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Tibor Heumann Publications

Publish Date
Discussion Paper
Abstract

We analyze the welfare impact of a monopolist able to segment a multiproduct market and offer differentiated price menus within each segment. We characterize a family of extremal distributions such that all achievable welfare outcomes can be reached by selecting segments from within these distributions. This family of distributions arises as the solution to the consumer maximizing distribution of values for multigood markets. With these results, we analyze the effect of segmentation on consumer surplus and prices in both interior and extremal markets, including conditions under which there exists a segmentation benefiting all consumers. Finally, we present an efficient algorithm for computing segmentations.

Discussion Paper
Abstract

We characterize the bidders' surplus maximizing information structure in an optimal auction for a single unit good and related extensions to multi-unit and multi-good problems. The bidders seeks to find a balance between participation (and the avoidance of exclusion) and efficiency. The information structure that maximizes the bidders surplus is given by a generalized Pareto distribution at the center of demand distribution, and displays complete information disclosure at either end of the Pareto distribution.

Discussion Paper
Abstract

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.

Discussion Paper
Abstract

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.

American Economic Review
Abstract

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.

Discussion Paper
Abstract

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.

Discussion Paper
Abstract

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.

Discussion Paper
Abstract

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.

Discussion Paper
Abstract

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.

Discussion Paper
Abstract

In digital advertising, a publisher selling impressions faces a trade-o¤ in deciding how precisely to match advertisers with viewers. A more precise match generates efficiency gains that the publisher can hope to exploit. A coarser match will generate a thicker market and thus more competition. The publisher can control the precision of the match by controlling the amount of information that advertisers have about viewers. We characterize the optimal trade-off when impressions are sold by auction. The publisher pools premium matches for advertisers (when there will be less competition on average) but gives advertisers full information about lower quality matches.

Discussion Paper
Abstract

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.

Abstract

We study a linear interaction model with asymmetric information. We first characterize the linear Bayes Nash equilibrium for a class of one dimensional signals. It is then shown that this class of one dimensional signals provide a comprehensive description of the first and second moments of the distribution of outcomes for any Bayes Nash equilibrium and any information structure.
We use our results in a variety of applications: (i) we study the connections between incomplete information and strategic interaction, (ii) we explain to what extent payoff environment and information structure of a economy are distinguishable through the equilibrium outcomes of the economy, and (iii) we analyze how equilibrium outcomes can be decomposed to understand the sources of individual and aggregate volatility.

Discussion Paper
Abstract

We consider demand function competition with a finite number of agents and private information. We analyze how the structure of the private information shapes the market power of each agent and the price volatility. 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 agents across all information structures, hence we can provide sharp and robust bounds on some but not all equilibrium statistics.

We then compare demand function competition with a different uniform price trading mechanism, namely Cournot competition. Interestingly, in Cournot competition, the market power is uniquely determined while the price volatility cannot be bounded by the variance of the aggregate shock.

Abstract

In an economy of interacting agents with both idiosyncratic and aggregate shocks, we examine how the structure of private information influences aggregate volatility. The maximal aggregate volatility is attained in a noise free information structure in which the agents confound idiosyncratic and aggregate shocks, and display excess response to the aggregate shocks, as in Lucas [14]. For any given variance of aggregate shocks, the upper bound on aggregate volatility is linearly increasing in the variance of the idiosyncratic shocks. Our results hold in a setting of symmetric agents with linear best responses and normal uncertainty. We establish our results by providing a characterization of the set of all joint distributions over actions and states that can arise in equilibrium under any information structure. This tractable characterization, extending results in Bergemann and Morris [8], can be used to address a wide variety of questions linking information with the statistical moments of the economy.

Abstract

We analyze a class of games with interdependent values and linear best responses. The payoff uncertainty is described by a multivariate normal distribution that includes the pure common and pure private value environment as special cases. We characterize the set of joint distributions over actions and states that can arise as Bayes Nash equilibrium distributions under any multivariate normally distributed signals about the payoff states. We characterize maximum aggregate volatility for a given distribution of the payoff states. We show that the maximal aggregate volatility is attained in a noise-free equilibrium in which the agents confound idiosyncratic and common components of the payoff state, and display excess response to the common component. We use a general approach to identify the critical information structures for the Bayes Nash equilibrium via the notion of Bayes correlated equilibrium, as introduced by Bergemann and Morris (2013b).