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Learning and Discovery

  • Simon Grant

    ()

    (Department of Economics, Rice University)

  • John Quiggin

    ()

    (Department of Economics, University of Queensland)

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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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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  1. Gilboa, Itzhak & Schmeidler, David, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 605-39, August.
  2. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  3. HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004. "Interactive unawareness," CORE Discussion Papers 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  5. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
  6. Hart, Sergiu & Heifetz, Aviad & Samet, Dov, 1996. ""Knowing Whether," "Knowing That," and The Cardinality of State Spaces," Journal of Economic Theory, Elsevier, vol. 70(1), pages 249-256, July.
  7. 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.
  8. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
  9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  10. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  11. Karni, E. & Safra, Z., 1988. "Behaviorally Consistent Optimal Stopping Rules," Papers 9-88, Tel Aviv.
  12. Karni, Edi, 2006. "Subjective expected utility theory without states of the world," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 325-342, June.
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