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Outcome destabilization

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  • Dilmé, Francesc

Abstract

In a game in extensive form, we say that a sequence of trembles destabilizes an outcome if there is no corresponding sequence of payoff perturbations and Nash outcomes converging to the outcome. We use equilibrium destabilization to characterize sequential equilibria and sequentially stable outcomes, and to reinterpret standard selection criteria in signaling games as a means of ruling out implausible equilibria by identifying destabilizing tremble sequences. We show that the existence of a maximally destabilizing sequence of trembles (destabilizing all outcomes but one) significantly simplifies studying strategically stable behavior in complex games such as finitely repeated games.

Suggested Citation

  • Dilmé, Francesc, 2026. "Outcome destabilization," Games and Economic Behavior, Elsevier, vol. 157(C), pages 34-49.
    • Handle: RePEc:eee:gamebe:v:157:y:2026:i:c:p:34-49
    DOI: 10.1016/j.geb.2026.01.004
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    References listed on IDEAS

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    1. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
    2. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June.
    3. Cho, In-Koo, 1987. "A Refinement of Sequential Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1367-1389, November.
    4. 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.
    5. Milgrom, Paul & Mollner, Joshua, 2021. "Extended proper equilibrium," Journal of Economic Theory, Elsevier, vol. 194(C).
    6. Osborne, Martin J., 1990. "Signaling, forward induction, and stability in finitely repeated games," Journal of Economic Theory, Elsevier, vol. 50(1), pages 22-36, February.
    7. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    8. McLennan, Andrew, 1985. "Justifiable Beliefs in Sequential Equilibrium," Econometrica, Econometric Society, vol. 53(4), pages 889-904, July.
    9. Gossner, Olivier, 1995. "The Folk Theorem for Finitely Repeated Games with Mixed Strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 95-107.
    10. Fudenberg, Drew & He, Kevin, 2021. "Player-compatible learning and player-compatible equilibrium," Journal of Economic Theory, Elsevier, vol. 194(C).
    11. Dilmé, Francesc, 2025. "Iterated exclusion of implausible types in signaling games," Games and Economic Behavior, Elsevier, vol. 152(C), pages 293-312.
    12. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    13. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-661, May.
    14. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
    15. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 453-478.
    16. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    17. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    18. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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