Dietrich, Franz (2016): Savage's Theorem Under Changing Awareness.
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Abstract
This paper proposes a simple unified framework of choice under changing awareness, addressing both outcome awareness and (nature) state awareness, and both how fine and how exhaustive the awareness is. Six axioms characterize an (essentially unique) expectedutility rationalization of preferences, in which utilities and probabilities are revised according to three revision rules when awareness changes: (R1) utilities of unaffected outcomes are transformed affinely; (R2) probabilities of unaffected events are transformed proportionally; (R3) enough probabilities 'objectively' never change (they represent revealed objective risk). Savage's Theorem is a special case, obtained in the case of fully fixed awareness, as then our axioms reduce to Savage's axioms, while R1 and R2 hold trivially and R3 reduces to Savage's requirement of atomless probabilities. Rule R2 parallels Karni and Viero's (2013) 'reverse Bayesianism' and Ahn and Ergin's (2010) 'partitiondependence'. The theorem draws mathematically on Kopylov (2007), Niiniluoto (1972) and Wakker (1981).
Item Type:  MPRA Paper 

Original Title:  Savage's Theorem Under Changing Awareness 
Language:  English 
Keywords:  Decision under uncertainty, outcome unawareness versus state unawareness, nonfine versus nonexhaustive awareness, utility revision versus probability revision, small worlds versus grand worlds 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D80  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  80744 
Depositing User:  Franz Dietrich 
Date Deposited:  11 Aug 2017 16:53 
Last Modified:  11 Aug 2017 16:54 
References:  Ahn, D., Ergin, H. (2010) Framing Contingencies, Econometrica 78: 655695 Anscombe, F. J., Aumann, R. J. (1963) A Definition of Subjective Probability, Annals of Mathematical Statistics 34 (1): 199205 Bolker, E. (1966) Functions Resembling Quotients of Measures, Transactions of the American Mathematical Society 124: 292312 Dekel, E., Lipman, B. L., Rustichini, A. (1998) Standard statespace models preclude unawareness, Econometrica 66: 15973 Halpern, J. Y. (2001) Alternative Semantics for Unawareness, Games and Economic Behavior 37: 32139 Halpern, J. Y., Rego, L. C. (2008) Interactive Unawareness Revisited, Games and Economic Behavior 62: 23262 Heifetz, A., Meier, M., Schipper, B. (2006) Interactive unawareness, Journal of Economic Theory 130: 7894 Hill, B. (2010) Awareness Dynamics, Journal of Philosophical Logic 39: 11337 Jeffrey, R. C. (1983) The Logic of Decision, 2nd ed., Chicago: University of Chicago Press Karni, E., Schmeidler, D. (1991) Utility Theory with Uncertainty. In: Handbook of Mathematical Economics, Vol. 4, edited by Werner Hildenbrand and Hugo Sonnenschein, 17631831, New York: Elsevier Science Karni, E., Viero, M. (2013) Reverse Bayesianism: a choicebased theory of growing awareness, American Economic Review 103: 27902810 Karni, E., Viero, M. (2015) Awareness of unawareness: a theory of decision making in the face of ignorance, working paper, Johns Hopkins University Kochov, A. (2016) A behavioral definition of unforeseen contingencies, working paper, University of Rochester Kopylov, I. (2007) Subjective probabilities on "small" domains, Journal of Economic Theory 133: 236265 Niiniluoto, I. (1972) A note on fine and tight qualitative probabilities, Annals of Mathematical Statistics 43: 158191 Pivato, M., Vergopoulos, V. (2015) Categorical decision theory, working paper, University CergyPontoise Savage, L. J. (1954) The Foundations of Statistics, New York: Wiley Schipper, B. (2013) Awarenessdependent subjective expected utility, International Journal of Game Theory 42: 725753 Schmeidler, D,, Wakker, P. (1987) Expected Utility and Mathematical Expectation. In: The New Palgrave: A Dictionary of Economics, first edition, edited by J. Eatwell, M. Milgate, and P. Newman, New York: Macmillan Press Tversky, A., Koehler, D.J. (1994) Support theory: a nonextensional representation of subjective probability, Psychological Rev. 101: 54767 Wakker, P. (1981) Agreeing probability measures for comparative probability structures, Annals of Statistics 9: 65862 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/80744 
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