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Learning and Discovery

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  • Simon Grant

    ()
    (Department of Economics, Rice University)

  • John Quiggin

    ()
    (Department of Economics, University of Queensland)

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 Risk and Sustainable Management Group, University of Queensland in its series Risk & Uncertainty Working Papers with number WP7R05.

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Date of creation: Jul 2005
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Handle: RePEc:rsm:riskun:r05_7

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References

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  1. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  2. Karni, E. & Safra, Z., 1988. "Behaviorally Consistent Optimal Stopping Rules," Papers 9-88, Tel Aviv.
  3. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
  4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  5. Karni, Edi, 2006. "Subjective expected utility theory without states of the world," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 325-342, June.
  6. Sergiu Hart & Aviad Heifetz & Dov Samet, 1994. "'Knowing Whether', 'Knowing That' and the Cardinality of State Spaces," Game Theory and Information 9404002, EconWPA.
  7. Grant, Simon & Chateauneuf, A. & Eichberger, J., 2002. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Working Papers 2002-10, Rice University, Department of Economics.
  8. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  9. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
  11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  12. 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.
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Cited by:
  1. Quiggin, John, 2008. "Risk Shifts in Australia: Implications of the Financial Crisis," Risk and Sustainable Management Group Working Papers 151520, University of Queensland, School of Economics.
  2. Simon Grant & Jeff Kline & John Quiggin, 2006. "Lost in Translation: Honest Misunderstandings and Ex Post Disputes," Risk & Uncertainty Working Papers WP3R06, Risk and Sustainable Management Group, University of Queensland.
  3. Grant, Simon & Quiggin, John, 2012. "Inductive Reasoning About Unwareness," Risk and Sustainable Management Group Working Papers 151202, University of Queensland, School of Economics.
  4. John Quiggin, . "Complexity, Climate Change and the Precautionary Principle," Climate Change Working Papers WPC07_3, 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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