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Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model

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  • Shuige Liu

Abstract

We define a modification of the standard Kripke model, called the ordered Kripke model, by introducing a linear order on the set of accessible states of each state. We first show this model can be used to describe the lexicographic belief hierarchy in epistemic game theory, and perfect rationalizability can be characterized within this model. Then we show that each ordered Kripke model is the limit of a sequence of standard probabilistic Kripke models with a modified (common) belief operator, in the senses of structure and the (epsilon-)permissibilities characterized within them.

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  • Shuige Liu, 2018. "Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model," Papers 1801.08767, arXiv.org.
    • Handle: RePEc:arx:papers:1801.08767
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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.
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    3. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, October.
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    6. 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..
    7. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    8. Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
    9. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, October.
    10. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 453-478.
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