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

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Savage State-Dependent Expected Utility Lecture IV
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Savage’s state dependent expected utility Savage’s subjective expected utility theory takes as the object of choice state dependent outcomes.
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( 29 11 1 11 x u x u ( 29 12 2 12 x u x u ( 29 13 3 13 x u x u ( 29 14 4 14 x u x u ( 29 15 5 15 x u x u ( 29 21 1 21 x u x u ( 29 22 2 22 x u x u ( 29 23 3 23 x u x u ( 29 24 4 24 x u x u ( 29 25 5 25 x u x u Security 1 Security 2
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Writing the expected utility of the gamble out, we have What is changing? The probability or the states? ( 29 ( 29 ( 29 ( 29 5 5 1 1 2 2 1 1 i i i i i i p i u x p i u x = =
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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. Specifically, the probabilities in the expected value framework may be endogenous.
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Dependent Expected Utility Start with some notation. In the state–preference format we speak of the
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Lecture04-2004 - Savage State-Dependent Expected Utility...

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