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. 

Communication is secret if a message is independent of the state; however, the receiver's subsequent action may still reveal that she has acted on hidden information. This paper studies when secret communication can also provide plausible deniability: under single-crossing preferences, every action induced by the sender's message must be rationalizable using the receiver's baseline information alone. We characterize joint information structures that satisfy both secrecy and plausible deniability. We show that plausible deniability restricts communication exactly when the baseline message is directional---meaning its likelihood is monotone in the state. Combining this restriction with secrecy, we show that, for directional messages, frontier communication reveals at most whether the state lies above or below a cutoff. Finally, we identify conditions under which a greatest feasible communication structure exists and can be explicitly constructed. 

We study why organizations conduct interim performance reviews when monetary rewards are limited. An interim review creates incentive capacity by allowing future work and career opportunities to serve as rewards for past performance. Optimal review policies map a continuum of performance outcomes into a simple incentive ladder: termination, tough or easy continuation, and, for exceptional performance, an early maximal reward with no future work. Review can even sustain high effort when terminal compensation alone cannot. Its timing balances two forces: waiting improves the information revealed by performance, but leaves less future work available to motivate the agent.

We study the monotonicity of information measures, functions that assign a value to each statistical experiment, with respect to the Blackwell and Lehmann orders. We show that such monotonicity can be characterized by local, first-order conditions. Under natural invariance properties, a measure is Blackwell monotone if and only if it decreases in the direction of signal replacements, and Lehmann monotone if and only if it decreases in the direction of reverse signal replacements, which replace signals with higher ones only in low states or with lower ones only in high states. We translate both conditions into the space of posterior beliefs and apply them to likelihood-separable and posterior-separable measures, showing in particular that the entropy cost is Lehmann monotone. Among posterior-separable measures, we further identify a Lehmann monotone subclass, posterior-mean-ratio measures, that characterizes the Lehmann order.