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Learning and Discovery

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  • Grant, Simon
  • Quiggin, John

Abstract

We formulate a dynamic framework for an individual decision-maker within which discovery of previously unconsidered propositions is possible. Using a standard game-theoretic representation of the state space as a tree structure generated by the actions of agents (including acts of nature), we show how unawareness of propositions can be represented by a coarsening of the state space. Furthermore we develop a semantics rich enough to describe the individual's awareness that currently undiscovered propositions may be discovered in the future. Introducing probability concepts, we derive a representation of ambiguity in terms of multiple priors, reflecting implicit beliefs about undiscovered proposition, and derive conditions for the special case in which standard Bayesian learning may be applied to a subset of unambiguous propositions. Finally, we consider exploration strategies appropriate to the context of discovery, comparing and contrasting them with learning strategies appropriate to the context of justification, and sketch applications to scientific research and entrepreneurship.

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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 151174.

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Date of creation: 27 Jul 2006
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Handle: RePEc:ags:uqsers:151174

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Related research

Keywords: Unawareness; bounded rationality; Institutional and Behavioral Economics; Public Economics; D80; D82;

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References

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  1. Chateauneuf, Alain & Eichberger, Jürgen & Grant, Simon, 2003. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Sonderforschungsbereich 504 Publications 03-10, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  2. Edi Karni, 2005. "Subjective Expected Utility Theory without States of the World," Economics Working Paper Archive 523, The Johns Hopkins University,Department of Economics.
  3. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  5. 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.
  6. Gilboa, Itzhak & Schmeidler, David, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 605-39, August.
  7. Sergiu Hart & Aviad Heifetz & Dov Samet, 1994. "'Knowing Whether', 'Knowing That' and the Cardinality of State Spaces," Game Theory and Information 9404002, EconWPA.
  8. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
  9. Karni, Edi & Safra, Zvi, 1990. "Behaviorally consistent optimal stopping rules," Journal of Economic Theory, Elsevier, vol. 51(2), pages 391-402, August.
  10. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  11. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
  12. 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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Citations

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Cited by:
  1. Grant, Simon & Kline, Jeff & Quiggin, John, 2006. "Lost in Translation: Honest Misunderstandings and Ex Post Disputes," Risk and Sustainable Management Group Working Papers 151177, University of Queensland, School of Economics.
  2. Simon Grant & John Quiggin, 2009. "Inductive reasoning about unawareness," Risk & Uncertainty Working Papers WPR09_1, Risk and Sustainable Management Group, University of Queensland.
  3. John Quiggin, . "Complexity, Climate Change and the Precautionary Principle," Climate Change Working Papers WPC07_3, Risk and Sustainable Management Group, University of Queensland.
  4. John Quiggin, 2009. "Risk Shifts in Australia: Implications of the Financial Crisis," Australian Public Policy Program Working Papers WPP09_1, Risk and Sustainable Management Group, University of Queensland.
  5. Halpern, Joseph Y. & Rêgo, Leandro C., 2009. "Reasoning about knowledge of unawareness," Games and Economic Behavior, Elsevier, vol. 67(2), pages 503-525, November.

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