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Foundations of Strategic Equilibrium

  • John Hillas

    (SUNY at Stony Brook)

  • Elon Kohlberg

    (Harvard)

Registered author(s):

    The central concept of noncooperative game theory is that of the \emph{strategic equilibrium} (or Nash equilibrium, or noncooperative equilibrium). In this chapter we discuss some of the conceptual issues surrounding this concept and its refinements. Many of these issues have received increasing attention in the last few years. We are not at all comprehensive in covering the approaches that have been taken to the question. In particular, we focus almost exclusively on the ``purely rational'' approach and say almost nothing about other approaches. We do survey some of the issues and approaches that do not fit neatly into the core of our argument in the final section.

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    Paper provided by EconWPA in its series Game Theory and Information with number 9606002.

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    Length: 2 pages
    Date of creation: 30 Jun 1996
    Date of revision: 18 Sep 1996
    Handle: RePEc:wpa:wuwpga:9606002
    Note: Type of Document - AMS LaTeX; prepared on IBM PC - emTEX ; to print on HP/PostScript; pages: 2 + 63; figures: included . Prepared for the \emph{Handbook of Game Theory with Economic Applications} edited by Robert J. Aumann and Sergiu Hart. Comments still welcomed by the authors, perhaps not by the editors. Postscript file redone embedding type 1 versions of the fonts, in the hope that a dpf file will be generated and the postsctipt file made directly available.
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    1. Mailath, George J & Samuelson, Larry & Swinkels, Jeroen M, 1993. "Extensive Form Reasoning in Normal Form Games," Econometrica, Econometric Society, vol. 61(2), pages 273-302, March.
    2. MERTENS, Jean-François, . "Ordinality in non cooperative games," CORE Discussion Papers RP -1738, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    4. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May.
    5. 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.
    6. Dhillon, Amrita & Mertens, Jean Francois, 1996. "Perfect Correlated Equilibria," Journal of Economic Theory, Elsevier, vol. 68(2), pages 279-302, February.
    7. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
    8. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    9. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
    11. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-61, May.
    12. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
    13. Adam Brandenburger, 1992. "Knowledge and Equilibrium in Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 83-101, Fall.
    14. Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40 Elsevier.
    15. Forges, F., 1987. "Universal mechanisms," CORE Discussion Papers 1987004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
    17. John Hillas, 1996. "On the Relation Between Perfect Equilibria in Extensive Form Games and Proper Equilibria in Normal Form Games," Game Theory and Information 9605002, EconWPA, revised 14 May 1996.
    18. GOVINDAN, Srihari, 1992. "Stability and the chain store paradox," CORE Discussion Papers 1992004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. repec:nys:sunysb:91-24 is not listed on IDEAS
    20. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
    21. 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.
    22. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
    23. Kaushik Basu, 2010. "Strategic Irrationality in Extensive Games," Levine's Working Paper Archive 375, David K. Levine.
    24. Basu, Kaushik, 1990. "On the Non-existence of a Rationality Definition for Extensive Games," International Journal of Game Theory, Springer, vol. 19(1), pages 33-44.
    25. John Hillas & Dries Vermeulen & Mathijs Jansen, 1996. "On the Finiteness of Stable Sets," Game Theory and Information 9605003, EconWPA, revised 15 Jun 1996.
    26. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
    27. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-94, July.
    28. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
    29. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
    30. R. J. Aumann & M. Maschler, 1972. "Some Thoughts on the Minimax Principle," Management Science, INFORMS, vol. 18(5-Part-2), pages 54-63, January.
    31. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    32. Elmes Susan & Reny Philip J., 1994. "On the Strategic Equivalence of Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 62(1), pages 1-23, February.
    33. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
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    35. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
    36. Bernheim, B Douglas, 1986. " Axiomatic Characterizations of Rational Choice in Strategic Environme nts," Scandinavian Journal of Economics, Wiley Blackwell, vol. 88(3), pages 473-88.
    37. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(01), pages 9-55, April.
    38. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
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