IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2110.02755.html
   My bibliography  Save this paper

Gambits: Theory and Evidence

Author

Listed:
  • Shiva Maharaj
  • Nicholas Polson
  • Christian Turk

Abstract

Gambits are central to human decision-making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study gambits and behavioral game theory. Our theory is based on the Bellman optimality path for sequential decision-making. This allows us to calculate the $Q$-values of a Gambit where material (usually a pawn) is sacrificed for dynamic play. On the empirical side, we study the effectiveness of a number of popular chess Gambits. This is a natural setting as chess Gambits require a sequential assessment of a set of moves (a.k.a. policy) after the Gambit has been accepted. Our analysis uses Stockfish 14.1 to calculate the optimal Bellman $Q$ values, which fundamentally measures if a position is winning or losing. To test whether Bellman's equation holds in play, we estimate the transition probabilities to the next board state via a database of expert human play. This then allows us to test whether the \emph{Gambiteer} is following the optimal path in his decision-making. Our methodology is applied to the popular Stafford and reverse Stafford (a.k.a. Boden-Kieretsky-Morphy) Gambit and other common ones including the Smith-Morra, Goring, Danish and Halloween Gambits. We build on research in human decision-making by proving an irrational skewness preference within agents in chess. We conclude with directions for future research.

Suggested Citation

  • Shiva Maharaj & Nicholas Polson & Christian Turk, 2021. "Gambits: Theory and Evidence," Papers 2110.02755, arXiv.org, revised Apr 2022.
    • Handle: RePEc:arx:papers:2110.02755
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2110.02755
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Insua, David Rios & Ruggeri, Fabrizio & Soyer, Refik & Wilson, Simon, 2020. "Advances in Bayesian decision making in reliability," European Journal of Operational Research, Elsevier, vol. 282(1), pages 1-18.
    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    5. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    6. Ramsey, Frank P., 1926. "Truth and Probability," Histoy of Economic Thought Chapters, in: Braithwaite, R. B. (ed.),The Foundations of Mathematics and other Logical Essays, chapter 7, pages 156-198, McMaster University Archive for the History of Economic Thought.
    7. Colin F. Camerer, 1997. "Progress in Behavioral Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 11(4), pages 167-188, Fall.
    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. repec:aia:aiaswp:124 is not listed on IDEAS
    2. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    3. Zhaoyu Cao & Xu Zhao & Yucheng Zou & Kairong Hong & Yanwei Zhang, 2021. "Multidimensional Fair Fuzzy Equilibrium Evaluation of Housing Expropriation Compensation from the Perspective of Behavioral Preference: A Case Study from China," Mathematics, MDPI, vol. 9(6), pages 1-22, March.
    4. Kairong Hong & Yucheng Zou & Mingyuan Zhu & Yanwei Zhang, 2021. "A Game Analysis of Farmland Expropriation Conflict in China under Multi-Dimensional Preference: Cooperation or Resistance?," Land, MDPI, vol. 10(2), pages 1-29, January.
    5. James Andreoni & Deniz Aydin & Blake Barton & B. Douglas Bernheim & Jeffrey Naecker, 2020. "When Fair Isn’t Fair: Understanding Choice Reversals Involving Social Preferences," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1673-1711.
    6. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    7. Antonides, Gerrit & Kroft, Maaike, 2005. "Fairness judgments in household decision making," Journal of Economic Psychology, Elsevier, vol. 26(6), pages 902-913, December.
    8. Ariane Lambert Mogiliansky & Shmuel Zamir & Herve Zwirn, 2003. "Type Indeterminacy: A Model of the KT(Kahneman-Tversky)-man," Discussion Paper Series dp343, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. Bingley, P. & Eriksson, T, 2001. "Pay Spread and Skewness. Employee Effort and Firm Productivity," Papers 01-2, Aarhus School of Business - Department of Economics.
    10. Sliwka, Dirk & Werner, Peter, 2016. "How Do Agents React to Dynamic Wage Increases? An Experimental Study," IZA Discussion Papers 9855, Institute of Labor Economics (IZA).
    11. Stefano DellaVigna, 2009. "Psychology and Economics: Evidence from the Field," Journal of Economic Literature, American Economic Association, vol. 47(2), pages 315-372, June.
    12. Stephan Schulmeister, 2000. "Technical Analysis and Exchange Rate Dynamics," WIFO Studies, WIFO, number 25857.
    13. Alexandre Truc, 2023. "Neuroeconomics: Hype or Hope? An Answer," Post-Print hal-04719266, HAL.
    14. James C. Cox & Vjollca Sadiraj, 2018. "Incentives," Experimental Economics Center Working Paper Series 2018-01, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
    15. He, Haoran & Wu, Keyu, 2016. "Choice set, relative income, and inequity aversion: An experimental investigation," Journal of Economic Psychology, Elsevier, vol. 54(C), pages 177-193.
    16. Smith, Vernon L., 2005. "Behavioral economics research and the foundations of economics," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 34(2), pages 135-150, March.
    17. Teck-Hua Ho & Juanjuan Zhang, 2008. "Designing Pricing Contracts for Boundedly Rational Customers: Does the Framing of the Fixed Fee Matter?," Management Science, INFORMS, vol. 54(4), pages 686-700, April.
    18. Gill, David & Stone, Rebecca, 2015. "Desert and inequity aversion in teams," Journal of Public Economics, Elsevier, vol. 123(C), pages 42-54.
    19. Lin, Chaonan & Chen, Hong-Yi & Ko, Kuan-Cheng & Yang, Nien-Tzu, 2021. "Time-dependent lottery preference and the cross-section of stock returns," Journal of Empirical Finance, Elsevier, vol. 64(C), pages 272-294.
    20. Alexander F. Tieman & Harold Houba & Gerard van der Laan, 1998. "Cooperation in a Multi-Dimensional Local Interaction Model," Game Theory and Information 9803002, University Library of Munich, Germany.
    21. Gill, David & Stone, Rebecca, 2010. "Fairness and desert in tournaments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 346-364, July.

    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:2110.02755. 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.