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Nested identification of subjective probabilities

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  • Jacques Dreze

Abstract

The theory of games against nature relies on complete preferences among all conceivable acts, i.e. among all potential assignments of consequeces to states of nature (case 1). Yet most decision problems call for choosing an element from a limited set of acts. And in games of strategy, the set of strategies available to a player is givent and not amenable to artificial extensions. In “Assessing Strategic Risk”,(ECON DP 2005-20) R.J. Aumann and J.H. Drèze extend the basic result of decision theory (maximisation of subjectvely expected utility) to situations where preferences are defined only for a given set of acts, and for lotteries among these and sure consequences (case 2). In this paper, we provide a similar extension for two other situations : those where only the set of optimal elements from a given set of acts is known (case 3); and those where only a single optimal act is known (case 4). To these four cases correspond four nested sets of admissible subjective probabilities over the states or the opponent’s strategies, namely a singleton in case 1 and increasing sets in cases 2-4. The results for case 3 and 4 also define the extent to which subjective probabilities must be specified in order to solve a given decision problem or play a given name.
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Suggested Citation

  • Jacques Dreze, 2012. "Nested identification of subjective probabilities," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 259-271, March.
    • Handle: RePEc:spr:series:v:3:y:2012:i:1:p:259-271
    DOI: 10.1007/s13209-011-0049-4
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    References listed on IDEAS

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    1. R. J. Aumann & J. H. Dreze, 2009. "Assessing Strategic Risk," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 1-16, February.
    2. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    3. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
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    Keywords

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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