Optimal and Myopic Information Acquisition

We consider the problem of optimal dynamic information acquisition from many correlated information sources. Each period, the decision-maker jointly takes an action and allocates a fixed number of observations across the available sources. His payoff depends on the actions taken and on an unknown state. In the canonical setting of jointly normal information sources, we show that the optimal dynamic information acquisition rule proceeds myopically after finitely many periods. If signals are acquired in large blocks each period, then the optimal rule turns out to be myopic from period 1. These results demonstrate the possibility of robust and "simple" optimal information acquisition, and simplify the analysis of dynamic information acquisition in a widely used informational environment

Bayesian Comparative Statics

We study how information affects equilibria and welfare in games. For an agent, more precise information about an unknown state of the world leads to a mean-preserving spread of beliefs. We provide necessary and sufficient conditions to obtain either a non-increasing-mean or a non-decreasing-mean spread of actions whenever information precision increases for at least one agent. We apply our Bayesian comparative statics framework to study informational externalities in strategic environments. In persuasion games, we derive sufficient conditions that lead to extremal disclosure of information. In oligopolistic markets, we characterize the incentives of firms to share information. In macroeconomic models, we show that information not only drives the amplitude of business cycles but also affects aggregate output. Finally, in a novel application, we compare the demand for information in covert and overt information acquisition games

Endogenous Public Information and Welfare

This paper performs a welfare analysis of economies with private information when public information is endogenously generated and agents can condition on noisy public statistics in the rational expectations tradition. Equilibrium is not (restricted) efficient even when feasible allocations share similar properties to the market context (e.g., linear in information). The reason is that the market in general does not internalize the informational externality when public statistics (e.g., prices) convey information and does not balance optimally non-fundamental volatility and the dispersion of actions. Under strategic substitutability, equilibrium prices will tend to convey too little information when the “informational” role of prices prevails over its “index of scarcity” role and too much information in the opposite case. Under strategic complementarity, prices always convey too little information. The welfare loss at the market solution may be increasing in the precision of private information. These results extend to the internal efficiency benchmark (accounting only for the collective welfare of the active players). Received results—on the relative weights placed by agents on private and public information, when the latter is exogenous—may be overturned.information externality, strategic complementarity and substitutability, asymmetric information, excess volatility, team solution, rational expectations, behavioral traders

Complementarities in information acquisition with short-term trades

In a financial market where agents trade for short-term profit and where news can increase the uncertainty of the public belief, there are strategic complementarities in the acquisition of private information and, if the cost of information is sufficiently small, a continuum of equilibrium strategies. Imperfect observation of past prices reduces the continuum of Nash equilibria to a Strongly Rational-Expectations Equilibrium. In that equilibrium, there are two sharply different regimes for the evolution of the price, the volume of trade, and information acquisition.Endogenous information, short-term gain, microstructure, strategic complementarity, multiple equilibria, Strongly Rational-Expectations Equilibrium, trading frenzies

Public and Private Learning from Prices, Strategic Substitutability and Complementarity, and Equilibrium Multiplicity

We study a general static noisy rational expectations model, where investors have private information about asset payoffs, with common and private components, and about their own exposure to an aggregate risk factor, and derive conditions for existence and uniqueness (or multiplicity) of equilibria. We find that a main driver of the characterization of equilibria is whether the actions of investors are strategic substitutes or complements. This latter property in turn is driven by the strength of a private learning channel from prices, arising from the multidimensional sources of asymmetric information, in relation to the usual public learning channel. When the private learning channel is strong (weak) in relation to the public we have strong (weak) strategic complementarity in actions and potentially multiple (unique) equilibria. The results enable a precise characterization of whether information acquisition decisions are strategic substitutes or complements. We find that the strategic substitutability in information acquisition result obtained in Grossman and Stiglitz (1980) is robust.rational expectations equilibrium, strategic complementarity, multiplicity of equilibria, asymmetric information, risk exposure, bedging, supply information

Measuring Agents' Reaction to Private and Public Information in Games with Strategic Complementarities

In games with strategic complementarities, public information about the state of the world has a larger impact on equilibrium actions than private information of the same precision, because the former is more informative about the likely behavior of others. This may lead to welfare-reducing ‘overreactions’ to public signals. We present an experiment based on a game of Morris and Shin (2002), in which agents’ optimal actions are a weighted average of the fundamental state and their expectations of other agents’ actions. We measure the responses to public and private signals and find that, on average, subjects put a larger weight on the public signal. However, the weight is smaller than in equilibrium and closer to level-2 reasoning. Stated second order beliefs indicate that subjects underestimate the information contained in public signals about other players’ beliefs, but this can account only for a part of the observed deviation of behavior from equilibrium. In the extreme case of a pure coordination game, subjects still use their private signals, preventing full coordination. Reconsidering the welfare effects of public and private information theoretically, we find for level-2 reasoning that increasing precision of public signals always raises expected welfare, while increasing precision of private signals may reduce expected welfare if coordination is socially desirable.coordination games, strategic uncertainty, private information, public information, higher-order beliefs, levels of reasoning

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Liquidity runs with endogenous information acquisition

This paper discusses a liquidity run model where investors optimally decide whether or not to acquire private information. This endogenizes the dichotomy "private information/no private information". The price of the information makes the equilibrium partitioning of the fundamentals two dimensional. For intermediate fundamentals multiplicity can be eliminated by the private information that investors can have. The dichotomy represents the information structures for low and high prices respectively. However, it presents a distorted view for intermediate prices and fundamentals for which unique equilibria without private information can occur. These results are preserved if the quality of the information is endogenized.Bank runs, information acquisition, coordination games