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Sequential Equilibria in a Class of Infinite Extensive Form Games

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  • Michael Greinecker
  • Martin Meier
  • Konrad Podczeck

Abstract

Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In standard finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of sequential equilibrium.

Suggested Citation

  • Michael Greinecker & Martin Meier & Konrad Podczeck, 2026. "Sequential Equilibria in a Class of Infinite Extensive Form Games," Papers 2604.25784, arXiv.org.
    • Handle: RePEc:arx:papers:2604.25784
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    1. Zdzisław Denkowski & Stanisław Migórski & Nikolas S. Papageorgiou, 2003. "An Introduction to Nonlinear Analysis: Theory," Springer Books, Springer, number 978-1-4419-9158-4, January.
    2. Pierpaolo Battigalli & Pietro Tebaldi, 2019. "Interactive epistemology in simple dynamic games with a continuum of strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 737-763, October.
    3. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    4. Joseph Y. Halpern, 2017. "Erratum to: A nonstandard characterization of sequential equilibrium, perfect equilibrium, and proper equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 591-594, May.
    5. Bagwell, Kyle, 1995. "Commitment and observability in games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 271-280.
    6. Perea y Monsuwe, Andres & Jansen, Mathijs & Peters, Hans, 1997. "Consistency of assessments in infinite signaling games," Journal of Mathematical Economics, Elsevier, vol. 27(4), pages 425-449, May.
    7. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-924, July.
    8. Giovanni Maggi, 1999. "The Value of Commitment with Imperfect Observability and Private Information," RAND Journal of Economics, The RAND Corporation, vol. 30(4), pages 555-574, Winter.
    9. Mendez-Naya L. & Garcia-Jurado, I. & Cesco, J. C., 1996. "Perfection of Nash equilibria in continous games," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 53-53, February.
    10. Alexander A. Yushkevich, 1997. "The Compactness of a Policy Space in Dynamic Programming Via an Extension Theorem for Carathéodory Functions," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 458-467, May.
    11. 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.
    12. Roger B. Myerson & Philip J. Reny, 2020. "Perfect Conditional ε‐Equilibria of Multi‐Stage Games With Infinite Sets of Signals and Actions," Econometrica, Econometric Society, vol. 88(2), pages 495-531, March.
    13. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
    14. Klaus Ritzberger, 1999. "Recall in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 69-87.
    15. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
    16. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-544, May.
    17. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    18. Manelli, Alejandro M, 1996. "Cheap Talk and Sequential Equilibria in Signaling Games," Econometrica, Econometric Society, vol. 64(4), pages 917-942, July.
    19. Hellman, Ziv, 2014. "A game with no Bayesian approximate equilibria," Journal of Economic Theory, Elsevier, vol. 153(C), pages 138-151.
    20. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
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