The work value of information

We present quantitative relations between work and information that are valid both for finite sized and internally correlated systems as well in the thermodynamical limit. We suggest work extraction should be viewed as a game where the amount of work an agent can extract depends on how well it can guess the micro-state of the system. In general it depends both on the agent's knowledge and risk-tolerance, because the agent can bet on facts that are not certain and thereby risk failure of the work extraction. We derive strikingly simple expressions for the extractable work in the extreme cases of effectively zero- and arbitrary risk tolerance respectively, thereby enveloping all cases. Our derivation makes a connection between heat engines and the smooth entropy approach. The latter has recently extended Shannon theory to encompass finite sized and internally correlated bit strings, and our analysis points the way to an analogous extension of statistical mechanics.Comment: 5 pages, 4 figure

The Value of Information Concealment

We consider a revenue optimizing seller selling a single item to a buyer, on whose private value the seller has a noisy signal. We show that, when the signal is kept private, arbitrarily more revenue could potentially be extracted than if the signal is leaked or revealed. We then show that, if the seller is not allowed to make payments to the buyer, the gap between the two is bounded by a multiplicative factor of 3, if the value distribution conditioning on each signal is regular. We give examples showing that both conditions are necessary for a constant bound to hold. We connect this scenario to multi-bidder single-item auctions where bidders' values are correlated. Similarly to the setting above, we show that the revenue of a Bayesian incentive compatible, ex post individually rational auction can be arbitrarily larger than that of a dominant strategy incentive compatible auction, whereas the two are no more than a factor of 5 apart if the auctioneer never pays the bidders and if each bidder's value conditioning on the others' is drawn according to a regular distribution. The upper bounds in both settings degrade gracefully when the distribution is a mixture of a small number of regular distributions

Value of Information in Feedback Control

In this article, we investigate the impact of information on networked control systems, and illustrate how to quantify a fundamental property of stochastic processes that can enrich our understanding about such systems. To that end, we develop a theoretical framework for the joint design of an event trigger and a controller in optimal event-triggered control. We cover two distinct information patterns: perfect information and imperfect information. In both cases, observations are available at the event trigger instantly, but are transmitted to the controller sporadically with one-step delay. For each information pattern, we characterize the optimal triggering policy and optimal control policy such that the corresponding policy profile represents a Nash equilibrium. Accordingly, we quantify the value of information $\operatorname{VoI}_k$ as the variation in the cost-to-go of the system given an observation at time $k$. Finally, we provide an algorithm for approximation of the value of information, and synthesize a closed-form suboptimal triggering policy with a performance guarantee that can readily be implemented

Positive value of information in games.

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments a la Blackwell.Information structures, value of information, Pareto optima.

The value of implementation and the value of information: combined and uneven development

<i>Aim</i>: In a budget-constrained health care system, the decision to invest in strategies to improve the implementation of cost-effective technologies must be made alongside decisions regarding investment in the technologies themselves and investment in further research. This article presents a single, unified framework that simultaneously addresses the problem of allocating funds between these separate but linked activities. <i>Methods</i>: The framework presents a simple 4-state world where both information and implementation can be either at the current level or "perfect". Through this framework, it is possible to determine the maximum return to further research and an upper bound on the value of adopting implementation strategies. The framework is illustrated through case studies of health care technologies selected from those previously considered by the UK National Institute for Health and Clinical Excellence (NICE). <i>Results</i>: Through the case studies, several key factors that influence the expected values of perfect information and perfect implementation are identified. These factors include the maximum acceptable cost-effectiveness ratio, the level of uncertainty surrounding the adoption decision, the expected net benefits associated with the technologies, the current level of implementation, and the size of the eligible population. <i>Conclusions</i>: Previous methods for valuing implementation strategies have not distinguished the value of efficacy research and the value of strategies to change the level of implementation. This framework demonstrates that the value of information and the value of implementation can be examined separately but simultaneously in a single framework. This can usefully inform policy decisions about investment in health care services, further research, and adopting implementation strategies that are likely to differ between technologies