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Full-Text Articles in Economics
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used …
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
Fixing a game with uncertain payoffs, information design identi.es the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used …
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
Given a game with uncertain payoffs, information design analyzes the extent to which the provision of information alone can influence the behavior of the players. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. We provide an introduction into the basic issues and insights of a …
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Information Design: A Unified Perspective, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
Given a game with uncertain payoffs, information design analyzes the extent to which the provision of information alone can influence the behavior of the players. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. We provide an introduction into the basic issues and insights of a …
The Comparison Of Information Structures In Games: Bayes Correlated Equilibrium And Individual Sufficiency, Dirk Bergemann, Stephen Morris
The Comparison Of Information Structures In Games: Bayes Correlated Equilibrium And Individual Sufficiency, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We define and characterize a notion of correlated equilibrium for games with incomplete information, which we call Bayes correlated equilibrium: The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the information structure is characterized and shown to be equivalent to the set of Bayes correlated equilibria. A game of incomplete information can be decomposed into a basic game, given by actions sets and payoff functions, and an information structure. We introduce a partial order on many player information structures — which we call individual …
The Comparison Of Information Structures In Games: Bayes Correlated Equilibrium And Individual Sufficiency, Dirk Bergemann, Stephen Morris
The Comparison Of Information Structures In Games: Bayes Correlated Equilibrium And Individual Sufficiency, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the given information structure is characterized and shown to be equivalent to the set of a version of incomplete information correlated equilibria which we dub Bayes correlated equilibria. A game of incomplete information can be decomposed into a basic game, given by actions sets and payoff functions, and an information structure. We introduce a partial order on many player information structures — which we call individual sufficiency — under which more information shrinks the set …
Bayes Correlated Equilibrium And The Comparison Of Information Structures In Games, Dirk Bergemann, Stephen Morris
Bayes Correlated Equilibrium And The Comparison Of Information Structures In Games, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the given information structure is equivalent to the set of a version of incomplete information correlated equilibrium which we dub Bayes correlated equilibrium . A game of incomplete information can be decomposed into a basic game, given by actions sets and payoff functions, and an information structure. We identify a partial order on many player information structures (individual sufficiency) under which more information shrinks the set of Bayes correlated equilibria.
Correlated Equilibrium And The Comparison Of Information Structures In Games, Dirk Bergemann, Stephen Morris
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. …
Bayes Correlated Equilibrium And The Comparison Of Information Structures, Dirk Bergemann, Stephen Morris
Bayes Correlated Equilibrium And The Comparison Of Information Structures, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call Bayes correlated equilibrium. We describe a partial order on many player information structures — which we call individual sufficiency — under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative definitions of correlated equilibrium in incomplete information games and of …
Correlated Equilibrium In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Correlated Equilibrium In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We define a notion of correlated equilibrium for games with incomplete information in a general setting with finite players, finite actions, and finite states, which we call Bayes correlated equilibrium. The set of Bayes correlated equilibria of a fixed incomplete information game equals the set of probability distributions over actions, states and types that might arise in any Bayes Nash equilibrium where players observed additional information. We show that more information always shrinks the set of Bayes correlated equilibria.
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for all possible private information structures that the agents may have. Our characterization of these robust predictions relies on an epistemic result which establishes a relationship between the set of Bayes Nash equilibria and the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior information of the analyst …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. The set of outcomes that can arise in equilibrium for some information structure is equal to the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information refines the set of equilibrium predictions. We consider information sharing among firms under demand uncertainty and find newly optimal information policies via …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information refines the set of equilibrium predictions. We consider information sharing among firms under demand uncertainty and find newly optimal information policies via …
Belief Free Incomplete Information Games, Dirk Bergemann, Stephen Morris
Belief Free Incomplete Information Games, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We consider the following belief free solution concepts for games with incomplete information: (i) incomplete information rationalizability, (ii) incomplete information correlated equilibrium and (iii) ex post equilibrium. We present epistemic foundations for these solution concepts and establish relationships between them. The properties of these solution concepts are further developed in supermodular games and potential games.
The Role Of The Common Prior In Robust Implementation, Dirk Bergemann, Stephen Morris
The Role Of The Common Prior In Robust Implementation, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We consider the role of the common prior for robust implementation in an environment with interdependent values. Specifically, we investigate a model of public good provision which allows for negative and positive informational externalities. In the corresponding direct mechanism, the agents’ reporting strategies are strategic complements with negative informational externalities and strategic substitutes with positive informational externalities. We derive the necessary and sufficient conditions for robust implementation in common prior type spaces and contrast this with our earlier results without the common prior. In the case of strategic complements the necessary and sufficient conditions for robust implementation do not depend …
Unmediated Communication In Games With Complete And Incomplete Information, Dino Gerardi
Unmediated Communication In Games With Complete And Incomplete Information, Dino Gerardi
Cowles Foundation Discussion Papers
In this paper we study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S U ( G ), the set of outcomes of a game G , that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G . A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more …