We study price discrimination in a market in which two firms engage in Bertrand competition. Some consumers are contested by both firms, and other consumers are “captive” to one of the firms. The market can be divided into segments, which have different relative shares of captive and contested consumers. It is shown that the revenue-maximizing segmentation involves dividing the market into “nested” markets, where exactly one firm may have captive consumers.
Consider a market with identical firms offering a homogeneous good. A consumer obtains price quotes from a subset of firms and buys from the firm offering the lowest price. The “price count” is the number of firms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we obtain a tight upper bound (under first-order stochastic dominance) on the equilibrium distribution of sale 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 ( firms know the price count) and no information (firms only know the ex-ante distribution of the price count). A qualitative implication of our results is that a small ex ante probability that the price count is one can lead to a large increase in the expected price. The bound also applies in a wide class of models where the price count distribution is endogenized, including models of simultaneous and sequential consumer search.
Consider a market with many identical firms offering a homogeneous good. A consumer obtains price quotes from a subset of firms and buys from the firm offering the lowest price. The “price count” is the number of firms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we obtain a tight upper bound (under first-order stochastic dominance) on the equilibrium distribution of sale prices. The bound holds across all models of firms’ common-prior higher-order beliefs about the price count, including the extreme cases of complete information ( firms know the price count exactly) and no information ( firms only know the ex ante distribution of the price count). A qualitative implication of our results is that even a small ex ante probability that the price count is one can lead to dramatic increases in the expected price. The bound also applies in a wide class of models where the price count distribution is endogenized, including models of simultaneous and sequential consumer search.
Consider a market with identical firms offering a homogeneous good. A consumer obtains price quotes from a subset of firms and buys from the firm offering the lowest price. The “price count” is the number of firms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we derive a tight upper bound (under first-order stochastic dominance) 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 (firms know the price count) and no information (firms only know the ex ante distribution of the price count). A qualitative 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, including models of simultaneous and sequential consumer search.
We compare the revenue of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave revenue functions and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This revenue bound obtains for any arbitrary number of segments and prices that the seller would use in case he would engage in third-degree price discrimination. We further establish that these conditions are tight, and that a weakening of common support or concavity leads to arbitrarily poor revenue comparisons.
We compare the revenue of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave revenue functions and common support, a uniform price is guaranteed to achieve one-half of the optimal monopoly profits. This revenue bound holds for any arbitrary number of segments and prices that the seller would use in case he would engage in third-degree price discrimination. We further establish that these conditions are tight and that a weakening of common support or concavity leads to arbitrarily poor revenue comparisons.
A data intermediary pays consumers for information about their preferences and sells the information so acquired to firms that use it to tailor their products and prices. The social dimension of the individual data - whereby an individual’s data are predictive of the behavior of others - generates a data externality that reduces the intermediary’s cost of acquiring information. We derive the intermediary’s optimal data policy and show that it preserves the privacy of the consumers’ identities while providing precise information about market demand to the firms. This enables the intermediary to capture the entire value of information as the number of consumers grows large.
We propose a model of data intermediation to analyze the incentives for sharing individual data in the presence of informational externalities. A data intermediary acquires signals from individual consumers regarding their preferences. The intermediary resells the information in a product market in which firms and consumers can tailor their choices to the demand data. The social dimension of the individual data - whereby an individual’s data are predictive of the behavior of others - generates a data externality that can reduce the intermediary’s cost of acquiring information. We derive the intermediary’s optimal data policy and establish that it preserves the privacy of consumer identities while providing precise information about market demand to the firms. This policy enables the intermediary to capture the total value of the information as the number of consumers becomes large.
A data intermediary pays consumers for information about their preferences, and sells the information so-acquired to firms that use it to tailor their product offers and prices. The social dimension of the individual data - whereby an individual’s data is predictive of the behavior of others - generates a data externality that reduces the intermediary’s cost of acquiring information. We derive the data intermediary’s optimal information policy, and show that it preserves privacy over the identity of the consumers, but provides precise information about market demand to the firms.
We propose a model of data intermediation to analyze the incentives for sharing individual data in the presence of informational externalities. A data intermediary acquires signals from individual consumers regarding their preferences. The intermediary resells the information in a product market wherein firms and consumers can tailor their choices to the demand data. The social dimension of the individual data - whereby an individual’s data are predictive of the behavior of others - generates a data externality that can reduce the intermediary’s cost of acquiring the information. We derive the intermediary’s optimal data policy and establish that it preserves the privacy of consumer identities while providing precise information about market demand to the firms. This policy enables the intermediary to capture the total value of the information as the number of consumers becomes large.
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.
We consider demand function competition with a finite number of agents and private information. We show that any degree of market power can arise in the unique equilibrium under an information structure that is arbitrarily close to complete information. In particular, regardless of the number of agents and the correlation of payoff shocks, market power may be arbitrarily close to zero (so we obtain the competitive outcome) or arbitrarily large (so there is no trade in equilibrium). By contrast, price volatility is always less than the variance of the aggregate shock across all information structures.
A single seller faces a sequence of buyers with unit demand. The buyers are forwardlooking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation.
We derive the optimal stationary mechanism in closed form and characterize its qualitative structure. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the buyer decides to participate in the mechanism. The resulting value function of each buyer cannot be too convex and must be continuously differentiable everywhere, reflecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each buyer: he participates either immediately or at a future random time.