Sander Heinsalu
ABSTRACT
This paper proves the Li (2009) unawareness structure equivalent to the single-agent propositionally generated logic of awareness of Fagin and Halpern (1988). 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, modelled with subjective state spaces coarser than the objective state space. Fagin and Halpern limit the agent's language or cognitive ability to reasoning only about a subset of the propositions describing the world. Equivalence of these approaches suggests they capture a natural notion of unawareness in a minimal way.
- D. S. Ahn. Hierarchies of ambiguous beliefs. Journal of Economic Theory, 136(1):286--301, 9 2007.Google Scholar
Cross Ref
- P. Battigalli and M. Siniscalchi. Hierarchies of conditional beliefs and interactive epistemology in dynamic games. Journal of Economic Theory, 88:188--230, 4 1999.Google ScholarCross Ref
- E. Dekel, B. L. Lipman, and A. Rustichini. Standard state-space models preclude unawareness. Econometrica, 66(1):159--173, 1 1998.Google ScholarCross Ref
- R. Fagin and J. Y. Halpern. Belief, awareness and limited reasoning. Artificial Intelligence, 34:39--76, 1988. Google ScholarDigital Library
- J. Y. Halpern. Alternative semantics for unawareness. Games and Economic Behavior, 37:321--339, 2001.Google ScholarCross Ref
- J. Y. Halpern and L. C. Rêgo. Interactive unawareness revisited. Games and Economic Behavior, 62:232--262, 2008.Google ScholarCross Ref
- J. Y. Halpern and L. C. Rêgo. Reasoning about knowledge of unawareness. Games and Economic Behavior, 67:503--525, 2009.Google ScholarCross Ref
- A. Heifetz, M. Meier, and B. K. Schipper. Interactive unawareness. Journal of Economic Theory, 130:78--94, 5 2006.Google ScholarCross Ref
- A. Heifetz, M. Meier, and B. K. Schipper. A canonical model for interactive unawareness. Games and Economic Behavior, 62:304--324, 2008.Google ScholarCross Ref
- J. Hintikka. Impossible possible worlds vindicated. In P. R. Hintikka, Carlson and Saarinen, editors, Studies in linguistics and philosophy, volume 5, pages 367--379. Springer Netherlands, 1978.Google Scholar
- J. Li. Information structures with unawareness. Journal of Economic Theory, 144:977--993, 11 2009.Google ScholarCross Ref
- J. F. Mertens and S. Zamir. Formulation of bayesian analysis for games with incomplete information. International Journal of Game Theory, 14:1--29, 1 1985.Google ScholarDigital Library
- S. Modica and A. Rustichini. Unawareness and partitional information structures. Games and economic behavior, 27:265--298, 1999.Google Scholar
- V. Rantala. Quantified modal logic: Non-normal worlds and propositional attitudes. Studia Logica, 41:41--65, 1982. 10.1007/BF00373492.Google ScholarCross Ref
- B. C. Schipper. Awareness-dependent subjective expected utility. Working Paper 10--22, University of California Davis, Department of Economics, One Shields Avenue, Davis, CA 95616, 12 2010.Google Scholar
- G. Sillari. Models of awareness. In G. Bonanno, W. van der Hoek, and M. Wooldridge, editors, LOFT06: Proceedings, pages 209--219. University of Liverpool, 2006.Google Scholar
- G. Sillari. Quantified logic of awareness and impossible possible worlds. The Review of Symbolic Logic, 1(4):1--16, 12 2008.Google ScholarCross Ref
- H. Wansing. A general possible worlds framework for reasoning about knowledge and belief. Studia Logica, 49:523--539, 1990. 10.1007/BF00370163.Google ScholarCross Ref
Index Terms
- Equivalence of the information structure with unawareness to the logic of awareness
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