IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2203.00070.html
   My bibliography  Save this paper

Decisions over Sequences

Author

Listed:
  • Bhavook Bhardwaj
  • Siddharth Chatterjee

Abstract

This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such as receiving recommendations. Within the class of decision rules, we study natural subclasses: stopping and uniform stopping rules. Our main result establishes the equivalence of these two subclasses of decision rules. Next, we introduce the notion of computability of decision rules using Turing machines and show that computable rules can be implemented using a simpler computational device: a finite automaton. We further show that computability of choice rules -- an important subclass of decision rules -- is implied by their continuity with respect to a natural topology. Finally, we introduce some natural heuristics in this framework and provide their behavioral characterization.

Suggested Citation

  • Bhavook Bhardwaj & Siddharth Chatterjee, 2022. "Decisions over Sequences," Papers 2203.00070, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2203.00070
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2203.00070
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    2. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    3. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
    4. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    5. Aguiar, Victor H. & Boccardi, Maria Jose & Dean, Mark, 2016. "Satisficing and stochastic choice," Journal of Economic Theory, Elsevier, vol. 166(C), pages 445-482.
    6. , & ,, 2006. "A model of choice from lists," Theoretical Economics, Econometric Society, vol. 1(1), pages 3-17, March.
    7. Yuval Salant, 2011. "Procedural Analysis of Choice Rules with Applications to Bounded Rationality," American Economic Review, American Economic Association, vol. 101(2), pages 724-748, April.
    8. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    9. , & ,, 2011. "Search, choice, and revealed preference," Theoretical Economics, Econometric Society, vol. 6(1), January.
    10. Christopher Tyson, 2015. "Satisficing behavior with a secondary criterion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 639-661, March.
    11. Papi, Mauro, 2012. "Satisficing choice procedures," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 451-462.
    12. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
    13. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    14. Alexander M. Jakobsen, 2020. "A Model of Complex Contracts," American Economic Review, American Economic Association, vol. 110(5), pages 1243-1273, May.
    15. Kovach, Matthew & Ülkü, Levent, 2020. "Satisficing with a variable threshold," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 67-76.
    16. Apesteguia, Jose & Ballester, Miguel A., 2010. "The Computational Complexity of Rationalizing Behavior," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 356-363, May.
    Full references (including those not matched with items on IDEAS)

    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. Christopher Tyson, 2015. "Satisficing behavior with a secondary criterion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 639-661, March.
    2. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J., 2016. "Partial knowledge restrictions on the two-stage threshold model of choice," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 41-47.
    3. Aguiar, Victor H. & Kimya, Mert, 2019. "Adaptive stochastic search," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 74-83.
    4. Xiaosheng Mu, 2021. "Sequential Choice with Incomplete Preferences," Working Papers 2021-35, Princeton University. Economics Department..
    5. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J., 2016. "Partial knowledge restrictions on the two-stage threshold model of choice," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 41-47.
    6. Salvador Barberà & Geoffroy de Clippel & Alejandro Neme & Kareen Rozen, 2022. "Order-k rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 1135-1153, June.
      • Salvador Barberà & Geoffroy De Clippel & Alejandro Neme & Kareen Rozen, 2019. "Order-k Rationality," Working Papers 1130, Barcelona School of Economics.
      • Salvador Barberà & Geoffroy De Cleppel & Alejandro Neme & Kareen Rozeen, 2020. "Order-k Rationality," Working Papers 4, Red Nacional de Investigadores en Economía (RedNIE).
      • Salvador Barber‡ & Geoffroy de Clippel & Alejandro Neme & Kareen Rozen, 2020. "Order-k Rationality," Working Papers 2020-10, Brown University, Department of Economics.
    7. Luigi Mittone & Mauro Papi, 2017. "Does inducing choice procedures make individuals better off? An experimental study," Theory and Decision, Springer, vol. 83(1), pages 37-59, June.
    8. Kovach, Matthew & Ülkü, Levent, 2020. "Satisficing with a variable threshold," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 67-76.
    9. Salvador Barberà & Alejandro Neme, 2015. "Ordinal Relative Satisficing Behavior: Theory and Experiments," Working Papers 790, Barcelona School of Economics.
    10. Bleile, Jörg, 2016. "Limited Attention in Case-Based Belief Formation," Center for Mathematical Economics Working Papers 518, Center for Mathematical Economics, Bielefeld University.
    11. Dinko Dimitrov & Saptarshi Mukherjee & Nozomu Muto, 2016. "‘Divide-and-choose’ in list-based decision problems," Theory and Decision, Springer, vol. 81(1), pages 17-31, June.
    12. Nishimura, Hiroki, 2018. "The transitive core: inference of welfare from nontransitive preference relations," Theoretical Economics, Econometric Society, vol. 13(2), May.
    13. Andrew Caplin & Mark Dean & Daniel Martin, 2011. "Search and Satisficing," American Economic Review, American Economic Association, vol. 101(7), pages 2899-2922, December.
    14. T. Hayashi & R. Jain & V. Korpela & M. Lombardi, 2023. "Behavioral strong implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1257-1287, November.
    15. Kashaev, Nail & Aguiar, Victor H., 2022. "A random attention and utility model," Journal of Economic Theory, Elsevier, vol. 204(C).
    16. Lleras, Juan Sebastián & Masatlioglu, Yusufcan & Nakajima, Daisuke & Ozbay, Erkut Y., 2017. "When more is less: Limited consideration," Journal of Economic Theory, Elsevier, vol. 170(C), pages 70-85.
    17. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J, 2015. "Partial Knowledge Restrictions on theTwo-Stage Threshold Model of Choice," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-58, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    18. Victor Aguiar & Maria Jose Boccardi & Mark Dean, 2015. "Satisficing and Stochastic Choice," Working Papers 2015-8, Brown University, Department of Economics.
    19. Gent Bajraj & Levent Ülkü, 2015. "Choosing two finalists and the winner," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 729-744, December.
    20. Gleb Koshevoy & Ernesto Savaglio, 2017. "Enveloped choice functions and path-independent rationality," Department of Economics University of Siena 765, Department of Economics, University of Siena.

    More about this item

    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:2203.00070. 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.