Dynamic Price Competition: Theory and Evidence from Airline Markets

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. JEL Classification: C70, C73, D21, D22, D43, D60, L13, L93

[1]  Xavier d'Haultfoeuille,et al.  Estimating the Gains (and Losses) of Revenue Management , 2022, 2206.04424.

[2]  Florian Zettelmeyer,et al.  How Market Power Affects Dynamic Pricing: Evidence from Inventory Fluctuations at Car Dealerships , 2021, Manag. Sci..

[3]  Kevin R. Williams,et al.  Intertemporal Price Discrimination in Sequential Quantity-Price Games , 2019, Mark. Sci..

[4]  Eilon Solan,et al.  Browder's Theorem through Brouwer's Fixed Point Theorem , 2021 .

[5]  Kevin R. Williams The Welfare Effects of Dynamic Pricing: Evidence from Airline Markets , 2021, SSRN Electronic Journal.

[6]  Chaim Fershtman,et al.  NBER WORKING PAPER SERIES ARTIFICIAL INTELLIGENCE AND PRICING : THE IMPACT OF ALGORITHM DESIGN , 2021 .

[7]  Mallesh M. Pai,et al.  Algorithmic Collusion: Supra-Competitive Prices via Independent Algorithms , 2020 .

[8]  J. Castillo,et al.  Who Benefits from Surge Pricing? , 2020 .

[9]  Emilio Calvano,et al.  Artificial Intelligence, Algorithmic Pricing and Collusion , 2018, American Economic Review.

[10]  R. Ulbricht,et al.  Dynamic Oligopoly Pricing: Evidence from the Airline Industry , 2015, International Journal of Industrial Organization.

[11]  James W. Roberts,et al.  A Model of Dynamic Limit Pricing with an Application to the Airline Industry , 2014, Journal of Political Economy.

[12]  Alexander Mackay,et al.  Competition in Pricing Algorithms , 2020, SSRN Electronic Journal.

[13]  C. Murry,et al.  Price Discrimination in International Airline Markets , 2018, The Review of Economic Studies.

[14]  Francesc Dilmé,et al.  Revenue Management Without Commitment: Dynamic Pricing and Periodic Flash Sales , 2018, The Review of Economic Studies.

[15]  X. Vives Strategic complementarities in oligopoly , 2018 .

[16]  Philipp Strack,et al.  Revenue-Maximizing Mechanisms with Strategic Customers and Unknown, Markovian Demand , 2018, Manag. Sci..

[17]  John Rust,et al.  Optimal Dynamic Hotel Pricing , 2018 .

[18]  Luis C. Corchón,et al.  Handbook of Game Theory and Industrial Organization, Volume I: Theory. An Introduction , 2017 .

[19]  Volker Nocke,et al.  Multiproduct-Firm Oligopoly: An Aggregative Games Approach , 2016 .

[20]  Andrzej Skrzypacz,et al.  Revenue Management with Forward-Looking Buyers , 2016, Journal of Political Economy.

[21]  I. Kerkemezos,et al.  Competition and Price Dispersion in the U.S. Airline Industry , 2015 .

[22]  A. Sengupta,et al.  Does Scarcity Drive Intra-Route Price Dispersion in Airlines? , 2012 .

[23]  Kalyan T. Talluri,et al.  Dynamic Price Competition with Fixed Capacities , 2011, Manag. Sci..

[24]  I. Hendel,et al.  Intertemporal Price Discrimination in Storable Goods Markets , 2011 .

[25]  John Lazarev The Welfare Effects of Intertemporal Price Discrimination : An Empirical Analysis of Airline Pricing in U . S . Monopoly Market s , 2011 .

[26]  Kristopher Gerardi,et al.  Does Competition Reduce Price Dispersion? New Evidence from the Airline Industry , 2009, Journal of Political Economy.

[27]  R. McAfee,et al.  Dynamic pricing in the airline industry , 2007 .

[28]  Anirban Sengupta,et al.  Airline Pricing, Price Dispersion and Ticket Characteristics on and Off the Internet , 2006 .

[29]  Dirk Bergemann,et al.  Dynamic Price Competition , 2003, J. Econ. Theory.

[30]  Zsolt Sándor,et al.  On price equilibrium with multi-product firms , 2004 .

[31]  Garrett J. van Ryzin,et al.  Revenue Management Under a General Discrete Choice Model of Consumer Behavior , 2004, Manag. Sci..

[32]  J. Stavins,et al.  Price Discrimination in the Airline Market: The Effect of Market Concentration , 2001, Review of Economics and Statistics.

[33]  Wenjiao Zhao,et al.  Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand , 2000 .

[34]  J. Dana,et al.  Equilibrium Price Dispersion Under Demand Uncertainty: The Roles of Costly Capacity and Market Structure , 1999 .

[35]  Ward Hanson,et al.  Optimizing Multinomial Logit Profit Functions , 1996 .

[36]  G. Ryzin,et al.  Optimal dynamic pricing of inventories with stochastic demand over finite horizons , 1994 .

[37]  Marc Dudey Dynamic Edgeworth-Bertrand Competition , 1992 .

[38]  Andrew Caplin,et al.  Aggregation and Imperfect Competition: On the Existence of Equilibrium , 1991 .

[39]  Paul R. Milgrom,et al.  Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities , 1990 .

[40]  Continuous functions and connected graphs , 1990 .

[41]  E. Maskin,et al.  A Theory of Dynamic Oligopoly, II: Price Competition , 1985 .

[42]  R. B. Kellogg,et al.  Uniqueness in the Schauder fixed point theorem , 1976 .