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

Firms racing to innovate often achieve interim technological breakthroughs that can accelerate final innovation. When these advances are acquired privately, firms face a choice: disclose the discovery or keep it secret. This paper studies how this tradeoff is shaped by the race structure and the intellectual property system. We develop a dynamic model where firms allocate resources between direct development and research for new technology. Our results show that excessively strong rewards from winning the race and strong prior-use protections can discourage disclosure, thereby impeding knowledge spillovers and slowing the social speed of innovation. 

We study the monotonicity of information costs: more informative experiments must be more costly. As criteria for informativeness, we consider the standard information orders introduced by Blackwell (1951, 1953) and Lehmann (1988). We provide simple necessary and sufficient conditions for a cost function to be monotone with respect to each order, grounded in their garbling characterizations. Finally, we examine several well-known cost functions from the literature through the lens of these conditions.