A Smooth Model of Decision Making Under Ambiguity

A Smooth Model of Decision Making Under Ambiguity

September 2002 | Peter Klibanoff, Massimo Marinacci, Sujoy Mukerji
This paper presents a model of decision making under ambiguity, where a decision maker prefers act f to act g if and only if the expected value of a transformation of the expected utility of f is greater than that of g. The model separates ambiguity, defined as the decision maker's subjective uncertainty about relevant probabilities, from ambiguity attitude, which reflects the decision maker's preferences towards uncertainty. The model shows that risk attitudes are determined by the shape of the von Neumann-Morgenstern utility function, while ambiguity attitudes are determined by the shape of the transformation function. The model allows for smooth, rather than kinked, indifference curves, leading to different behavior and improved tractability. The model is distinct from other models in the literature on ambiguity, as it allows for a clear separation between subjective beliefs and ambiguity attitude. The model is also shown to be related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). The model is particularly useful in economic modeling involving comparative statics and ambiguity, as it allows for a clear separation of an agent's subjective uncertainty from his attitude towards that uncertainty. The model is shown to be able to capture ambiguity aversion, which is defined as an aversion to mean preserving spreads in the distribution of expected utility values. The model is also shown to be able to capture ambiguity neutrality, where the decision maker is indifferent to the spread in the distribution of expected utility values. The model is further shown to be able to capture ambiguity love, where the decision maker prefers mean preserving spreads in the distribution of expected utility values. The model is also shown to be able to capture the behavior observed in the Ellsberg paradox, where a decision maker prefers an act that is more certain in its outcome. The model is shown to be able to capture the behavior observed in the example of expert opinion, where different experts may report different probability numbers. The model is also shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecast the realization of an observable variable. The model is shown to be able to capture the behavior observed in the example of a monetary policy maker setting policy on the basis of a model which, given parameters, solves to yield a probability distribution on a set of macroeconomic variables of interest. The model is shown to be able to capture the behavior observed in the example of a decision maker in charge of policy whose impact is contingent on long term realizations of environmental/climatic variables. The model is shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecast the realization of an observable variable. The model is shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecast the realization of an observable variable. The model is shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecastThis paper presents a model of decision making under ambiguity, where a decision maker prefers act f to act g if and only if the expected value of a transformation of the expected utility of f is greater than that of g. The model separates ambiguity, defined as the decision maker's subjective uncertainty about relevant probabilities, from ambiguity attitude, which reflects the decision maker's preferences towards uncertainty. The model shows that risk attitudes are determined by the shape of the von Neumann-Morgenstern utility function, while ambiguity attitudes are determined by the shape of the transformation function. The model allows for smooth, rather than kinked, indifference curves, leading to different behavior and improved tractability. The model is distinct from other models in the literature on ambiguity, as it allows for a clear separation between subjective beliefs and ambiguity attitude. The model is also shown to be related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). The model is particularly useful in economic modeling involving comparative statics and ambiguity, as it allows for a clear separation of an agent's subjective uncertainty from his attitude towards that uncertainty. The model is shown to be able to capture ambiguity aversion, which is defined as an aversion to mean preserving spreads in the distribution of expected utility values. The model is also shown to be able to capture ambiguity neutrality, where the decision maker is indifferent to the spread in the distribution of expected utility values. The model is further shown to be able to capture ambiguity love, where the decision maker prefers mean preserving spreads in the distribution of expected utility values. The model is also shown to be able to capture the behavior observed in the Ellsberg paradox, where a decision maker prefers an act that is more certain in its outcome. The model is shown to be able to capture the behavior observed in the example of expert opinion, where different experts may report different probability numbers. The model is also shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecast the realization of an observable variable. The model is shown to be able to capture the behavior observed in the example of a monetary policy maker setting policy on the basis of a model which, given parameters, solves to yield a probability distribution on a set of macroeconomic variables of interest. The model is shown to be able to capture the behavior observed in the example of a decision maker in charge of policy whose impact is contingent on long term realizations of environmental/climatic variables. The model is shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecast the realization of an observable variable. The model is shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecast the realization of an observable variable. The model is shown to be able to capture the behavior observed in the example of a decision maker applying a model to forecast
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