Comparing information in general monotone decision problems

I study the value of information in monotone decision problems with potentially multidimensional action spaces. As a criterion for comparing information structures, I develop a condition called monotone quasi-garbling, which involves adding reversely monotone noise to an existing information structure. Specifically, this noise is more likely to return a higher signal in a lower state and a lower signal in a higher state. I show that monotone quasi-garbling is a necessary and sufficient condition for decision makers to obtain a higher ex-ante expected payoff. This new criterion refines the garbling condition by Blackwell (1951, 1953) and is equivalent to the accuracy condition by Lehmann (1988) under the monotone likelihood ratio property. To illustrate, I apply the result to problems in nonlinear monopoly pricing and optimal insurance.