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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
Date of revision:
Handle: RePEc:rsm:riskun:r05_7
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  1. Edi Karni, 2005. "Subjective Expected Utility Theory without States of the World," Economics Working Paper Archive 523, The Johns Hopkins University,Department of Economics.
  2. 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.
  3. Modica, Salvatore & Rustichini, Aldo, 1999. "Unawareness and Partitional Information Structures," Games and Economic Behavior, Elsevier, vol. 27(2), pages 265-298, May.
  4. 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.
  5. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  6. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
  7. repec:tpr:qjecon:v:110:y:1995:i:3:p:605-39 is not listed on IDEAS
  8. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
  9. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," Post-Print hal-00753144, HAL.
  10. Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
  11. Karni, Edi & Safra, Zvi, 1990. "Behaviorally consistent optimal stopping rules," Journal of Economic Theory, Elsevier, vol. 51(2), pages 391-402, August.
  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.
  13. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
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