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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.

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This chapter was published in:

  • R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3, 00.
    This item is provided by Elsevier in its series Handbook of Game Theory with Economic Applications with number 3-41.

    Handle: RePEc:eee:gamchp:3-41

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    Cited by:
    1. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
    2. Srihari Govindan & Robert Wilson, 2007. "On Forward Induction," Levine's Bibliography 321307000000000788, UCLA Department of Economics.
    3. Srihari Govindan & Robert Wilson, 2009. "Axiomatic Theory of Equilibrium Selection for Games with Two Players, Perfect Information, and Generic Payoffs," Levine's Working Paper Archive 814577000000000125, David K. Levine.
    4. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‚ÄźPlayer Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, 07.
    5. repec:ebl:ecbull:v:3:y:2004:i:3:p:1-8 is not listed on IDEAS
    6. Gunnthorsdottir, Anna & Vragov, Roumen & seifert, Stefan & McCabe, Kevin, 2008. "on the efficiency of team-based meritocracies," MPRA Paper 8627, University Library of Munich, Germany.
    7. Fabrizio Germano, 2003. "On some geometry and equivalence classes of normal form games," Economics Working Papers 669, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Damme, E.E.C. van & Hurkens, J.P.M., 1997. "Games with imperfectly observable commitment," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74216, Tilburg University.
    9. 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.
    10. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, EconWPA, revised 18 Sep 1996.
    11. Giovanni Rossi, 2009. "Measuring conflict and power in strategic settings," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 75-104.
    12. 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.

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