We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by Blackwell [Bla51, Bla53]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. A recent paper by Bergemann et al. [BBS18] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and m ≥ 3 actions, we provide an O(m)-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. We also provide a sufficient condition under which selling only the fully informative experiment achieves the optimal revenue.
For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism.
We characterize the revenue-maximizing information structure in the second price auction. The seller faces a classic economic trade-o§: providing more information improves the e¢ - ciency of the allocation but also 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 will be high) but to pool high values (where competition will be 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 conáation in digital advertising.
As large amounts of data become available and can be communicated more easily and processed more effectively, information has come to play a central role for economic activity and welfare in our age. This essay overviews contributions to the industrial organization of information markets and nonmarkets, while attempting to maintain a balance between foundational frameworks and more recent developments. We start by reviewing mechanism-design approaches to modeling the trade of information. We then cover ratings, predictions, and recommender systems. We turn to forecasting contests, prediction markets, and other institutions designed for collecting and aggregating information from decentralized participants. Finally, we discuss science as a prototypical information nonmarket with participants who interact in a non-anonymous way to produce and disseminate information. We aim to familiarize the reader with the central notions and insights in this burgeoning literature and also point to some critical open questions that future research will have to address.
We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing—a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a)each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested.
We exhibit two distinct sets of sufficient conditions. The first set of conditions weakens the monotonicity requirement of types and virtual values but maintains a regularity assumption, i.e., that the product-by-product revenue curves are single-peaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS)—the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption.
Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer’s types are monotone, the seller can equivalently post a vector of single-item prices: upgrade pricing and separate pricing are equivalent.
We characterize the revenue-maximizing information structure in the second price auction. The seller faces a classic economic trade-o¤: providing more information improves the efficiency of the allocation but also 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 will be high) but to pool high values (where competition will be 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 analyze nonlinear pricing with finite information. We consider a multi-product environment where each buyer has preferences over a d-dimensional variety of goods. The seller is limited to offering a finite number n of d-dimensional choices. The limited menu reflects a finite communication capacity between the buyer and seller.
We identify necessary conditions that the optimal finite menu must satisfy, for either the socially efficient or the revenue-maximizing mechanism. These conditions require that information be bundled, or "quantized," optimally. We introduce vector quantization and establish that the losses due to finite menus converge to zero at a rate of 1/n2/d_ In the canonical model with one-dimensional products and preferences, this establishes that the loss resulting from using the n-item menu converges to zero at a rate proportional to 1 /n2 .
We analyze nonlinear pricing with finite information. We consider a multi-product environment where each buyer has preferences over a d-dimensional variety of goods. The seller is limited to offering a finite number n of d-dimensional choices. The limited menu reflects a finite communication capacity between the buyer and seller.
We identify necessary conditions that the optimal finite menu must satisfy, for either the socially efficient or the revenue-maximizing mechanism. These conditions require that information be bundled, or “quantized,” optimally.
We introduce vector quantization and establish that the losses due to finite menus converge to zero at a rate of 1/n2/d. In the canonical model with one-dimensional products and preferences, this establishes that the loss resulting from using the n-item menu converges to zero at a rate proportional to 1/n2.
As large amounts of data become available and can be communicated more easily and processed more e¤ectively, information has come to play a central role for economic activity and welfare in our age. This essay overviews contributions to the industrial organization of information markets and nonmarkets, while attempting to maintain a balance between foundational frameworks and more recent developments. We start by reviewing mechanism-design approaches to modeling the trade of information. We then cover ratings, predictions, and recommender systems. We turn to forecasting contests, prediction markets, and other institutions designed for collecting and aggregating information from decentralized participants. Finally, we discuss science as a prototypical information nonmarket with participants who interact in a non-anonymous way to produce and disseminate information. We aim to make the reader familiar with the central notions and insights in this burgeoning literature and also point to some open critical questions that future research will have to address.
As large amounts of data become available and can be communicated more easily and processed more effectively, information has come to play a central role for economic activity and welfare in our age. This essay overviews contributions to the industrial organization of information markets and nonmarkets, while attempting to maintain a balance between foundational frameworks and more recent developments. We start by reviewing mechanism-design approaches to modeling the trade of information. We then cover ratings, predictions, and recommender systems. We turn to forecasting contests, prediction markets, and other institutions designed for collecting and aggregating information from decentralized participants. Finally, we discuss science as a prototypical information nonmarket with participants who interact in a non-anonymous way to produce and disseminate information. We aim to familiarize the reader with the central notions and insights in this burgeoning literature and also point to some critical open questions that future research will have to address.
Consider a market with identical firms offering a homogeneous good. For any given ex ante distribution of the price count (the number of firms from which a consumer obtains a quote), we derive a tight upper bound on the equilibrium distribution of sales prices. The bound holds across all models of firms’ common-prior higher-order beliefs about the price count, including the extreme cases of full information and no information. One implication of our results is that a small ex ante probability that the price count is equal to one can lead to a large increase in the expected price. The bound also applies in a large class of models where the price count distribution is endogenously determined.
We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing—a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a) each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested.
We exhibit two distinct sets of sufficient conditions. The first set of conditions weakens the monotonicity requirement of types and virtual values but maintains a regularity assumption, i.e., that the product-by-product revenue curves are single-peaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS)—the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption.
Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer’s types are monotone, the seller can equivalently post a vector of single-item prices: upgrade pricing and separate pricing are equivalent.