IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v12y2012i1n5.html

Information Theory and Observational Limitations in Decision Making

Author

Listed:
  • Wolpert David

    (NASA Ames Research Center, Santa Fe Institute, and Los Alamos National Laboratory, david.h.wolpert@gmail.com)

  • Leslie David S.

    (University of Bristol, david.leslie@bristol.ac.uk)

Abstract

We introduce a general framework for formalizing and analyzing the problem faced by a Decision Maker (DM) working under information-theoretic constraints on their observational ability. The random utility model and the "hedonic utility" model of Netzer and Robson (NR) are special cases of this framework. We begin by applying information theory to our framework to derive general results concerning the expected regret of DM under observational limitations. We then turn our attention to the effects of observational limitations on choice behavior (rather than their effects on the regret values induced by that behavior). We focus on the special case of NR. First we derive two postulates assumed by NR. We then provide a simple derivation of the result of NR that a particular hedonic utility function satisfies certain optimality principles. Next we extend NR to allow a countable, rather than uncountable, set of states of the world. In particular we show how to use dynamic programming to solve for the optimal preference order of DM in this extension. We also extend NR by considering the case where more than two options are presented to DM. In particular, we show that the results of NR change in such a case, implying that the number of options being presented is a crucial aspect of choice problems.

Suggested Citation

  • Wolpert David & Leslie David S., 2012. "Information Theory and Observational Limitations in Decision Making," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-43, January.
    • Handle: RePEc:bpj:bejtec:v:12:y:2012:i:1:n:5
    DOI: 10.1515/1935-1704.1749
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1935-1704.1749
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/1935-1704.1749?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    3. Sims, Christopher A., 2010. "Rational Inattention and Monetary Economics," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 4, pages 155-181, Elsevier.
    4. Bester, Helmut & Guth, Werner, 1998. "Is altruism evolutionarily stable?," Journal of Economic Behavior & Organization, Elsevier, vol. 34(2), pages 193-209, February.
    5. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    6. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287, World Scientific Publishing Co. Pte. Ltd..
    7. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    8. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, January.
    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. Herold, Florian & Netzer, Nick, 2023. "Second-best probability weighting," Games and Economic Behavior, Elsevier, vol. 138(C), pages 112-125.
    2. Michael Woodford, 2014. "An Optimizing Neuroeconomic Model of Discrete Choice," NBER Working Papers 19897, National Bureau of Economic Research, Inc.

    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. Marden, Jason R. & Shamma, Jeff S., 2015. "Game Theory and Distributed Control****Supported AFOSR/MURI projects #FA9550-09-1-0538 and #FA9530-12-1-0359 and ONR projects #N00014-09-1-0751 and #N0014-12-1-0643," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Georgios Chasparis & Jeff Shamma, 2012. "Distributed Dynamic Reinforcement of Efficient Outcomes in Multiagent Coordination and Network Formation," Dynamic Games and Applications, Springer, vol. 2(1), pages 18-50, March.
    3. Federico Echenique & Aaron Edlin, 2001. "Mixed Equilibria in Games of Strategic Complements are Unstable," Levine's Working Paper Archive 563824000000000161, David K. Levine.
    4. Emerson Melo, 2021. "Learning in Random Utility Models Via Online Decision Problems," Papers 2112.10993, arXiv.org, revised Aug 2022.
    5. Xie, Erhao, 2021. "Empirical properties and identification of adaptive learning models in behavioral game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 798-821.
    6. Heifetz, Aviad & Shannon, Chris & Spiegel, Yossi, 2007. "What to maximize if you must," Journal of Economic Theory, Elsevier, vol. 133(1), pages 31-57, March.
    7. William Sandholm, 2014. "Probabilistic Interpretations of Integrability for Game Dynamics," Dynamic Games and Applications, Springer, vol. 4(1), pages 95-106, March.
    8. Harri Ehtamo & Simo Heliövaara & Timo Korhonen & Simo Hostikka, 2010. "Game Theoretic Best-Response Dynamics For Evacuees' Exit Selection," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 113-134.
    9. Wolpert, David H., 2010. "Why income comparison is rational," Games and Economic Behavior, Elsevier, vol. 69(2), pages 458-474, July.
    10. Paolo Crosetto & Alexia Gaudeul, 2011. "Do consumers prefer offers that are easy to compare? An experimental investigation," Jena Economics Research Papers 2011-044, Friedrich-Schiller-University Jena.
    11. Mészáros, József, 2005. "A társadalombiztosítási nyugdíjrendszerek mint közjószágok [Social-insurance pension systems as public goods]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(3), pages 275-288.
    12. Engwerda, J.C., 2012. "Prospects of Tools from Differential Games in the Study Of Macroeconomics of Climate Change," Other publications TiSEM cac36d07-227b-4cf2-83cb-7, Tilburg University, School of Economics and Management.
    13. Jehiel, Philippe & Singh, Juni, 2021. "Multi-state choices with aggregate feedback on unfamiliar alternatives," Games and Economic Behavior, Elsevier, vol. 130(C), pages 1-24.
    14. Mauersberger, Felix, 2019. "Thompson Sampling: Endogenously Random Behavior in Games and Markets," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203600, Verein für Socialpolitik / German Economic Association.
    15. Veller, Carl & Hayward, Laura K., 2016. "Finite-population evolution with rare mutations in asymmetric games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 93-113.
    16. John P. Conley & Myrna Wooders, 2005. "Memetics & Voting: How Nature May Make us Public Spirited," Vanderbilt University Department of Economics Working Papers 0514, Vanderbilt University Department of Economics.
    17. Garcia, Alfredo & Reaume, Daniel & Smith, Robert L., 2000. "Fictitious play for finding system optimal routings in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 147-156, February.
    18. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    19. John Conley & Myrna H. Wooders & Ali Toossi, 2001. "Evolution & Voting: How Nature Makes us Public Spirited," Economics Bulletin, AccessEcon, vol. 28(24), pages 1.
    20. David H. Wolpert & Charlie E. M. Strauss & Dev Rajnarayan, 2006. "Advances In Distributed Optimization Using Probability Collectives," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 383-436.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:bpj:bejtec:v:12:y:2012:i:1:n:5. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    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.