," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 111-130, September.
    13. Jianming Xia, 2020. "Decision Making under Uncertainty: A Game of Two Selves," Papers 2012.07509, arXiv.org.
    14. Wakker, Peter P. & Yang, Jingni, 2019. "A powerful tool for analyzing concave/convex utility and weighting functions," Journal of Economic Theory, Elsevier, vol. 181(C), pages 143-159.
    15. Gul, Faruk & Pesendorfer, Wolfgang, 2020. "Calibrated uncertainty," Journal of Economic Theory, Elsevier, vol. 188(C).
    16. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    17. Klaus Nehring, 2006. "Bernoulli Without Bayes: A Theory of Utility-Sophisticated Preferences under Ambiguity," Economics Working Papers 0072, Institute for Advanced Study, School of Social Science.
    18. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    19. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    20. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.

    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:eee:mateco:v:113:y:2024:i:c:s030440682400065x. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.