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Inductive Reasoning About Unwareness

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  • Grant, Simon
  • Quiggin, John

Abstract

We develop a model of games with awareness that allows for differential levels of awareness. We show that, for the standard modal logical interpretations of belief and awareness, a player cannot believe there exist propositions of which he is unaware. Nevertheless, we argue that a boundedly rational individual may regard the possibility that there exist propositions of which she is unaware as being supported by inductive reasoning, based on past experience and consideration of the limited awareness of others. In this paper, we provide a formal representation of inductive reasoning in the context of a dynamic game with awareness. We show that, given differential awareness over time and between players, individuals can derive inductive support for propositions expressing their own unawareness.

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Bibliographic Info

Paper provided by University of Queensland, School of Economics in its series Risk and Sustainable Management Group Working Papers with number 151188.

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Date of creation: 16 Jun 2009
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Handle: RePEc:ags:uqsers:151188

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Keywords: Unawareness; bounded rationality; induction; Risk and Uncertainty; D80; D82;

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References

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  1. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
  2. Gollier, Christian & Jullien, Bruno & Treich, Nicolas, 2000. "Scientific progress and irreversibility: an economic interpretation of the 'Precautionary Principle'," Journal of Public Economics, Elsevier, vol. 75(2), pages 229-253, February.
  3. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  4. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
  5. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2009. "Dynamic Unawareness and Rationalizable Behavior," MPRA Paper 15058, University Library of Munich, Germany.
  6. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.
  7. Simon Grant & John Quiggin, 2008. "Bounded rationality and small worlds," Risk & Uncertainty Working Papers WPR08_2, Risk and Sustainable Management Group, University of Queensland.
  8. Grant, Simon & Quiggin, John, 2012. "Bounded Awareness, Heuristics and the Precautionary Principle," Risk and Sustainable Management Group Working Papers 151203, University of Queensland, School of Economics.
  9. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
  10. Simon Grant & John Quiggin, 2005. "Learning and Discovery," Risk & Uncertainty Working Papers WP7R05, Risk and Sustainable Management Group, University of Queensland.
  11. repec:ecl:ucdeco:09-10 is not listed on IDEAS
  12. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  13. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2005. "Interactive Unawareness," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 52, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  14. Leandro Rêgo & Joseph Halpern, 2012. "Generalized solution concepts in games with possibly unaware players," International Journal of Game Theory, Springer, vol. 41(1), pages 131-155, February.
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Citations

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Cited by:
  1. Edi Karni & Marie-Louise Vierø, 2014. "Awareness of Unawareness: A Theory of Decision Making in the Face of Ignorance," Working Papers 1322, Queen's University, Department of Economics.
  2. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
  3. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
  4. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer, vol. 42(3), pages 725-753, August.
  5. Grant, Simon & Kline, Jeff & Quiggin, John, 2012. "Differential awareness, ambiguity, and incomplete contracts: a model of contractual disputes," Risk and Sustainable Management Group Working Papers 151200, University of Queensland, School of Economics.
  6. Grant, Simon & Quiggin, John, 2013. "Bounded awareness, heuristics and the Precautionary Principle," Journal of Economic Behavior & Organization, Elsevier, vol. 93(C), pages 17-31.
  7. Quiggin, John, 2013. "The value of information and the value of awareness," Risk and Sustainable Management Group Working Papers 151207, University of Queensland, School of Economics.
  8. Burkhard Schipper & Hee Yeul Woo, 2014. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Working Papers 148, University of California, Davis, Department of Economics.
  9. 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.
  10. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 124, University of California, Davis, Department of Economics.
  11. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer, vol. 56(2), pages 219-249, June.
  12. Edi Karni & Marie-Louise Vier?, 2013. ""Reverse Bayesianism": A Choice-Based Theory of Growing Awareness," American Economic Review, American Economic Association, vol. 103(7), pages 2790-2810, December.
  13. Feinberg, Yossi, 2012. "Games with Unawareness," Research Papers 2122, Stanford University, Graduate School of Business.
  14. Oliver Walker, 2011. "Unawareness with ‘possible’ possible worlds," Grantham Research Institute on Climate Change and the Environment Working Papers 69, Grantham Research Institute on Climate Change and the Environment.

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