The value of information for auctioneers

An auctioneer wants to sell an indivisible object to one of multiple bidders, who have private information about their valuations of the object. A bidder's information structure determines the accuracy with which the bidder knows her private valuation. The main result of the paper is that the auctioneer's revenue is a convex function of bidders' information structures. One implication is that assigning asymmetric information structures instead of symmetric information structures to bidders is always revenue-enhancing. This paper generalizes a result of Bergemann and Pesendorfer [D. Bergemann, M. Pesendorfer, Information structures in optimal auctions, J. Econ. Theory 137 (2007) 580–609], who show that revenue-maximizing information structures are asymmetric.     

The social value of public information with costly information acquisition

In a beauty contest framework, public authorities decide the accuracy of public information evaluating how it affects individual actions and private information acquisition. More precise public information increases welfare whenever its marginal cost does not exceed that of private information.     

Recursive utility and preferences for information

Summary. This paper presents an axiomatic foundation for recursive utility that captures the role of the timing of resolution of uncertainty without relying on exogenously specified objective beliefs. Two main representation results are proved. In the first one, future utility enters the recursion through the type of general aggregators considered in Skiadas (1997a), and as a result the formulation is purely ordinal and free of any probabilities. In the second representation these aggregators are conditional expectations relative to subjective beliefs. A new recursive representation incorporating disappointment aversion is also suggested. The main methodological innovation of the paper derives from the fact that the basic objects of choice are taken to be pairs of state-contingent consumption plans and information filtrations, rather than the temporal (objective) lotteries of the existing literature. It is shown that this approach has the additional benefit of being directly applicable to the continuous-time version of recursive utility developed by Duffie and Epstein (1992). Received: February 18, 1997; revised version: July 18, 1997     

The value of a stochastic information structure

Upon observing a signal, a Bayesian decision maker updates her probability distribution over the state space, chooses an action, and receives a payoff that depends on the state and the action taken. An information structure determines the set of possible signals and the probability of each signal given a state. For a fixed decision problem, the value of an information structure is the maximal expected utility that the decision maker can get when the observed signals are governed by this structure. Thus, every decision problem induces a preference order over information structures according to their value. We characterize preference orders that can be obtained in this way. We also characterize the functions defined over information structures that measure their value.     

Monetary policy with uncertain central bank preferences

This paper considers monetary policy when policy makers’ preferences are private information. I show that in the first period of a two-period term, all policy makers but the least inflation averse inflate less - but respond more to shocks - than if there were no private information. Moderately inflation-averse policy makers may reduce their inflation most. A tendency toward increased conservatism in their second period increases inflation in the first. With T<∞ period terms, inflation depends solely on the policy maker's time left in office. With unchanging preferences and no discounting, inflation is lower the longer he has left.     

The social value of public information with convex costs of information acquisition

In a beauty contest framework, welfare can decrease with public information if the precision of private information is exogenous, whereas welfare necessarily increases with public information if the precision is endogenous with linear costs of information acquisition. The purpose of this paper is to reconcile these results by considering nonlinear costs of information acquisition. The main result of this paper is a necessary and sufficient condition for welfare to increase with public information. Using it, we show that costs of information acquisition are linear if and only if welfare necessarily increases with public information. Thus, welfare can decrease with public information for any strictly convex costs. This is because convex costs mitigate the so-called crowding-out effect of public information on private information, thereby making the social value of public information with endogenous precision closer to that with exogenous precision.     

The value of information in asymmetric all-pay auctions

This note analyzes a two-player all-pay auction with incomplete information. More precisely, one bidder is uncertain about the size of the initial advantage of his rival modeled as a head start in the auction.I derive the unique Bayesian Nash equilibrium outcome for a large class of cumulative distribution functions of the head start. The stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. I identify why my results for an uncertain head start differ qualitatively from uncertainty about a cost function or a valuation.     

The social value of information on product quality

In the context of a seller with private information about product quality, I show that revelation of information on product quality is sometimes, but not always, socially valuable. When it is socially valuable, there is generally a tradeoff between the acquisition and revelation of finer, but more costly information and the revelation of coarser, but less costly information. As a result, it can be socially optimal for firms to reveal only coarse private information.     

The value of information in monotone decision problems

We study the information preferences and information demand of decision-makers facing uncertainty. We focus on monotone decision problems in which the posterior beliefs induced by the decision-maker’s information can be ordered so that higher actions are chosen in response to higher signal realizations. We provide necessary and sufficient conditions for decision makers with different classes of payoff functions to prefer one information structure to another. We also provide conditions under which two decision-makers in a given class can be ranked in terms of their information demand. Applications and examples are given.     

The changing nature of the real exchange rate: The role of central bank preferences

We investigate the sources of real exchange rate fluctuations. We do so, first, in the context of a DSGE model that explicitly considers the central bank's preferences. Then we estimate SVAR models, where shocks are identified by sign restrictions derived from the DSGE model. We perform this exercise for twelve countries, nine of which have adopted inflation targeting during the period analyzed. In sharp contrast to the previous evidence in the literature, we find that exchange rate (country risk premium) shocks have become the main drivers of real exchange rate dynamics, while real shocks play a less important role. Evidence from the DSGE model reveals that, as the central bank becomes more averse to inflation movements, and cares less about nominal exchange rate fluctuations, the impact of nominal shocks on the real exchange rate tends to increase, while the impact of real shocks decreases. Our results suggest that the adoption of inflation targeting, along with a floating exchange rate, contributes to a shift in the relative importance of demand and country risk premium shocks in determining the RER.     

The value of public information in a Cournot duopoly

We derive alternative sufficient conditions for the value of public information to be either positive or negative in a Cournot duopoly where firms technology exhibits constant returns to scale.     

The value of information in a simple duopoly model

This paper is concerned with the evaluation of information in a duopoly model in which the cost functions are subject to uncertainty. It explores how changes in information about the costs available to either firm affects the welfare of both firms along with the welfare of consumers. By comparing the ten possible types of information structures, it is shown that information may be detrimental, that improved information for one firm may or may not benefit the other firm and/or the consumer, and that it may be more desirable for a firm to gather information about the rival's cost rather than its own. All of these “irregular” results depend on the values of the variances of the costs and their correlation coefficient.     

The value of information in oligopoly with demand uncertainty

This paper discusses the value of information in supermodular and submodular games, using a simple duopoly model where the level of demand is uncertain. It is shown that the value of information issuperadditive (resp.,subadditive) between players if the game issupermodular (resp.,submodular). For example, in a Bertrand (resp., Cournot) market with (possibly imperfect) substitute products, one firm's information acquisition increases (resp., decreases) the other firm's incentive to acquire the same information. Furthermore, when the game is either supermodular or submodular, the value of information is higher when the player isexpected to be informed according to the opponent's belief than when the player is expected to be uninformed; this result is reversed when the game has asymmetric modularity (i.e., one player's action is substitutional to the other's, and the latter's action is complemental to the former's). These qualitative observations have a potential to be applied to a larger class of games with uncertainty where payoffs are smooth (e.g., twice continuously differentiable) in actions and states.     

Existence and fairness of value allocation without convex preferences

Shafer (Econometrica, 48 (1980), 467–476) proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations by introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations may discriminate in favor of or against a coalition of agents.     

Regulating a manager whose empire-building preferences are private information

We obtain the optimal contract for the government (principal) to regulate a manager (agent) who has a taste for empire-building that is his/her private information. This taste for empire-building is modeled as a utility premium that is proportional to the difference between the contracted output and a reference output. We find that output is distorted upward when the manager’s taste for running large firms is weak, downward when it is strong, and equals a reference output when it is intermediate (in this case, the participation constraint is binding). We also obtain an endogenous reference output (equal to the expected output, which depends on the reference output), and find that the response of output to cost is null in the short-run (in which the reference output is fixed), whenever the manager’s type is in the intermediate range, and negative in the long-run (after the adjustment of the reference output to equal expected output).     

Assessing information provision and respondent involvement effects on preferences

We develop a test of the effect of information and respondent involvement on preferences for passive-use values using three treatments. Individuals from a rural community participated in one of three groups, each with a different level of involvement in the valuation assessment. The first group was highly involved, attending three meetings which allowed for information acquisition and preference construction. The second group was involved in a single meeting, and the third group was minimally involved through telephone contact and the completion of a mail administered survey. The hypothesis examined was that the degree of involvement in the exercise would affect the magnitude and consistency of preferences across the groups. The hypothesis that the preferences differ was not accepted. Furthermore, the hypothesis that variances in preferences would be higher in less involved groups was also rejected. While the analysis is based on relatively small samples the findings suggest caution in claiming that increasing degrees of respondent involvement improve economic measures of trade-offs.     

Social value of public information re-examined

As an extension of Hirshleifer's horse race example into a competitive exchange market framework, this paper quantitatively re-examines the condition under which social value of public information can be positive. For a prototype economy of two risk averse traders, we prove that their discordance of beliefs makes the social value of a certain class of inconclusive information either positive or negative depending on whether their endowments are or are not predominantly associated with states they regard as more probable, whereas it has been known that information acquisition is always socially wasteful under concordant beliefs.