IDEAS home Printed from https://ideas.repec.org/a/eee/soceco/v98y2022ics2214804322000490.html
   My bibliography  Save this article

Measuring tree complexity with response times

Author

Listed:
  • Grabiszewski, Konrad
  • Horenstein, Alex

Abstract

Game-theoretic trees vary in complexity. This paper introduces the concept of graph-based complexity and relies on the subjects’ behavior to empirically derive a measure of tree complexity. Data comes from the mobile app Blues and Reds, designed specifically to conduct experiments. The sample consists of 6637 subjects from 143 countries who play 27 different dynamic games. Based on subjects’ response times, we find that two measures – the average response time spent at the first round and the average total time spent solving the tree – are the best candidates for the empirical measure of tree complexity. We focus on two-person, finite, zero-sum dynamic games with perfect and complete information.

Suggested Citation

  • Grabiszewski, Konrad & Horenstein, Alex, 2022. "Measuring tree complexity with response times," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 98(C).
    • Handle: RePEc:eee:soceco:v:98:y:2022:i:c:s2214804322000490
    DOI: 10.1016/j.socec.2022.101876
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2214804322000490
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.socec.2022.101876?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. Larbi Alaoui & Antonio Penta, 2016. "Endogenous Depth of Reasoning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1297-1333.
    2. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    3. Ian Krajbich & Bastiaan Oud & Ernst Fehr, 2014. "Benefits of Neuroeconomic Modeling: New Policy Interventions and Predictors of Preference," American Economic Review, American Economic Association, vol. 104(5), pages 501-506, May.
    4. Steven D. Levitt & John A. List & Sally E. Sadoff, 2011. "Checkmate: Exploring Backward Induction among Chess Players," American Economic Review, American Economic Association, vol. 101(2), pages 975-990, April.
    5. Benjamin Enke & Florian Zimmermann, 2019. "Correlation Neglect in Belief Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 313-332.
    6. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: A Study of Response Times," Economic Journal, Royal Economic Society, vol. 117(523), pages 1243-1259, October.
    7. Antoni Bosch-Domènech & José G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
    8. repec:mpr:mprres:7497 is not listed on IDEAS
    9. David Gill & Victoria Prowse, 2023. "Strategic Complexity and the Value of Thinking," The Economic Journal, Royal Economic Society, vol. 133(650), pages 761-786.
    10. Yan Chen & Joseph Konstan, 2015. "Online field experiments: a selective survey of methods," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 1(1), pages 29-42, July.
    11. Benito-Ostolaza, Juan M. & Hernández, Penélope & Sanchis-Llopis, Juan A., 2016. "Do individuals with higher cognitive ability play more strategically?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 5-11.
    12. Recalde, María P. & Riedl, Arno & Vesterlund, Lise, 2018. "Error-prone inference from response time: The case of intuitive generosity in public-good games," Journal of Public Economics, Elsevier, vol. 160(C), pages 132-147.
    13. Carpenter, Jeffrey & Graham, Michael & Wolf, Jesse, 2013. "Cognitive ability and strategic sophistication," Games and Economic Behavior, Elsevier, vol. 80(C), pages 115-130.
    14. Gill, David & Prowse, Victoria L., 2017. "Using Response Times to Measure Strategic Complexity and the Value of Thinking in Games," IZA Discussion Papers 10518, Institute of Labor Economics (IZA).
    15. Elie Ofek & Muhamet Yildiz & Ernan Haruvy, 2007. "The Impact of Prior Decisions on Subsequent Valuations in a Costly Contemplation Model," Management Science, INFORMS, vol. 53(8), pages 1217-1233, August.
    16. Tracy Xiao Liu & Jiang Yang & Lada A. Adamic & Yan Chen, 2014. "Crowdsourcing with All-Pay Auctions: A Field Experiment on Taskcn," Management Science, INFORMS, vol. 60(8), pages 2020-2037, August.
    17. Agranov, Marina & Potamites, Elizabeth & Schotter, Andrew & Tergiman, Chloe, 2012. "Beliefs and endogenous cognitive levels: An experimental study," Games and Economic Behavior, Elsevier, vol. 75(2), pages 449-463.
    18. Kiss, H.J. & Rodriguez-Lara, I. & Rosa-García, A., 2016. "Think twice before running! Bank runs and cognitive abilities," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 12-19.
    19. David Gill & Victoria Prowse, 2016. "Cognitive Ability, Character Skills, and Learning to Play Equilibrium: A Level-k Analysis," Journal of Political Economy, University of Chicago Press, vol. 124(6), pages 1619-1676.
    20. Dietmar Fehr & Steffen Huck, 2016. "Who knows it is a game? On strategic awareness and cognitive ability," Experimental Economics, Springer;Economic Science Association, vol. 19(4), pages 713-726, December.
    21. Ernst Fehr & Antonio Rangel, 2011. "Neuroeconomic Foundations of Economic Choice--Recent Advances," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 3-30, Fall.
    22. Johnson, Eric J. & Camerer, Colin & Sen, Sankar & Rymon, Talia, 2002. "Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining," Journal of Economic Theory, Elsevier, vol. 104(1), pages 16-47, May.
    23. Andrew Caplin & Daniel Martin, 2016. "The Dual-Process Drift Diffusion Model: Evidence From Response Times," Economic Inquiry, Western Economic Association International, vol. 54(2), pages 1274-1282, April.
    24. Ariel Rubinstein, 2016. "A Typology of Players: Between Instinctive and Contemplative," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(2), pages 859-890.
    25. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    26. Yan Chen & Grace Jeon & Yong-Mi Kim, 2014. "A day without a search engine: an experimental study of online and offline searches," Experimental Economics, Springer;Economic Science Association, vol. 17(4), pages 512-536, December.
    27. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: Response Times Study," Levine's Bibliography 321307000000001011, UCLA Department of Economics.
    28. Clithero, John A., 2018. "Response times in economics: Looking through the lens of sequential sampling models," Journal of Economic Psychology, Elsevier, vol. 69(C), pages 61-86.
    29. Grabiszewski, Konrad & Horenstein, Alex, 2020. "Effort is not a monotonic function of skills: Results from a global mobile experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 634-652.
    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. Duarte Gonc{c}alves, 2024. "Speed, Accuracy, and Complexity," Papers 2403.11240, arXiv.org, revised Jun 2024.

    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. Konrad Grabiszewski & Alex Horenstein, 2022. "Profiling dynamic decision-makers," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-22, April.
    2. Grabiszewski, Konrad & Horenstein, Alex, 2020. "Effort is not a monotonic function of skills: Results from a global mobile experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 634-652.
    3. Carlos Alós-Ferrer & Johannes Buckenmaier, 2021. "Cognitive sophistication and deliberation times," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 558-592, June.
    4. Sean Duffy & J. J. Naddeo & David Owens & John Smith, 2024. "Cognitive Load and Mixed Strategies: On Brains and Minimax," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 1-34, September.
    5. Clithero, John A., 2018. "Response times in economics: Looking through the lens of sequential sampling models," Journal of Economic Psychology, Elsevier, vol. 69(C), pages 61-86.
    6. Recalde, María P. & Riedl, Arno & Vesterlund, Lise, 2018. "Error-prone inference from response time: The case of intuitive generosity in public-good games," Journal of Public Economics, Elsevier, vol. 160(C), pages 132-147.
    7. Oren Bar-Gill & Christoph Engel, 2020. "Property is Dummy Proof: An Experiment," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2020_02, Max Planck Institute for Research on Collective Goods.
    8. Alaoui, Larbi & Janezic, Katharina A. & Penta, Antonio, 2020. "Reasoning about others' reasoning," Journal of Economic Theory, Elsevier, vol. 189(C).
    9. Bayer, Ralph C. & Renou, Ludovic, 2016. "Logical omniscience at the laboratory," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 41-49.
    10. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    11. Guidon Fenig & Giovanni Gallipoli & Yoram Halevy, 2018. "Piercing the 'Payoff Function' Veil: Tracing Beliefs and Motives," Working Papers tecipa-619, University of Toronto, Department of Economics.
    12. Bendoly, Elliot & van Wezel, Wout & Bachrach, Daniel G. (ed.), 2015. "The Handbook of Behavioral Operations Management: Social and Psychological Dynamics in Production and Service Settings," OUP Catalogue, Oxford University Press, number 9780199357222.
    13. Roman M. Sheremeta, 2016. "Impulsive Behavior in Competition: Testing Theories of Overbidding in Rent-Seeking Contests," Working Papers 16-21, Chapman University, Economic Science Institute.
    14. Masiliūnas, Aidas, 2017. "Overcoming coordination failure in a critical mass game: Strategic motives and action disclosure," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 214-251.
    15. Avoyan, Ala & Schotter, Andrew, 2020. "Attention in games: An experimental study," European Economic Review, Elsevier, vol. 124(C).
    16. Allred, Sarah & Duffy, Sean & Smith, John, 2016. "Cognitive load and strategic sophistication," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 162-178.
    17. Piotr Evdokimov & Umberto Garfagnini, 2023. "Cognitive Ability and Perceived Disagreement in Learning," Rationality and Competition Discussion Paper Series 381, CRC TRR 190 Rationality and Competition.
    18. Manzini, Paola & Mariotti, Marco, 2018. "Dual random utility maximisation," Journal of Economic Theory, Elsevier, vol. 177(C), pages 162-182.
    19. Merkel, Anna & Lohse, Johannes, 2016. "Is fairness intuitive? An experiment accounting for the role of subjective utility differences under time pressure," Working Papers 0627, University of Heidelberg, Department of Economics.
    20. Dan Levin & Luyao Zhang, 2022. "Bridging Level-K to Nash Equilibrium," Papers 2202.12292, arXiv.org, revised Feb 2022.

    More about this item

    Keywords

    Tree; Complexity; Backward induction; Experimental game theory; Mobile experiment;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General

    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:soceco:v:98:y:2022:i:c:s2214804322000490. 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/inca/620175 .

    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.