IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v180y2019icp383-437.html
   My bibliography  Save this article

Optimal learning before choice

Author

Listed:
  • Ke, T. Tony
  • Villas-Boas, J. Miguel

Abstract

A Bayesian decision maker is choosing among two alternatives with uncertain payoffs and an outside option with known payoff. Before deciding which alternative to adopt, the decision maker can purchase sequentially multiple informative signals on each of the two alternatives. To maximize the expected payoff, the decision maker solves the problem of optimal dynamic allocation of learning efforts as well as optimal stopping of the learning process. We show that the decision maker considers an alternative for learning or adoption if and only if the expected payoff of the alternative is above a threshold. Given both alternatives in the decision maker's consideration set, we find that if the outside option is weak and the decision maker's beliefs about both alternatives are relatively low, it is optimal for the decision maker to learn information from the alternative that has a lower expected payoff and less uncertainty, given all other characteristics of the two alternatives being the same. If the decision maker subsequently receives enough positive informative signals, the decision maker will switch to learning the better alternative; otherwise the decision maker will rule out this alternative from consideration and adopt the currently more preferred alternative. We find that this strategy works because it minimizes the decision maker's learning efforts. We also characterize the optimal learning policy when the outside option is relatively high, and discuss several extensions.

Suggested Citation

  • Ke, T. Tony & Villas-Boas, J. Miguel, 2019. "Optimal learning before choice," Journal of Economic Theory, Elsevier, vol. 180(C), pages 383-437.
  • Handle: RePEc:eee:jetheo:v:180:y:2019:i:c:p:383-437
    DOI: 10.1016/j.jet.2019.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053119300092
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Rothschild, Michael, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 689-711, July/Aug..
    2. Benjamin Scheibehenne & Rainer Greifeneder & Peter M. Todd, 2010. "Can There Ever Be Too Many Options? A Meta-Analytic Review of Choice Overload," Journal of Consumer Research, Oxford University Press, vol. 37(3), pages 409-425, October.
    3. Roberts, Kevin & Weitzman, Martin L, 1981. "Funding Criteria for Research, Development, and Exploration Projects," Econometrica, Econometric Society, vol. 49(5), pages 1261-1288, September.
    4. T. Tony Ke & Zuo-Jun Max Shen & J. Miguel Villas-Boas, 2016. "Search for Information on Multiple Products," Management Science, INFORMS, vol. 62(12), pages 3576-3603, December.
    5. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    6. Bergemann, Dirk & Valimaki, Juuso, 1996. "Learning and Strategic Pricing," Econometrica, Econometric Society, vol. 64(5), pages 1125-1149, September.
    7. J. J. McCall, 1970. "Economics of Information and Job Search," The Quarterly Journal of Economics, Oxford University Press, vol. 84(1), pages 113-126.
    8. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    9. Helen Weeds, 2002. "Strategic Delay in a Real Options Model of R&D Competition," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 729-747.
    10. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2006. "Irreversible investment in alternative projects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 425-448, June.
    11. Strulovici, Bruno & Szydlowski, Martin, 2015. "On the smoothness of value functions and the existence of optimal strategies in diffusion models," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 1016-1055.
    12. Bruno Strulovici & Martin Szydlowski, 2012. "On the Smoothness of Value Functions," Discussion Papers 1542, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    14. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    15. Felli, Leonardo & Harris, Christopher, 1996. "Learning, Wage Dynamics, and Firm-Specific Human Capital," Journal of Political Economy, University of Chicago Press, vol. 104(4), pages 838-868, August.
    16. Giuseppe Moscarini & Lones Smith, 2001. "The Optimal Level of Experimentation," Econometrica, Econometric Society, vol. 69(6), pages 1629-1644, November.
    17. Brendan Daley & Brett Green, 2012. "Waiting for News in the Market for Lemons," Econometrica, Econometric Society, vol. 80(4), pages 1433-1504, July.
    18. Drew Fudenberg & Tomasz Strzalecki, 2015. "Dynamic Logit With Choice Aversion," Econometrica, Econometric Society, vol. 83, pages 651-691, March.
    19. Dmitri Kuksov & J. Miguel Villas-Boas, 2010. "When More Alternatives Lead to Less Choice," Marketing Science, INFORMS, vol. 29(3), pages 507-524, 05-06.
    20. Hebert, Benjamin & Woodford, Michael, 2017. "Rational Inattention with Sequential Information Sampling," Research Papers repec:ecl:stabus:3457, Stanford University, Graduate School of Business.
    21. John K.-H. Quah & Bruno Strulovici, 2013. "Discounting, Values, and Decisions," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 896-939.
    22. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-654, May.
    23. Fernando Branco & Monic Sun & J. Miguel Villas-Boas, 2012. "Optimal Search for Product Information," Management Science, INFORMS, vol. 58(11), pages 2037-2056, November.
    24. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    25. Diamond, Peter A., 1971. "A model of price adjustment," Journal of Economic Theory, Elsevier, vol. 3(2), pages 156-168, June.
    26. Doval, Laura, 2018. "Whether or not to open Pandora's box," Journal of Economic Theory, Elsevier, vol. 175(C), pages 127-158.
    27. Michael Rothschild, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown: A Summary," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 1, pages 293-294, National Bureau of Economic Research, Inc.
    28. Adam, Klaus, 2001. "Learning While Searching for the Best Alternative," Journal of Economic Theory, Elsevier, vol. 101(1), pages 252-280, November.
    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. Raluca M. Ursu & Qingliang Wang & Pradeep K. Chintagunta, 2020. "Search Duration," Marketing Science, INFORMS, vol. 39(5), pages 849-871, September.
    2. T. Tony Ke & Song Lin, 2020. "Informational Complementarity," Management Science, INFORMS, vol. 66(8), pages 3699-3716, August.

    More about this item

    Keywords

    Information; Bayesian learning; Search theory; Dynamic allocation; Optimal stopping; Consideration set;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

    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:eee:jetheo:v:180:y:2019:i:c:p:383-437. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.