Anticipated Utility and Rational Expectations as Approximations of Bayesian Decision Making
For a Markov decision problem in which unknown transition probabilities serve as hidden state variables, we study the quality of two approximations to the decision rule of a Bayesian who each period updates his subjective distribu- tion over the transition probabilities by Bayes’ law. The first is the usual ratio- nal expectations approximation that assumes that the decision maker knows the transition probabilities. The second approximation is a version of Kreps’ (1998) anticipated utility model in which decision makers update using Bayes’ law but optimize in a way that is myopic with respect to their updating of probabili- ties. For a range of consumption smoothing examples, the anticipated utility approximation outperforms the rational expectations approximation. The an- ticipated utility and Bayesian models augment market prices of risk relative to the rational expectations approximation.
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