We introduce a model of dynamic pricing in perishable goods markets with competition and provide conditions for equilibrium uniqueness. Pricing dynamics are rich because both own and competitor scarcity affect future profits. We identify new competitive forces that can lead to misallocation due to selling units too quickly: the Bertrand scarcity trap. We empirically estimate our model using daily prices and bookings for competing U.S. airlines. We compare competitive equilibrium outcomes to those where firms use pricing heuristics based on observed internal pricing rules at a large airline. We find that pricing heuristics increase revenues (4-5%) and consumer surplus (3%).
We propose a demand estimation method that allows for a large number of zero sale observations, rich unobserved heterogeneity, and endogenous prices. We do so by modeling small market sizes through Poisson arrivals. Each of these arriving consumers solves a standard discrete choice problem. We present a Bayesian IV estimation approach that addresses sampling error in product shares and scales well to rich data environments. The data requirements are traditional market-level data as well as a measure of market sizes or consumer arrivals. After presenting simulation studies, we demonstrate the method in an empirical application of air travel demand.
Firms facing complex objectives often decompose the problems they face, delegating different parts of the decision to distinct subordinates. Using comprehensive data and internal models from a large U.S. airline, we establish that airline pricing is inconsistent with canonical dynamic pricing models. However, we show that observed prices can be rationalized as an equilibrium of a game played by departments who each have decision rights for different inputs that are supplied to the observed pricing heuristic. Incorrectly assuming that the firm solves a standard profit maximization problem as a single entity understates overall welfare actually achieved but affects business and leisure consumers differently. Likewise, we show that assuming prices are set through standard profit maximization leads to incorrect inferences about consumer demand elasticities and thus welfare.
We introduce a model of oligopoly dynamic pricing where ﬁrms with limited capacity face a sales deadline. We establish conditions under which the equilibrium is unique and converges to a system of diﬀerential equations. Using unique and comprehensive pricing and bookings data for competing U.S. airlines, we estimate our model and ﬁnd that dynamic pricing results in higher output but lower welfare than under uniform pricing. Our theoretical and empirical ﬁndings run counter to standard results in single-ﬁrm settings due to the strategic role of competitor scarcity. Pricing heuristics commonly used by airlines increase welfare relative to estimated equilibrium predictions.
We propose an approach to modeling and estimating discrete choice demand that allows for a large number of zero sale observations, rich unobserved heterogeneity, and endogenous prices. We do so by modeling small market sizes through Poisson arrivals. Each of these arriving consumers then solves a standard discrete choice problem. We present a Bayesian IV estimation approach that addresses sampling error in product shares and scales well to rich data environments. The data requirements are traditional market-level data and measures of consumer search intensity. After presenting simulation studies, we consider an empirical application of air travel demand where product-level sales are sparse. We ﬁnd considerable variation in demand over time. Periods of peak demand feature both larger market sizes and consumers with higher willingness to pay. This ampliﬁes cyclicality. However, observed frequent price and capacity adjustments oﬀset some of this compounding eﬀect.
Firms often involve multiple departments for critical decisions that may result in coordination failures. Using data from a large U.S. airline, we document the presence of important pricing biases that differ significantly from dynamically optimal profit maximization. However, these biases can be rationalized as a “second-best” after accounting for department decision rights. We show that assuming prices are generated through profit maximization biases demand estimates and that second-best prices can persist, even under improvements to pricing algorithm inputs. Our results suggest caution in abstracting from organizational structure and drawing inferences from firms’ pricing decisions alone.
We study how organizational boundaries aﬀect pricing decisions using comprehensive data from a large U.S. airline. We document that the ﬁrm’s advanced pricing algorithm, utilizing inputs from diﬀerent organizational teams, is subject to multiple biases. To quantify the impacts of these biases, we estimate a structural demand model using sales and search data. We recover the demand curves the ﬁrm believes it faces using forecasting data. In counterfactuals, we show that correcting biases introduced by organizational teams individually have little impact on market outcomes, but coordinating organizational outcomes leads to higher prices/revenues and increased deadweight loss in the markets studied.
The quantal response equilibrium (QRE) notion of McKelvey and Palfrey (1995) has recently attracted considerable attention, due largely to its widely documented ability to rationalize observed behavior in games played by experimental subjects. We show that this ability to ﬁt the data, as typically measured in this literature, is uninformative. Without a priori distributional assumptions, a QRE can match any distribution of behavior by each player in any normal form game. We discuss approaches that might be taken to provide valid empirical evaluation of the QRE and discuss its potential value as an approximating empirical structure.