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Full-Text Articles in Economics
First-Price Auctions With General Information Structures: A Short Introduction, Dirk Bergemann, Benjamin Brooks, Stephen Morris
First-Price Auctions With General Information Structures: A Short Introduction, Dirk Bergemann, Benjamin Brooks, Stephen Morris
Cowles Foundation Discussion Papers
In a recent paper, [Bergemann et al. 2017a], we derive results about equilibrium behavior in the first-price auction that hold across all common-prior information structures. The purpose of this letter is to give an informal introduction into the results. At the end we offer a brief discussion of related work.
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
Cowles Foundation Discussion Papers
We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and …
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
Cowles Foundation Discussion Papers
We explore the impact of private information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders uncertain whether they will win or lose and indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We report further analytic and computational characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has …
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
Cowles Foundation Discussion Papers
We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We report further analytic and computational characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning …
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
First Price Auctions With General Information Structures: Implications For Bidding And Revenue, Dirk Bergemann, Benjamin Brooks, Stephen Morris
Cowles Foundation Discussion Papers
This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In particular, we characterize maximum and minimum revenue across all information structures when bidders may not know their own values, and maximum revenue when they do know their values. Revenue is maximized when buyers know who has the highest valuation, but the highest valuation buyer has partial information about others’ values. Revenue is minimized when buyers are uncertain …
Ex Post Implementation, Dirk Bergemann, Stephen Morris
Ex Post Implementation, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and — in economic environments — sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints. In many economically significant environments, ex post implementation can be achieved in the direct mechanism. We show by means of two classic examples that ex post monotonicity does not imply nor is …