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Social and Behavioral Sciences Commons

Open Access. Powered by Scholars. Published by Universities.®

Economics

Yale University

2013

Bayes correlated equilibrium

Articles 1 - 9 of 9

Full-Text Articles in Social and Behavioral Sciences

Information And Volatility, Dirk Bergemann, Tibor Heumann, Stephen Morris Dec 2013

Information And Volatility, Dirk Bergemann, Tibor Heumann, Stephen Morris

Cowles Foundation Discussion Papers

In an economy of interacting agents with both idiosyncratic and aggregate shocks, we examine how the structure of private information influences aggregate volatility. The maximal aggregate volatility is attained in a noise free information structure in which the agents confound idiosyncratic and aggregate shocks, and display excess response to the aggregate shocks, as in Lucas [14]. For any given variance of aggregate shocks, the upper bound on aggregate volatility is linearly increasing in the variance of the idiosyncratic shocks. Our results hold in a setting of symmetric agents with linear best responses and normal uncertainty. We establish our results by …


Information And Volatility, Dirk Bergemann, Tibor Heumann, Stephen Morris Dec 2013

Information And Volatility, Dirk Bergemann, Tibor Heumann, Stephen Morris

Cowles Foundation Discussion Papers

In an economy of interacting agents with both idiosyncratic and aggregate shocks, we examine how the information structure determines aggregate volatility. We show that the maximal aggregate volatility is attained in a noise free information structure in which the agents confound idiosyncratic and common components of the payoff state, and display excess response to the common component, as in Lucas (1972). The upper bound on aggregate volatility is linearly increasing in the variance of idiosyncratic shocks, for any given variance of aggregate shocks. Our results hold in a setting of symmetric agents with linear best responses and normal uncertainty. We …


Information, Interdependence, And Interaction: Where Does The Volatility Come From?, Dirk Bergemann, Tibor Heumann, Stephen Morris Dec 2013

Information, Interdependence, And Interaction: Where Does The Volatility Come From?, Dirk Bergemann, Tibor Heumann, Stephen Morris

Cowles Foundation Discussion Papers

We analyze a class of games with interdependent values and linear best responses. The payoff uncertainty is described by a multivariate normal distribution that includes the pure common and pure private value environment as special cases. We characterize the set of joint distributions over actions and states that can arise as Bayes Nash equilibrium distributions under any multivariate normally distributed signals about the payoff states. We characterize maximum aggregate volatility for a given distribution of the payoff states. We show that the maximal aggregate volatility is attained in a noise-free equilibrium in which the agents confound idiosyncratic and common components …


Extremal Information Structures In The First Price Auction, Dirk Bergemann, Benjamin Brooks, Stephen Morris Nov 2013

Extremal Information Structures In The First Price Auction, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We study how the outcomes of a private-value first price auction can vary with bidders’ information, for a fixed distribution of private values. In a two bidder, two value, setting, we characterize all combinations of bidder surplus and revenue that can arise, and identify the information structure that minimizes revenue. The extremal information structure that minimizes revenue entails each bidder observing a noisy and correlated signal about the other bidder’s value. In the general environment with many bidders and many values, we characterize the minimum bidder surplus of each bidder and maximum revenue across all information structures. The extremal information …


Correlated Equilibrium And The Comparison Of Information Structures In Games, Dirk Bergemann, Stephen Morris Sep 2013

Correlated Equilibrium And The Comparison Of Information Structures In Games, Dirk Bergemann, Stephen Morris

Cowles Foundation Discussion Papers

A game of incomplete information can be decomposed into a basic game and an information structure. The basic game defines the set of actions, the set of payoff states the payoff functions and the common prior over the payoff states. The information structure refers to the signals that the players receive in the game. We characterize the set of outcomes that can arise in Bayes Nash equilibrium if players observe the given information structure but may also observe additional signals. The characterization corresponds to the set of (a version of) incomplete information correlated equilibria which we dub Bayes correlated equilibria. …


The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris May 2013

The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We analyze the welfare consequences of a monopolist having additional information about consumers’ tastes, beyond the prior distribution; the additional information can be used to charge different prices to different segments of the market, i.e., carry out “third degree price discrimination.” We show that the segmentation and pricing induced by the additional information can achieve every combination of consumer and producer surplus such that: (i) consumer surplus is non-negative, (ii) producer surplus is at least as high as profits under the uniform monopoly price, and (iii) total surplus does not exceed the efficient gains from trade. As well as characterizing …


The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris May 2013

The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We analyze the welfare consequences of a monopolist having additional information about consumers’ tastes, beyond the prior distribution; the additional information can be used to charge different prices to different segments of the market, i.e., carry out “third degree price discrimination.” We show that the segmentation and pricing induced by the additional information can achieve every combination of consumer and producer surplus such that: (i) consumer surplus is non-negative, (ii) producer surplus is at least as high as profits under the uniform monopoly price, and (iii) total surplus does not exceed the surplus generated by efficient trade.


The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris May 2013

The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We analyze the welfare consequences of a monopolist having additional information about consumers’ tastes, beyond the prior distribution; the additional information can be used to charge different prices to different segments of the market, i.e., carry out “third degree price discrimination.” We show that the segmentation and pricing induced by the additional information can achieve every combination of consumer and producer surplus such that: (i) consumer surplus is non-negative, (ii) producer surplus is at least as high as profits under the uniform monopoly price, and (iii) total surplus does not exceed the efficient gains from trade. As well as characterizing …


The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris May 2013

The Limits Of Price Discrimination, Dirk Bergemann, Benjamin Brooks, Stephen Morris

Cowles Foundation Discussion Papers

We analyze the welfare consequences of a monopolist having additional information about consumers’ tastes, beyond the prior distribution; the additional information can be used to charge different prices to different segments of the market, i.e., carry out “third degree price discrimination.” We show that the segmentation and pricing induced by the additional information can achieve every combination of consumer and producer surplus such that: (i) consumer surplus is non-negative, (ii) producer surplus is at least as high as profits under the uniform monopoly price, and (iii) total surplus does not exceed the surplus generated by efficient trade.