IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v17y4i2020p277-298.html
   My bibliography  Save this article

Optimal Off-line Experimentation for Games

Author

Listed:
  • Theodore T. Allen

    (Integrated Systems Engineering, The Ohio State University, Columbus, Ohio 43210)

  • Olivia K. Hernand

    (Integrated Systems Engineering, The Ohio State University, Columbus, Ohio 43210)

  • Abdullah Alomair

    (Integrated Systems Engineering, The Ohio State University, Columbus, Ohio 43210)

Abstract

Many business situations can be called “games” because outcomes depend on multiple decision makers with differing objectives. Yet, in many cases, the payoffs for all combinations of player options are not available, but the ability to experiment off-line is available. For example, war-gaming exercises, test marketing, cyber-range activities, and many types of simulations can all be viewed as off-line gaming-related experimentation. We address the decision problem of planning and analyzing off-line experimentation for games with an initial procedure seeking to minimize the errors in payoff estimates. Then, we provide a sequential algorithm with reduced selections from option combinations that are irrelevant to evaluating candidate Nash, correlated, cumulative prospect theory or other equilibria. We also provide an efficient formula to estimate the chance that given Nash equilibria exists, provide convergence guarantees relating to general equilibria, and provide a stopping criterion called the estimated expected value of perfect off-line information (EEVPOI). The EEVPOI is based on bounded gains in expected utility from further off-line experimentation. An example of using a simulation model to illustrate all the proposed methods is provided based on a cyber security capture-the-flag game. The example demonstrates that the proposed methods enable substantial reductions in both the number of test runs (half) compared with a full factorial and the computational time for the stopping criterion.

Suggested Citation

  • Theodore T. Allen & Olivia K. Hernand & Abdullah Alomair, 2020. "Optimal Off-line Experimentation for Games," Decision Analysis, INFORMS, vol. 17(4), pages 277-298, December.
    • Handle: RePEc:inm:ordeca:v:17:y:4:i:2020:p:277-298
    DOI: 10.1287/deca.2020.0412
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/deca.2020.0412
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.2020.0412?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
    ---><---

    References listed on IDEAS

    as
    1. Martin Shubik, 1955. "The Uses of Game Theory in Management Science," Management Science, INFORMS, vol. 2(1), pages 40-54, October.
    2. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    5. Chun-Wa Ko & Jon Lee & Maurice Queyranne, 1995. "An Exact Algorithm for Maximum Entropy Sampling," Operations Research, INFORMS, vol. 43(4), pages 684-691, August.
    6. Kleijnen, Jack P.C. & Mehdad, Ehsan, 2014. "Multivariate versus univariate Kriging metamodels for multi-response simulation models," European Journal of Operational Research, Elsevier, vol. 236(2), pages 573-582.
    7. Soham R. Phade & Venkat Anantharam, 2019. "On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences," Decision Analysis, INFORMS, vol. 16(2), pages 142-156, June.
    8. Martin Shubik, 2002. "Game Theory and Operations Research: Some Musings 50 Years Later," Operations Research, INFORMS, vol. 50(1), pages 192-196, February.
    9. Rahul Savani & Bernhard Stengel, 2015. "Game Theory Explorer: software for the applied game theorist," Computational Management Science, Springer, vol. 12(1), pages 5-33, January.
    10. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    11. Deng Huang & Theodore T. Allen, 2005. "Design and analysis of variable fidelity experimentation applied to engine valve heat treatment process design," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(2), pages 443-463, April.
    12. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    13. Kerim Keskin, 2016. "Equilibrium Notions for Agents with Cumulative Prospect Theory Preferences," Decision Analysis, INFORMS, vol. 13(3), pages 192-208, September.
    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. Soham R. Phade & Venkat Anantharam, 2023. "Learning in Games with Cumulative Prospect Theoretic Preferences," Dynamic Games and Applications, Springer, vol. 13(1), pages 265-306, March.
    2. Ali Yekkehkhany & Timothy Murray & Rakesh Nagi, 2021. "Stochastic Superiority Equilibrium in Game Theory," Decision Analysis, INFORMS, vol. 18(2), pages 153-168, June.
    3. Soham R. Phade & Venkat Anantharam, 2020. "Black-Box Strategies and Equilibrium for Games with Cumulative Prospect Theoretic Players," Papers 2004.09592, arXiv.org.
    4. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    5. Soham R. Phade & Venkat Anantharam, 2021. "Mechanism Design for Cumulative Prospect Theoretic Agents: A General Framework and the Revelation Principle," Papers 2101.08722, arXiv.org.
    6. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    7. Stuart, Harborne Jr., 1997. "Common Belief of Rationality in the Finitely Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 19(1), pages 133-143, April.
    8. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    10. Tsakas, Elias, 2014. "Rational belief hierarchies," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 121-127.
    11. Soham R. Phade & Venkat Anantharam, 2019. "On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences," Decision Analysis, INFORMS, vol. 16(2), pages 142-156, June.
    12. Arnaud Wolff, 2019. "On the Function of Beliefs in Strategic Social Interactions," Working Papers of BETA 2019-41, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    13. Bach, Christian W. & Perea, Andrés, 2020. "Two definitions of correlated equilibrium," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 12-24.
    14. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    15. Giuseppe Attanasi & Pierpaolo Battigalli & Elena Manzoni, 2016. "Incomplete-Information Models of Guilt Aversion in the Trust Game," Management Science, INFORMS, vol. 62(3), pages 648-667, March.
    16. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    17. Hendrik Vollmer, 2013. "What kind of game is everyday interaction?," Rationality and Society, , vol. 25(3), pages 370-404, August.
    18. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    19. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
    20. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.

    More about this item

    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:inm:ordeca:v:17:y:4:i:2020:p:277-298. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.