Lecture04-2004 - Savage State-Dependent Expected Utility...

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Savage State-Dependent Expected Utility Lecture IV I. Savage’s state dependent expected utility A. Savage’s subjective expected utility theory takes as the object of choice state dependent outcomes. () 11 1 11 xu x 12 2 12 x 13 3 13 x 14 4 14 x 15 5 15 x 21 1 21 x 22 2 22 x 23 3 23 x 24 4 24 x 25 5 25 x Security 1 Security 2 B. Writing the expected utility of the gamble out, we have () ( ) () ( ) 55 11 2 2 ii i i p iu x == ∑∑ 1. What is changing? The probability or the states? 2. Savage proved a similar result to the von Neumann-Morgenstern model–if agents’ preferences obey certain axioms they have an expected utlity representation through both the probabilities of each outcome and the utility function. 3. Specifically, the probabilities in the expected value framework may be endogenous. II. Axiomatization of State–Dependent Expected Utility A. Start with some notation. 1. In the state–preference format we speak of the utility function “mapping” from state-space into preferences: :
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Lecture04-2004 - Savage State-Dependent Expected Utility...

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