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On the state-space model of unawareness

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  • Alex A. T. Rathke

Abstract

We show that the knowledge of an agent carrying non-trivial unawareness violates the standard property of 'necessitation', therefore necessitation cannot be used to refute the standard state-space model. A revised version of necessitation preserves non-trivial unawareness and solves the classical Dekel-Lipman-Rustichini result. We propose a generalised knowledge operator consistent with the standard state-space model of unawareness, including the model of infinite state-space.

Suggested Citation

  • Alex A. T. Rathke, 2023. "On the state-space model of unawareness," Papers 2304.04626, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2304.04626
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    References listed on IDEAS

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    1. Spyros Galanis, 2013. "Unawareness of theorems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 41-73, January.
    2. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    3. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
    4. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    6. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    7. Fukuda, Satoshi, 2021. "Unawareness without AU Introspection," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    8. Yi-Chun Chen & Jeffrey Ely & Xiao Luo, 2012. "Note on unawareness: Negative Introspection versus AU Introspection (and KU Introspection)," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 325-329, May.
    9. John Geanakoplos, 1989. "Game Theory Without Partitions, and Applications to Speculation and Consensus," Cowles Foundation Discussion Papers 914, Cowles Foundation for Research in Economics, Yale University.
    10. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 153, University of California, Davis, Department of Economics.
    11. Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
    12. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 145, University of California, Davis, Department of Economics.
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