IDEAS home Printed from https://ideas.repec.org/p/bca/bocawp/19-50.html
   My bibliography  Save this paper

Monetary Payoff and Utility Function in Adaptive Learning Models

Author

Listed:
  • Erhao Xie

Abstract

When players repeatedly face an identical or similar game (e.g., coordination game, technology adoption game, or product choice game), they may learn through experience to perform better in the future. This learning behaviour has important economic implications. It determines which economic outcome a game will reach and how fast it will get there. Given the importance of players’ learning behaviours, economists have proposed various adaptive models to study them. These models are usually estimated and tested using experimental data. Moreover, economists usually assume that individuals’ preference—their utility—is equal to the monetary reward they obtain. However, such an assumption can be wrong since players are not necessarily risk neutral. They could be risk averse or risk loving. I study the consequences of this false assumption and propose a method to deal with it. I then apply the method to an existing experimental dataset. The estimation results show that utility does not necessarily equal monetary reward. Imposing such a false assumption leads researchers to draw incorrect conclusions about players’ learning behaviours. For instance, we may incorrectly estimate the speed of learning and wrongly predict the final outcome of a game. In contrast, the method I propose in this paper allows researchers to achieve more accurate estimates.

Suggested Citation

  • Erhao Xie, 2019. "Monetary Payoff and Utility Function in Adaptive Learning Models," Staff Working Papers 19-50, Bank of Canada.
  • Handle: RePEc:bca:bocawp:19-50
    as

    Download full text from publisher

    File URL: https://www.bankofcanada.ca/wp-content/uploads/2019/12/swp2019-50.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
    2. Sarin, Rajiv & Vahid, Farshid, 2001. "Predicting How People Play Games: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 34(1), pages 104-122, January.
    3. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    4. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
    5. Cominetti, Roberto & Melo, Emerson & Sorin, Sylvain, 2010. "A payoff-based learning procedure and its application to traffic games," Games and Economic Behavior, Elsevier, vol. 70(1), pages 71-83, September.
    6. Mookherjee Dilip & Sopher Barry, 1994. "Learning Behavior in an Experimental Matching Pennies Game," Games and Economic Behavior, Elsevier, vol. 7(1), pages 62-91, July.
    7. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    8. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard H, 1986. "Fairness and the Assumptions of Economics," The Journal of Business, University of Chicago Press, vol. 59(4), pages 285-300, October.
    9. Chmura, Thorsten & Goerg, Sebastian J. & Selten, Reinhard, 2014. "Generalized Impulse Balance: An Experimental Test for a Class of 3 × 3 Games," Review of Behavioral Economics, now publishers, vol. 1(1-2), pages 27-53, January.
    10. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2009. "Measuring Strategic Uncertainty in Coordination Games," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 181-221.
    11. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    12. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2003. "Risk averse behavior in generalized matching pennies games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 97-113, October.
    13. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    14. Mookherjee, Dilip & Sopher, Barry, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Games and Economic Behavior, Elsevier, vol. 19(1), pages 97-132, April.
    15. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
    16. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    17. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    18. Francesco Feri & Bernd Irlenbusch & Matthias Sutter, 2010. "Efficiency Gains from Team-Based Coordination—Large-Scale Experimental Evidence," American Economic Review, American Economic Association, vol. 100(4), pages 1892-1912, September.
    19. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-966, June.
    20. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    21. 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.
    22. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945.
    23. Antonio Cabrales & Walter Garcia Fontes, 2000. "Estimating learning models from experimental data," Economics Working Papers 501, Department of Economics and Business, Universitat Pompeu Fabra.
    24. Camerer, Colin F. & Ho, Teck-Hua & Chong, Juin-Kuan, 2002. "Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games," Journal of Economic Theory, Elsevier, vol. 104(1), pages 137-188, May.
    25. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
    26. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
    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. Shachat, Jason & Swarthout, J. Todd, 2012. "Learning about learning in games through experimental control of strategic interdependence," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 383-402.
    2. Aguirregabiria, Victor & Xie, Erhao, 2016. "Identification of Biased Beliefs in Games of Incomplete Information Using Experimental Data," CEPR Discussion Papers 11275, C.E.P.R. Discussion Papers.
    3. Duffy, John, 2006. "Agent-Based Models and Human Subject Experiments," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 19, pages 949-1011, Elsevier.
    4. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    5. Asim Ansari & Ricardo Montoya & Oded Netzer, 2012. "Dynamic learning in behavioral games: A hidden Markov mixture of experts approach," Quantitative Marketing and Economics (QME), Springer, vol. 10(4), pages 475-503, December.
    6. repec:wyi:journl:002151 is not listed on IDEAS
    7. Chmura, Thorsten & Goerg, Sebastian J. & Selten, Reinhard, 2012. "Learning in experimental 2×2 games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 44-73.
    8. Rutström, E. Elisabet & Wilcox, Nathaniel T., 2009. "Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test," Games and Economic Behavior, Elsevier, vol. 67(2), pages 616-632, November.
    9. Chernov, G. & Susin, I., 2019. "Models of learning in games: An overview," Journal of the New Economic Association, New Economic Association, vol. 44(4), pages 77-125.
    10. Rapoport, Amnon & Stein, William E. & Parco, James E. & Nicholas, Thomas E., 2003. "Equilibrium play and adaptive learning in a three-person centipede game," Games and Economic Behavior, Elsevier, vol. 43(2), pages 239-265, May.
    11. Zhang, Yang & Du, Xiaomin, 2017. "Network effects on strategic interactions: A laboratory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 143(C), pages 133-146.
    12. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
    13. Yechiam, Eldad & Busemeyer, Jerome R., 2008. "Evaluating generalizability and parameter consistency in learning models," Games and Economic Behavior, Elsevier, vol. 63(1), pages 370-394, May.
    14. Nathaniel T Wilcox, 2003. "Heterogeneity and Learning Principles," Levine's Bibliography 666156000000000435, UCLA Department of Economics.
    15. Garcia-Pola, Bernardo & Iriberri, Nagore, 2019. "Naivete and Sophistication in Initial and Repeated Play in Games," CEPR Discussion Papers 14088, C.E.P.R. Discussion Papers.
    16. Philippe Jehiel & Juni Singh, 2019. "Multi-state choices with aggregate feedback on unfamiliar alternatives," PSE Working Papers halshs-02183444, HAL.
    17. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    18. Shafran, Aric P., 2012. "Learning in games with risky payoffs," Games and Economic Behavior, Elsevier, vol. 75(1), pages 354-371.
    19. Teck H. Ho & Xin Wang & Colin F. Camerer, 2008. "Individual Differences in EWA Learning with Partial Payoff Information," Economic Journal, Royal Economic Society, vol. 118(525), pages 37-59, January.
    20. Todd Guilfoos & Andreas Duus Pape, 2020. "Estimating Case-Based Learning," Games, MDPI, Open Access Journal, vol. 11(3), pages 1-25, September.
    21. Sebastian J. Goerg & Tibor Neugebauer & Abdolkarim Sadrieh, 2016. "Impulse Response Dynamics in Weakest Link Games," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 284-297, August.

    More about this item

    Keywords

    Econometric and statistical methods; Economic models;

    JEL classification:

    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

    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:bca:bocawp:19-50. 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: . General contact details of provider: https://edirc.repec.org/data/bocgvca.html .

    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: (email available below). General contact details of provider: https://edirc.repec.org/data/bocgvca.html .

    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.