Uncertain demand, consumer loss aversion, and flat-rate tariffs

We consider a model of firm pricing and consumer choice, where consumers are loss averse and uncertain about their future demand. Possibly, consumers in our model prefer a flat rate to a measured tariff, even though this choice does not minimize their expected billing amount—a behavior in line with ample empirical evidence. We solve for the profit-maximizing two-part tariff, which is a flat rate if (a) marginal costs are not too high, (b) loss aversion is intense, and (c) there are strong variations in demand. Moreover, we analyze the optimal nonlinear tariff. This tariff has a large flat part when a flat rate is optimal among the class of two-part tariffs.Consumer loss aversion, flat-rate tariffs, nonlinear pricing, uncertain demand

Essays on Dynamic Mechanism Design

We consider the allocation of one or several units of a good in a dynamic environment. The time horizon is finite and in each period, a random number of potential buyers arrives. In Chapter 1, we study revenue maximization in an environment where buyers are privately informed about their valuations and their deadlines. Depending on the type distribution, the incentive compatibility constraint for the deadline may or may not be binding in the optimal mechanism. We identify a static and a dynamic pricing effect that drive incentive compatibility and violations thereof. Both effects are related to distinct properties of the type distribution and sufficient conditions are given under which each effect leads to a binding or slack incentive constraint for the deadline. An optimal mechanism for the binding case is derived for the special case of one object, two periods and two buyers. It can be implemented by a fixed price in period one and an asymmetric auction in period two. In order to prevent buyer one from buying in the first period when his deadline is two, the seller sets a reserve price that is lower than in the classic (Myerson, 1981) optimal auction and gives him a (non-linear) bonus. The bonus leads to robust bunching at the top of the type-space. Chapter 2 contains a characterization of asymmetric reduced form auctions. In chapter 3, we consider a more general dynamic environment in which buyers' valuations may depend on the time of allocation in an arbitrary way. We show that the static Vickrey auction can be generalized to the dynamic framework. This yields a simple payment rule for the implementation of the efficient allocation rule of a single object. To define the dynamic Vickrey auction, we show that the multi-dimensional type-space can be reduced to essentially one dimension. This allows to define the winner's payment as the lowest valuation in the reduced type-space, that suffices to win. Finally we define an ascending clock-auction with an equilibrium-outcome that coincides with the outcome of the dynamic Vickrey auction

Auction Design with Data-Driven Misspecifications

We consider auction environments in which at the time of the auction bidders observe signals about their ex-post value. We introduce a model of novice bidders who do not know know the joint distribution of signals and instead build a statistical model relating others' bids to their own ex post value from the data sets accessible from past similar auctions. Crucially, we assume that only ex post values and bids are accessible while signals observed by bidders in past auctions remain private. We consider steady-states in such environments, and importantly we allow for correlation in the signal distribution. We first observe that data-driven bidders may behave suboptimally in classical auctions such as the second-price or first-price auctions whenever there are correlations. Allowing for a mix of rational (or experienced) and data-driven (novice) bidders results in inefficiencies in such auctions, and we show the inefficiency extends to all auction-like mechanisms in which bidders are restricted to submit one-dimensional (real-valued) bids

Generalized reduced-form auctions: a network-flow approach

We develop a network-flow approach for characterizing interim-allocation rules that can be implemented by ex post allocations. Our method can be used to characterize feasible interim allocations in general multi-unit auctions where agents face capacity constraints, both ceilings and floors. Applications include a variety of settings of practical interest, ranging from individual and group-specific capacity constraints, set-aside sale, partnership dissolution, and government license reallocation.Reduced-form auctions, network-flow approach, feasible circulation flow, paramodular capacity constraints

Auctions with Limited Commitment

We study auction design in the standard symmetric independent private values environment, where the seller lacks the commitment power to withhold an unsold object off the market. The seller has a single object and can conduct an infinite sequence of standard auctions with reserve prices to maximize her expected profit. In each period, the seller can commit to a reserve price for the current period but cannot commit to future reserve prices. We analyze the problem with limited commitment through an auxiliary mechanism design problem with full commitment, in which an additional constraint reflects the sequential rationality of the seller. We characterize the maximal profit achievable in any perfect Bayesian equilibrium in the limit as the period length vanishes. The static full commitment profit is not achievable but the seller can always guarantee the profit of an efficient auction. If the number of buyers exceeds a cutoff which is small for many distributions, the efficient auction is optimal. Otherwise, the efficient auction is not optimal, and we give conditions under which the optimal solution consists of an initial auction with a non-trivial reserve price followed by a continuously decreasing price path. The solution is described by a simple ordinary differential equation. Our analysis combines insights from bargaining, auctions, and mechanism design

Keeping the Listener Engaged: a Dynamic Model of Bayesian Persuasion

We consider a dynamic model of Bayesian persuasion in which information takes time and is costly for the sender to generate and for the receiver to process, and neither player can commit to their future actions. Persuasion may totally collapse in a Markov perfect equilibrium (MPE) of this game. However, for persuasion costs sufficiently small, a version of a folk theorem holds: outcomes that approximate Kamenica and Gentzkow (2011)'s sender-optimal persuasion as well as full revelation and everything in between are obtained in MPE, as the cost vanishes

Coasian Equilibria in Sequential Auctions

We study stationary equilibria in a sequential auction setting. A seller runs a sequence of standard first-price or second-price auctions to sell an indivisible object to potential buyers. The seller can commit to the rule of the auction and the reserve price of the current period but not to reserve prices of future periods. We prove the existence of stationary equilibria and establish a uniform Coase conjecture—at any point in time and in any stationary equilibrium, the seller’s profit from running sequential auctions converges to the profit of running an efficient auction as the period length goes to zero. Keywords: Coase conjecture, auctions with limited commitment, sequential auction