IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v47y2018i3d10.1007_s00182-018-0626-x.html
   My bibliography  Save this article

Game theory with translucent players

Author

Listed:
  • Joseph Y. Halpern

    (Cornell University)

  • Rafael Pass

    (Cornell University)

Abstract

A traditional assumption in game theory is that players are opaque to one another—if a player changes strategies, then this change in strategies does not affect the choice of other players’ strategies. In many situations this is an unrealistic assumption. We develop a framework for reasoning about games where the players may be translucent to one another; in particular, a player may believe that if she were to change strategies, then the other player would also change strategies. Translucent players may achieve significantly more efficient outcomes than opaque ones. Our main result is a characterization of strategies consistent with appropriate analogues of common belief of rationality. Common Counterfactual Belief of Rationality (CCBR) holds if (1) everyone is rational, (2) everyone counterfactually believes that everyone else is rational (i.e., all players i believe that everyone else would still be rational even if i were to switch strategies), (3) everyone counterfactually believes that everyone else is rational, and counterfactually believes that everyone else is rational, and so on. CCBR characterizes the set of strategies surviving iterated removal of minimax-dominated strategies, where a strategy $$\sigma $$ σ for player i is minimax dominated by $$\sigma '$$ σ ′ if the worst-case payoff for i using $$\sigma '$$ σ ′ is better than the best possible payoff using $$\sigma $$ σ .

Suggested Citation

  • Joseph Y. Halpern & Rafael Pass, 2018. "Game theory with translucent players," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 949-976, September.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:3:d:10.1007_s00182-018-0626-x
    DOI: 10.1007/s00182-018-0626-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-018-0626-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-018-0626-x?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. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(2), pages 133-163, October.
    2. Joseph Y. Halpern, 1999. "Hypothetical knowledge and counterfactual reasoning," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 315-330.
    3. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    4. Ehud Kalai & Eitan Zemel, 1988. "On The Order of Eliminating Dominated Strategies," Discussion Papers 789, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Kalai, Adam Tauman & Kalai, Ehud & Lehrer, Ehud & Samet, Dov, 2010. "A commitment folk theorem," Games and Economic Behavior, Elsevier, vol. 69(1), pages 127-137, May.
    6. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    8. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    9. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
    10. Zambrano Eduardo, 2004. "Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-25, November.
    11. Wolfgang Spohn, 2003. "Dependency Equilibria and the Casual Structure of Decision and Game Situations," Homo Oeconomicus, Institute of SocioEconomics, vol. 20, pages 195-255.
    12. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    13. 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..
    14. Masel, Joanna, 2007. "A Bayesian model of quasi-magical thinking can explain observed cooperation in the public good game," Journal of Economic Behavior & Organization, Elsevier, vol. 64(2), pages 216-231, October.
    15. Solan, Eilon & Yariv, Leeat, 2004. "Games with espionage," Games and Economic Behavior, Elsevier, vol. 47(1), pages 172-199, April.
    16. Di Tillio, Alfredo & Halpern, Joseph Y. & Samet, Dov, 2014. "Conditional belief types," Games and Economic Behavior, Elsevier, vol. 87(C), pages 253-268.
    17. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    18. Basu, Kaushik, 1994. "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory," American Economic Review, American Economic Association, vol. 84(2), pages 391-395, May.
    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. repec:cup:judgdm:v:16:y:2021:i:4:p:844-897 is not listed on IDEAS
    2. Todd Larson Landes & Piers Douglas Howe & Yoshihisa Kashima, 2021. "A hierarchy of mindreading strategies in joint action participation," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(4), pages 844-897, July.

    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. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    3. Feinberg, Yossi, 2005. "Subjective reasoning--dynamic games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 54-93, July.
    4. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    5. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
    6. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    7. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    8. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    9. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    10. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
    11. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    12. Perea Andrés, 2003. "Rationalizability and Minimal Complexity in Dynamic Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. 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.
    14. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Interactive beliefs, epistemic independence and strong rationalizability," Research in Economics, Elsevier, vol. 53(3), pages 247-273, September.
    15. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1997. "An Epistemic Characterization of Extensive Form Rationalizability," Working Papers 1009, California Institute of Technology, Division of the Humanities and Social Sciences.
    16. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    17. Xiao Luo, 2016. "Rational beliefs in rationalizability," Theory and Decision, Springer, vol. 81(2), pages 189-198, August.
    18. Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.
    19. 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.
    20. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.

    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:spr:jogath:v:47:y:2018:i:3:d:10.1007_s00182-018-0626-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.