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 structure that simultaneously attains these bounds entails an efficient allocation, bidders knowing whether they will win or lose, losers bidding their true value and winners being induced to bid high by partial information about the highest losing bid. Our analysis uses a linear algebraic characterization of equilibria across all information structures, and we report simulations of properties of the set of all equilibria.
We analyze data pricing and targeted advertising. Advertisers seek to tailor their spending to the value of each consumer. A monopolistic data provider sells cookies. informative signals about individual consumers.preferences. We characterize the set of consumers targeted by the advertisers and the optimal monopoly price of cookies. The ability to influence the composition of the targeted set provides incentives to lower prices. Thus, the price of data decreases with the reach of the database and increases with the fragmentation of data sales. We characterize the optimal policy for selling information and its implementation through nonlinear pricing of cookies.
We develop a model of data pricing and targeted advertising. A monopolistic data provider determines the price to access “cookies,” i.e., informative signals about individual consumers’ preferences. The demand for information is generated by advertisers who seek to tailor their spending to the value of each consumer. We characterize the set of consumers targeted by the advertisers and the optimal monopoly price of cookies. The ability to influence the composition of the set of targeted consumers provides incentives to lower prices. Thus, the monopoly price of data is decreasing in the reach of the database and increasing in the number of competing sellers of exclusive data. Finally, we explore the implications of nonlinear pricing of information and characterize the exclusive data sales that emerge as part of the optimal mechanism.
We propose a model of data provision and data pricing. A single data provider controls a large database that contains information about the match value between individual consumers and individual firms (advertisers). Advertisers seek to tailor their spending to the individual match value. The data provider prices queries about individual consumers’ characteristics (cookies). We determine the equilibrium data acquisition and pricing policies. Advertisers choose positive and/or negative targeting policies. The optimal query price influences the composition of the targeted set. The price of data decreases with the reach of the database and increases with the fragmentation of data sales.
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 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 the partial order on information structures to others, including Blackwell’s for the single player case.
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.
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 of Bayes correlated equilibria.
We discuss the relation of the solution concept to alternative definitions of correlated equilibrium in incomplete information games and of the partial order on information structures to others, including Blackwell’s for the single player case.
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.
We identify a partial order on many player information structures (individual sufficiency) under which more information shrinks the set of Bayes correlated equilibria. This order captures the role of information in imposing (incentive) constraints on behavior.
We consider the design of an optimal auction in which the seller can determine the allocation and the disclosure rule of the mechanism. Thus, in contrast to the standard analysis of a optimal auctions, the seller can explicitly design the disclosure of the information received by each bidder as his private information.
We show that the optimal disclosure rule is a sequential disclosure rule, implemented in an ascending price auction. In the optimal disclosure mechanism, each losing bidder learns his true valuation, but the winning bidder only learns that his valuation is sufficiently high to win the auction. We show that in the optimal auction, the posterior incentive and participation constraints of all the bidders are satisfied. In the special case in which the bidders have no private information initially, the seller can extract the entire surplus.
We propose a sequential auction mechanism for a single object in which the seller jointly determines the allocation and the disclosure policy. A sequential disclosure rule is shown to implement an ascending price auction in which each losing bidder learns his true valuation, but the winning bidder’s information is truncated from below. As the auction ends, the winning bidder only has limited information, namely that his valuation is sufficiently high to win the auction. The sequential mechanism implements the allocation of the handicap auction of Esö and Szentes [10] but strengthens the participation constraints of the bidders from interim to posterior constraints. Due to the limited disclosure of information, the participation constraints (and incentive constraints) of all the bidders are satisfied with respect to all information revealed by the mechanism. In the special case in which the bidders have no private information initially, the seller can extract the entire surplus.
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 welfare impact of price discrimination, we examine the limits of how prices and quantities can change under price discrimination. We also examine the limits of price discrimination in richer environments with quantity discrimination and limited ability to segment the market.
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.
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 welfare impact of price discrimination, we examine the limits of how prices and quantities can change under price discrimination. We also examine the limits of price discrimination in richer environments with quantity discrimination and limited ability to segment the market.
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.