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.
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.
We introduce an innovation game in which two firms dynamically allocate resources across two distinct research and development (R&D) paths: (i) developing an innovative product with the currently available technology; (ii) conducting research to discover a faster technology for posterior development. Firms' optimal R&D strategies depend on the information about their rivals' progress. This creates an incentive for firms to conceal their technological discoveries, thereby slowing down the overall pace of social innovation.
formerly circulated under the title "The Direct vs. the Sequential Approach in Project Management" [this version]
I study a dynamic principal-agent problem where there are two routes of completing a project: directly attacking it or splitting it into two subprojects. When the project is split, the principal can better monitor the agent by verifying the completion of the first subproject. However, the inflexible nature of this approach may generate inefficiencies. To mitigate moral hazard, the principal needs to commit to a deadline, which also affects her choice of project management strategy. The optimal contract is determined by the interplay of these three factors: monitoring, efficiency, and an endogenous deadline.