Extending Blackwell and Lehmann: The Monotone Quasi-Garbling Order
58 Pages Posted: 30 Sep 2018
Date Written: September 2, 2018
How should one evaluate information in a monotone decision problem where a higher action is optimal for a higher signal realization? As a criterion for comparing information structures in such environments, I develop a condition called monotone quasi-garbling meaning that an information structure is obtained by adding reversely monotone noise to another. This new criterion generally permits more comparisons than the garbling condition by Blackwell [1951, 1953] and the effectiveness condition by Lehmann . For a general class of monotone decision problems, it is shown that monotone quasi-garbling is a sufficient condition for decision makers to get a higher ex-ante expected payoff. To illustrate, I apply the result to an optimal insurance problem and to a nonlinear monopoly pricing problem.
Keywords: Information, monotonicity, Blackwell condition, Lehmnann condition, optimal insurance, nonlinear pricing
JEL Classification: C44, C60, D81, D86
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