IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.00502.html
   My bibliography  Save this paper

Robust Sequential Search

Author

Listed:
  • Karl H. Schlag
  • Andriy Zapechelnyuk

Abstract

We study sequential search without priors. Our interest lies in decision rules that are close to being optimal under each prior and after each history. We call these rules dynamically robust. The search literature employs optimal rules based on cutoff strategies that are not dynamically robust. We derive dynamically robust rules and show that their performance exceeds 1/2 of the optimum against binary environments and 1/4 of the optimum against all environments. This performance improves substantially with the outside option value, for instance, it exceeds 2/3 of the optimum if the outside option exceeds 1/6 of the highest possible alternative.

Suggested Citation

  • Karl H. Schlag & Andriy Zapechelnyuk, 2020. "Robust Sequential Search," Papers 2008.00502, arXiv.org.
    • Handle: RePEc:arx:papers:2008.00502
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.00502
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    2. Sylvain Chassang, 2013. "Calibrated Incentive Contracts," Econometrica, Econometric Society, vol. 81(5), pages 1935-1971, September.
    3. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    4. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-654, May.
    5. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    6. Alexei Parakhonyak & Anton Sobolev, 2015. "Non‐Reservation Price Equilibrium and Search without Priors," Economic Journal, Royal Economic Society, vol. 0(584), pages 887-909, May.
    7. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    8. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    9. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    10. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    11. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    12. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    13. Janssen, Maarten C.W. & Parakhonyak, Alexei & Parakhonyak, Anastasia, 2017. "Non-reservation price equilibria and consumer search," Journal of Economic Theory, Elsevier, vol. 172(C), pages 120-162.
    14. Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
    15. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    16. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    17. Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.
    18. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    19. Joseph L. Gastwirth, 1976. "On Probabilistic Models of Consumer Search for Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 38-50.
    20. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    21. Prasad Kislaya, 2003. "Non-robustness of some economic models," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-9, May.
    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. Bernhard Kasberger & Kyle Woodward, 2021. "Bidding in Multi-Unit Auctions under Limited Information," Papers 2112.11320, arXiv.org, revised Apr 2023.

    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. Saghafian, Soroush, 2018. "Ambiguous partially observable Markov decision processes: Structural results and applications," Journal of Economic Theory, Elsevier, vol. 178(C), pages 1-35.
    2. Daniele Pennesi, 2013. "Asset Prices in an Ambiguous Economy," Carlo Alberto Notebooks 315, Collegio Carlo Alberto.
    3. Hansen, Peter G., 2022. "New formulations of ambiguous volatility with an application to optimal dynamic contracting," Journal of Economic Theory, Elsevier, vol. 199(C).
    4. Carroll, Gabriel, 2016. "Informationally robust trade and limits to contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 334-361.
    5. Peter G. Hansen, 2021. "New Formulations of Ambiguous Volatility with an Application to Optimal Dynamic Contracting," Papers 2101.12306, arXiv.org.
    6. Swagata Bhattacharjee, 2019. "Dynamic Contracting for Innovation Under Ambiguity," Working Papers 1022, Ashoka University, Department of Economics, revised Aug 2019.
    7. Bhattacharjee, Swagata, 2022. "Dynamic contracting for innovation under ambiguity," Games and Economic Behavior, Elsevier, vol. 132(C), pages 534-552.
    8. Li, Jian, 2019. "The K-armed bandit problem with multiple priors," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 22-38.
    9. Farzad Pourbabaee, 2021. "Robust Experimentation in the Continuous Time Bandit Problem," Papers 2104.00102, arXiv.org.
    10. Hansen, Lars Peter & Sargent, Thomas J., 2022. "Structured ambiguity and model misspecification," Journal of Economic Theory, Elsevier, vol. 199(C).
    11. Isaiah Andrews & Jesse M. Shapiro, 2021. "A Model of Scientific Communication," Econometrica, Econometric Society, vol. 89(5), pages 2117-2142, September.
    12. Charles F. Manski, 2018. "Reasonable patient care under uncertainty," Health Economics, John Wiley & Sons, Ltd., vol. 27(10), pages 1397-1421, October.
    13. Karl Schlag & Andriy Zapechelnyuk, 2017. "Robust Sequential Search," Discussion Paper Series, School of Economics and Finance 201803, School of Economics and Finance, University of St Andrews, revised 05 Mar 2020.
    14. Christian Traeger, 2014. "Why uncertainty matters: discounting under intertemporal risk aversion and ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 627-664, August.
    15. Aleksey Tetenov, 2016. "An economic theory of statistical testing," CeMMAP working papers CWP50/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Charles F. Manski & Aleksey Tetenov, 2015. "Clinical trial design enabling ε-optimal treatment rules," CeMMAP working papers 60/15, Institute for Fiscal Studies.
    17. Michael Barnett & William Brock & Lars Peter Hansen, 2022. "Climate Change Uncertainty Spillover in the Macroeconomy," NBER Macroeconomics Annual, University of Chicago Press, vol. 36(1), pages 253-320.
    18. Barron, Daniel & Georgiadis, George & Swinkels, Jeroen M., 2020. "Optimal contracts with a risk-taking agent," Theoretical Economics, Econometric Society, vol. 15(2), May.
    19. Jianjun Miao & Alejandro Rivera, 2016. "Robust Contracts in Continuous Time," Econometrica, Econometric Society, vol. 84, pages 1405-1440, July.
    20. Farzad Pourbabaee, 2022. "Robust experimentation in the continuous time bandit problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 151-181, February.

    More about this item

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2008.00502. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.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.