Nested identification of subjective probabilities
AbstractThe 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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Bibliographic InfoPaper provided by Université catholique de Louvain, Département des Sciences Economiques in its series Discussion Papers (ECON - Département des Sciences Economiques) with number 2005061.
Date of creation: 01 Nov 2005
Date of revision:
Other versions of this item:
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-03-25 (All new papers)
- NEP-GTH-2006-03-25 (Game Theory)
- NEP-UPT-2006-03-25 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- R.J., AUMANN & Jacques-Henri, DREZE, 2005.
"Assessing Strategic Risk,"
Discussion Papers (ECON - DÃ©partement des Sciences Economiques)
2005020, Université catholique de Louvain, Département des Sciences Economiques.
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- AUMANN, Robert J. & DREZE, Jacques H., 2005. "Assessing strategic risk," CORE Discussion Papers 2005020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- R. J. Aumann & J. H. Dreze, 2004. "Assessing Strategic Risk," Discussion Paper Series dp361, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Juan Dubra & Fabio Maccheroni & Efe Oki, 2001.
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ICER Working Papers - Applied Mathematics Series
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- 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.
- Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
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