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Foundations of strategic equilibrium

In: Handbook of Game Theory with Economic Applications

Author

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  • Hillas, John
  • Kohlberg, Elon

Abstract

This chapter examines the conceptual foundations of the concept of strategic equilibrium and its various variants and refinements. The emphasis is very much on the underlying ideas rather than on any technical details.After an examination of some pre-equilibrium ideas, in particular the concept of rationalizability, the concept of strategic (or Nash) equilibrium is introduced. Various interpretations of this concept are discussed and a proof of the existence of such equilibria is sketched.Next, the concept of correlated equilibrium is introduced. This concept can be thought of as retaining the self-enforcing aspect of the idea of equilibrium while relaxing the independence assumption.Most of the remainder of the chapter is concerned with the ideas underlying the refinement of equilibrium: admissibility and iterated dominance; backward induction; forward induction; and ordinality and various invariances to changes in the player set. This leads to a consideration of the concept of strategic stability, a strong refinement satisfying these various ideas.Finally there is a brief examination of the epistemic approach to equilibrium and the relation between strategic equilibrium and correlated equilibrium.

Suggested Citation

  • Hillas, John & Kohlberg, Elon, 2002. "Foundations of 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 42, pages 1597-1663, Elsevier.
    • Handle: RePEc:eee:gamchp:3-42
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    Citations

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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. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    3. Govindan, Srihari & Wilson, Robert B., 2005. "Justification of Stable Equilibria," Research Papers 1896, Stanford University, Graduate School of Business.
    4. Gatti, Nicola & Gilli, Mario & Marchesi, Alberto, 2020. "A characterization of quasi-perfect equilibria," Games and Economic Behavior, Elsevier, vol. 122(C), pages 240-255.
    5. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
    6. , & , B., 2006. "Sufficient conditions for stable equilibria," Theoretical Economics, Econometric Society, vol. 1(2), pages 167-206, June.
    7. R. J. Aumann & J. H. Dreze, 2005. "When All is Said and Done, How Should You Play and What Should You Expect?," Discussion Paper Series dp387, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    8. Françoise Forges & József Sákovics, 2022. "Tenable threats when Nash equilibrium is the norm," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 589-605, November.
    9. Lauren Larrouy & Guilhem Lecouteux, 2017. "Mindreading and endogenous beliefs in games," Journal of Economic Methodology, Taylor & Francis Journals, vol. 24(3), pages 318-343, July.
    10. Nicola, Gatti & Mario, Gilli & Fabio, Panozzo, 2016. "Further results on verification problems in extensive-form games," Working Papers 347, University of Milano-Bicocca, Department of Economics, revised 15 Jul 2016.
    11. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    12. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.
    13. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    14. Srihari Govindan & Robert Wilson, 2008. "Metastable Equilibria," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 787-820, November.
    15. Srihari Govindan & Robert Wilson, 2008. "Axiomatic Theory of Equilibrium Selection in Signalling Games with Generic Payoffs," Levine's Working Paper Archive 122247000000002381, David K. Levine.
    16. Man, Priscilla T.Y., 2012. "Forward induction equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 265-276.
    17. Govindan, Srihari & Wilson, Robert B., 2005. "Refinements of Nash Equilibrium," Research Papers 1897, Stanford University, Graduate School of Business.
    18. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    19. Sun, Lan, 2016. "Hypothesis testing equilibrium in signaling games," Center for Mathematical Economics Working Papers 557, Center for Mathematical Economics, Bielefeld University.

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    • C - Mathematical and Quantitative Methods

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