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Strategic Equilibrium

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  • van Damme, E.E.C.

    (Tilburg University, School of Economics and Management)

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 indicate
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Suggested Citation

  • van Damme, E.E.C., 2000. "Strategic Equilibrium," Other publications TiSEM ae143f73-1fd0-40da-9c57-6, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:ae143f73-1fd0-40da-9c57-61c04fdb435c
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    References listed on IDEAS

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    Cited by:

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