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Strategic equilibrium

In: Handbook of Game Theory with Economic Applications

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  • Van Damme, Eric

Abstract

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 indicated.

Suggested Citation

  • Van Damme, Eric, 2002. "Strategic equilibrium," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 41, pages 1521-1596, Elsevier.
    • Handle: RePEc:eee:gamchp:3-41
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    1. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    2. 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..
    3. 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.
    4. Kyle Bagwell & Garey Ramey, 1996. "Capacity, Entry, and Forward Induction," RAND Journal of Economics, The RAND Corporation, vol. 27(4), pages 660-680, Winter.
    5. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    6. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    7. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(2), pages 179-214, October.
    8. Basu, Kaushik, 1988. "Strategic irrationality in extensive games," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 247-260, June.
    9. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    10. Blume Andreas, 1994. "Equilibrium Refinements in Sender-Receiver Games," Journal of Economic Theory, Elsevier, vol. 64(1), pages 66-77, October.
    11. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(1), pages 9-55, April.
    12. 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.
    13. 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.
    14. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-661, May.
    15. 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.
    16. Blume, Andreas, 1996. "Neighborhood Stability in Sender-Receiver Games," Games and Economic Behavior, Elsevier, vol. 13(1), pages 2-25, March.
    17. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    18. 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.
    19. 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.
    20. 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.
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    Cited by:

    1. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
    2. 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.
    3. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
    4. 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.
    5. 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.
    6. 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.
    7. Milchtaich, Igal, 2019. "Polyequilibrium," Games and Economic Behavior, Elsevier, vol. 113(C), pages 339-355.
    8. 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.
    9. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
    10. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, University Library of Munich, Germany, revised 18 Sep 1996.
    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.

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