The Value Of Information In Monotone Decision Problems

Central European Journal of Economic Modelling and Econometrics, 2015

Various approaches have been introduced over the years to evaluate information in the expected utility framework. This paper analyzes the relationship between the degree of risk aversion and the selling price of information in a lottery setting with two actions. We show that the initial decision on the lottery as well as the attitude of the decision maker towards risk as a function of the initial wealth level are critical to characterizing this relationship. When the initial decision is to reject, a non-decreasingly risk averse decision maker asks for a higher selling price as he gets less risk averse. Conversely, when the initial decision is to accept, non-increasingly risk averse decision makers ask a higher selling price as they get more risk averse if information is collected on bounded lotteries. We also show that the assumption of the lower bound for lotteries can be relaxed for the quadratic utility family.

High Frequency, 2019

This paper treats the decision problem related to theobservation of a Markov process by decision makers. The informationdelivered to the players is based on the aggregation of thehigh-frequency data by some functions. Admissible strategies arestopping moments related to the available information. The paymentsare defined by the state at the time of stopping. The players' decision to stop has various effects which depend on the decisionmakers' type. The type β player's stopping decision assignsthe state of the process with chance β, and it offers thisstate to the opponent with probability 1 −. The knowledgeabout the type of the players is not public and in this way, thepayers have also different information. The details of thedescription allow to formulate the problem as a Bayesian game withsets of strategies based on the stopping times. It is an extensionof Dynkin's game related to the observation of a Markov process withthe random assignment mechanism of states to the players. Some examples related to the best choice problem (BCP) are analyzed.

Journal of Economic Dynamics and Control, 1997

We generalize the economic decision problem considered by in which a decision-maker chooses an action after observing a signal correlated to the state of nature. Unlike Blackwell's case where the feasible set is fixed, in our framework the feasible set of actions depends on the signal and the information system. We argue that such a framework has more significance to economic models. As was demonstrated by Hirshleifer (1971) in such cases, contrary to Blackwell's well-known result. more information may be disadvantageous.

Theory and Decision, 2007

It is not unusual in real-life that one has to choose among finitely many alternatives when the merit of each alternative is not perfectly known. Instead of observing the actual utilities of the alternatives at hand, one typically observes more or less precise signals that are positively correlated with these utilities. In addition, the decision-maker may, at some cost or disutility of effort, choose to increase the precision of these signals, for example by way of a careful study or the hiring of expertise. We here develop a model of such decision problems. We begin by showing that a version of the monotone likelihood-ratio property is sufficient, and also essentially necessary, for the optimality of the heuristic decision rule to always choose the alternative with the highest signal. Second, we show that it is not always advantageous to face alternatives with higher utilities, a non-monotonicity result that holds even if the decision-maker optimally chooses the signal precision. We finally establish an operational first-order condition for the optimal precision level in a canonical class of decision-problems, and we show that the optimal precision level may be discontinuous in the precision cost.

This paper analyzes the information acquisition problem in a two-action lottery setting. Information is evaluated using the buying price approach. We investigate the relationship between risk aversion and the value of information in the case of two one-switch utility function families: sumex, and linear plus exponential utility. We derive conditions under which there exists a monotonic relationship between the decision maker’s risk tolerance and the value of information.

Automation and Remote Control, 2017

This paper suggests two approaches to the construction of a two-player game of best choice under incomplete information with the choice priority of one player and the equal weights of both players. We consider a sequence of independent identically distributed random variables (x i , y i), i = 1. .. , n, which represent the quality of incoming objects. The first component is announced to the players and the second component is hidden. Each player chooses an object based on the information available. The winner is the player whose object has a greater sum of the quality components than the opponent's object. We derive the optimal threshold strategies and compare them for both approaches.

Journal of Mathematical Economics, 2004

We develop an axiomatic approach to decision under uncertainty that explicitly takes into account the information available to the decision maker. The information is described by a set of priors and a reference prior. We define a notion of imprecision for this informational setting and show that a decision maker who is averse to information imprecision maximizes the minimum expected utility computed with respect to a subset of the set of initially given priors. The extent to which this set is reduced can be seen as a measure of imprecision aversion. This approach thus allows a lot of flexibility in modelling the decision maker attitude towards imprecision. In contrast, applying Gilboa and Schmeidler (1989) maxmin criterion to the initial set of priors amounts to assuming extreme pessimism. We thank M. Cohen, J.Y. Jaffray, M. Scarsini and B. Walliser for useful discussions and comments. The comments of a referee were very helpful to clarify the exposition of the paper. Financial support from the French Ministry of Research (Action concertée incitative) is gratefully acknowledged.

The Japanese Economic Review, 2005

We present a model of incomplete information games, where each player is endowed with a set of priors. Upon arrival of private information, it is assumed that each player "updates" his set of priors to a set of posterior beliefs, and then evaluates his actions by the most pessimistic posterior beliefs. So each player's preferences may exhibit aversion to ambiguity or uncertainty. We define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players' views on uncertainty about the environment affect the strategic outcomes. JEL Classification Numbers: C72, D81, D82.

AIP Conference Proceedings, 2004

Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions [1]. Based on this analogy, a utility density function can de defined as the derivative of a normalized utility function. A utility density function is non-negative and integrates to unity. These two properties of a utility density function form the basis of a correspondence between utility and probability, which allows the application of many tools from one domain to the other. For example, La Place's principle of insufficient reason translates to a principle of insufficient preference. The notion of uninformative priors translates to uninformative utility functions about a decision maker's preferences. A natural application of this analogy is a maximum entropy principle to assign maximum entropy utility values. Maximum entropy utility interprets many of the common utility functions based on the preference information needed for their assignment, and helps assign utility values based on partial preference information. This paper reviews maximum entropy utility, provides axiomatic justification for its use, and introduces further results that stem from the duality between probability and utility, such as joint utility density functions, utility inference, and the notion of mutual preference.

2005

Abstract We present a discussion of the concept of information in Economics. We begin by presenting the prevalent model, closely associated with the Maximization of Expected Utility hypothesis. While it has proved to be useful in many ways, it also exhibits many shortcomings, which we illustrate with some examples.