How should a seller offer quantity or quality differentiated products if they have no information about the distribution of demand? We consider a seller who cares about the "profit guarantee" of a pricing rule, that is, the minimum ratio of expected profits to expected social surplus for any distribution of demand.
We show that the profit guarantee is maximized by setting the price markup over cost equal to the elasticity of the cost function. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible demand distributions. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible demand distributions and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers.
We ask how the advertising mechanisms of digital platforms impact product prices. We present a model that integrates three fundamental features of digital advertising markets: (i) advertisers can reach customers on and off-platform, (ii) additional data enhances the value of matching advertisers and consumers, and (iii) bidding follows auction-like mechanisms. We compare data-augmented auctions, which leverage the platform’s data advantage to improve match quality, with managed campaign mechanisms, where advertisers’ budgets are transformed into personalized matches and prices through auto-bidding algorithms. In data-augmented second-price auctions, advertisers increase off-platform product prices to boost their competitiveness on-platform. This leads to socially efficient allocations on-platform, but inefficient allocations off-platform due to high product prices. The platform-optimal mechanism is a sophisticated managed campaign that conditions on-platform prices for sponsored products on off-platform prices set by all advertisers. Relative to auctions, the optimal managed campaign raises off-platform product prices and further reduces consumer surplus.
We develop an auction model for digital advertising. A monopoly platform has access to data on the value of the match between advertisers and consumers. The platform support bidding with additional information and increase the feasible surplus for on-platform matches. Advertisers jointly determine their pricing strategy both on and off the platform, as well as their bidding for digital advertising on the platform.
We compare a data-augmented second-price auction and a managed campaign mechanism. In the data-augmented auction, the bids by the advertisers are informed by the data of the platform regarding the value of the match. This results in a socially efficient allocation on the platform, but the advertisers increase their product prices off the platform to be more competitive on the platform. In consequence, the allocation off the platform is inefficient due to excessively high product prices.
The managed campaign mechanism allows advertisers to submit budgets that are then transformed into matches and prices through an autobidding algorithm. Compared to the data-augmented second-price auction, the optimal managed campaign mechanism increases the revenue of the digital platform. The product prices off the platform increase and the consumer surplus decreases.
We analyze digital markets where a monopolist platform uses data to match multiproduct sellers with heterogeneous consumers who can purchase both on and o§ the platform. The platform sells targeted ads to sellers that recommend their products to consumers and reveals information to consumers about their values. The revenueoptimal mechanism is a managed advertising campaign that matches products and preferences e¢ ciently. In equilibrium, sellers o§er higher qualities at lower unit prices on than o§ the platform. Privacy-respecting data-governance rules such as organic search results or federated learning can lead to welfare gains for consumers.
We consider a nonlinear pricing environment with private information. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible distributions of willingness to pay and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers.
We characterize the revenue-maximizing information structure in the second-price auction. The seller faces a trade-off: more information improves the efficiency of the allocation but creates higher information rents for bidders. The information disclosure policy that maximizes the revenue of the seller is to fully reveal low values (where competition is high) but to pool high values (where competition is low). The size of the pool is determined by a critical quantile that is independent of the distribution of values and only dependent on the number of bidders. We discuss how this policy provides a rationale for conflation in digital advertising.
We propose a model of intermediated digital markets where data and heterogeneity in tastes and products are defining features. A monopolist platform uses superior data to match consumers and multiproduct advertisers. Consumers have heterogenous preferences for the advertisers' product lines and shop on- or off-platform. The platform monetizes its data by selling targeted advertising space that allows advertisers to tailor their products to each consumer's preferences. We derive the equilibrium product lines and advertising prices. We identify search costs and informational advantages as two sources of the platform's bargaining power. We show that privacy-enhancing data-governance rules, such as those corresponding to federated learning, can lead to welfare gains for the consumers.
A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived. Each buyer has private information about his arrival time and valuation where the latter evolves according to a geometric Brownian motion. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We establish that the optimal stationary allocation policy can be implemented by a simple posted price. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem which determines the first time at which the buyer participates in the mechanism. The optimal mechanism thus induces progressive participation by each buyer: he either participates immediately or at a future random time.
We consider a general nonlinear pricing environment with private information. The seller can control both the signal that the buyers receive about their value and the selling mechanism. We characterize the optimal menu and information structure that jointly maximize the seller's profits. The optimal screening mechanism has finitely many items even with a continuum of values. We identify sufficient conditions under which the optimal mechanism has a single item. Thus the seller decreases the variety of items below the efficient level as a by-product of reducing the information rents of the buyer.
We consider a general nonlinear pricing environment with private information. The seller can control both the signal that the buyers receive about their value and the selling mechanism. We characterize the optimal menu and information structure that jointly maximize the seller's profit. The optimal screening mechanism has finitely many items even with a continuum of values. We identify sufficient conditions under which the optimal mechanism has a single item. Thus the seller decreases the variety of items below the efficient level in order to reduce the information rents of the buyers.
We consider a general nonlinear pricing environment with private information. We characterize the information structure that maximizes the sellerís proﬁts. The seller who cannot observe the buyerís willingness to pay can control both the signal that a buyer receives about his value and the selling mechanism. The optimal screening mechanism has ﬁnitely many items even with a continuum of types. We identify suﬀicient conditions under which the optimal mechanism has a single item. Thus, the socially eﬀicient variety of items is decreased drastically at the expense of higher revenue and lower information rents.
A data intermediary acquires signals from individual consumers regarding their preferences. The intermediary resells the information in a product market wherein firms and consumers tailor their choices to the demand data. The social dimension of the individual data—whereby a consumer's data are predictive of others' behavior—generates a data externality that can reduce the intermediary's cost of acquiring the information. The intermediary optimally preserves the privacy of consumers' identities if and only if doing so increases social surplus. This policy enables the intermediary to capture the total value of the information as the number of consumers becomes large.