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Equivalence of the information structure with unawareness to the logic of awareness

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  • Heinsalu, Sander

Abstract

This paper proves the Li (2009) [13] unawareness structure equivalent to the single-agent propositionally generated logic of awareness of Fagin and Halpern (1988) [4]. For any model of one type one can construct a model of the other type describing the same belief and awareness. Li starts from an agent unable to perceive aspects of the world and distinguish states, modeled with subjective state spaces coarser than the objective state space. Fagin and Halpern limit the agentʼs language or cognitive ability to reasoning only about a subset of the primitive propositions describing the world. Equivalence of these approaches suggests they capture a natural notion of unawareness in a minimal way.

Suggested Citation

  • Heinsalu, Sander, 2012. "Equivalence of the information structure with unawareness to the logic of awareness," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2453-2468.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:6:p:2453-2468 DOI: 10.1016/j.jet.2012.05.010
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    References listed on IDEAS

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    1. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, pages 188-230.
    2. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    3. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    4. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2008. "A canonical model for interactive unawareness," Games and Economic Behavior, Elsevier, vol. 62(1), pages 304-324, January.
    6. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    7. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    8. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    9. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
    10. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
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    Cited by:

    1. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    2. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    3. Oliver Walker, 2011. "Unawareness with �possible� possible worlds," GRI Working Papers 69, Grantham Research Institute on Climate Change and the Environment.
    4. repec:eee:matsoc:v:87:y:2017:i:c:p:11-21 is not listed on IDEAS
    5. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.

    More about this item

    Keywords

    Unawareness; Awareness; State space models; Modal logic; Information;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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