IDEAS home Printed from
   My bibliography  Save this paper

Strategic Equilibrium


  • van Damme, E.E.C.

    (Tilburg University, Center For Economic Research)


This chapter of the Handbook of Game Theory (Vol. 3) provides an overview of the theory of Nash equilibrium and its refinements. The starting-point is the rationalistic approach to games and the question whether there exists a convincing, self-enforcing theory of rational behavior in non-cooperative games. Given the assumption of independent behavior of the players, it follows that a self-enforcing theory has to prescribe a Nash equilibrium, i.e., a strategy profile such that no player can gain by a unilateral deviation. Nash equilibria exist and for generic (finite) games there is a finite number of Nash equilibrium outcomes. The chapter first describes some general properties of Nash equilibria. Next it reviews the arguments why not all Nash equilibria can be considered self-enforcing. For example, some equilibria do not satisfy a backward induction property: as soon as a certain subgame is reached, a player has an incentive to deviate. The concepts of subgame perfect equilibria, perfect equilibria and sequential equilibria are introduced to solve this problem. The chapter defines these concepts, derives properties of these concepts and relates them to other refinements such as proper equilibria and persistent equilibria. It turns out that none of these concepts is fully satisfactory as the outcomes that are implied by any of these concepts are not invariant w.r.t. inessential changes in the game. In addition, these concepts do not satisfy a forward induction requirement. The chapter continues with formalizing these notions and it describes concepts of stable equilibria that do satisfy these properties. This set-valued concept is then related to the other refinements. In the final section of the chapter, the theory of equilibrium selection that was proposed by Harsanyi and Selten is described and applied to several examples. This theory selects a unique equilibrium for every game. Some drawbacks of this theory are noted and avenues for future research are indicate
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • van Damme, E.E.C., 2000. "Strategic Equilibrium," Discussion Paper 2000-115, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:ae143f73-1fd0-40da-9c57-61c04fdb435c

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    4. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(1), pages 9-55, April.
    5. Cho, In-Koo & Sobel, Joel, 1990. "Strategic stability and uniqueness in signaling games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 381-413, April.
    6. Ben-Porath, Elchanan & Dekel, Eddie, 1992. "Signaling future actions and the potential for sacrifice," Journal of Economic Theory, Elsevier, vol. 57(1), pages 36-51.
    7. Basu, Kaushik, 1988. "Strategic irrationality in extensive games," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 247-260, June.
    8. Blume Andreas, 1994. "Equilibrium Refinements in Sender-Receiver Games," Journal of Economic Theory, Elsevier, vol. 64(1), pages 66-77, October.
    9. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    10. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 488-500.
    11. Blume, Andreas, 1996. "Neighborhood Stability in Sender-Receiver Games," Games and Economic Behavior, Elsevier, vol. 13(1), pages 2-25, March.
    12. Basu, Kaushik, 1990. "On the Non-existence of a Rationality Definition for Extensive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 33-44.
    13. 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..
    14. Kyle Bagwell & Garey Ramey, 1996. "Capacity, Entry, and Forward Induction," RAND Journal of Economics, The RAND Corporation, vol. 27(4), pages 660-680, Winter.
    15. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    16. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(2), pages 179-214, October.
    17. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    18. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-661, May.
    19. Bernheim, B. Douglas & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria II. Applications," Journal of Economic Theory, Elsevier, vol. 42(1), pages 13-29, June.
    20. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    2. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
    3. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
    4. Gunnthorsdottir, Anna & Vragov, Roumen & Seifert, Stefan & McCabe, Kevin, 2010. "Near-efficient equilibria in contribution-based competitive grouping," Journal of Public Economics, Elsevier, vol. 94(11-12), pages 987-994, December.
    5. Milchtaich, Igal, 2019. "Polyequilibrium," Games and Economic Behavior, Elsevier, vol. 113(C), pages 339-355.
    6. Giuseppe De Marco & Jacqueline Morgan, 2007. "Slightly Altruistic Equilibria in Normal Form Games," CSEF Working Papers 185, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    7. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, University Library of Munich, Germany, revised 18 Sep 1996.
    8. Giovanni Rossi, 2009. "Measuring conflict and power in strategic settings," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(2), pages 75-104.
    9. Govindan, Srihari & Wilson, Robert, 2009. "Axiomativ Theory of Equilibrium Selection for Games with Two Players, Perfect Information, and Generic Payoffs," Research Papers 2008, Stanford University, Graduate School of Business.
    10. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
    11. repec:ebl:ecbull:v:3:y:2004:i:3:p:1-8 is not listed on IDEAS
    12. Gunnthorsdottir, Anna & Vragov, Roumen & seifert, Stefan & McCabe, Kevin, 2008. "on the efficiency of team-based meritocracies," MPRA Paper 8627, University Library of Munich, Germany.

    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. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, University Library of Munich, Germany, revised 18 Sep 1996.
    2. Sobel, Joel, 2017. "A note on pre-play communication," Games and Economic Behavior, Elsevier, vol. 102(C), pages 477-486.
    3. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    4. Norman, Thomas W.L., 2018. "Inefficient stage Nash is not stable," Journal of Economic Theory, Elsevier, vol. 178(C), pages 275-293.
    5. Marek Mikolaj Kaminski, 2019. "Generalized Backward Induction: Justification for a Folk Algorithm," Games, MDPI, vol. 10(3), pages 1-25, August.
    6. Ambrus, Attila, 2009. "Theories of Coalitional Rationality," Scholarly Articles 3204917, Harvard University Department of Economics.
    7. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    8. Weibull, Jörgen W., 1992. "An Introduction to Evolutionary Game Theory," Working Paper Series 347, Research Institute of Industrial Economics.
    9. Shimoji, Makoto & Watson, Joel, 1998. "Conditional Dominance, Rationalizability, and Game Forms," Journal of Economic Theory, Elsevier, vol. 83(2), pages 161-195, December.
    10. Dominiak, Adam & Lee, Dongwoo, 2023. "Testing rational hypotheses in signaling games," European Economic Review, Elsevier, vol. 160(C).
    11. W. Bentley MacLeod, 2006. "Reputations, Relationships and the Enforcement of Incomplete Contracts," CESifo Working Paper Series 1730, CESifo.
    12. Mehmet Ekmekci & Nenad Kos, 2020. "Signaling Covertly Acquired Information," Working Papers 658, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Ernesto Pasten, 2020. "Prudential Policies and Bailouts: A Delicate Interaction," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 38, pages 181-197, October.
    14. Abhijit Banerjee & Jörgen W. Weibull & Ken Binmore, 1996. "Evolution and Rationality: Some Recent Game-Theoretic Results," International Economic Association Series, in: Beth Allen (ed.), Economics in a Changing World, chapter 4, pages 90-117, Palgrave Macmillan.
    15. Heller, Yuval, 2010. "Minority-proof cheap-talk protocol," Games and Economic Behavior, Elsevier, vol. 69(2), pages 394-400, July.
    16. Adriani, Fabrizio & Deidda, Luca G., 2011. "Competition and the signaling role of prices," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 412-425, July.
    17. Nick Feltovich & Rick Harbaugh & Ted To, 1998. "Too Cool for School? A Theory of Countersignaling," Game Theory and Information 9811002, University Library of Munich, Germany.
    18. Peter Eso & James Schummer, 2005. "Robust Deviations from Signaling Equilibria," Discussion Papers 1406, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. 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).
    20. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.

    More about this item


    noncooperative games; equilibrium analysis;


    Access and download statistics


    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:tiu:tiucen:ae143f73-1fd0-40da-9c57-61c04fdb435c. 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: Richard Broekman (email available below). General contact details of provider: .

    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.