Revenue Management with Forward-Looking Buyers

A seller wishes to sell multiple goods by a deadline, for example, the end of a season. Potential buyers enter over time and can strategically time their purchases. Each period, the profit-maximizing mechanism awards units to the buyers with the highest valuations exceeding a sequence of cutoffs. We show that these cutoffs are deterministic, depending only on the inventory and time remaining; in the continuous-time limit, the optimal mechanism can be implemented by posting anonymous prices. When incoming demand decreases over time, the optimal cutoffs satisfy a one-period-look-ahead property and prices are defined by an intuitive differential equation.

[1]  R. G. Miller,et al.  Optimal Persistence Policies , 1960 .

[2]  Sheldon M. Ross,et al.  INFINITESIMAL LOOK-AHEAD STOPPING RULES , 1971 .

[3]  C. Derman,et al.  A Sequential Stochastic Assignment Problem , 1972 .

[4]  S. Albright.  Optimal Sequential Assignments with Random Arrival Times , 1974 .

[5]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Vol. II , 1976 .

[6]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[7]  M. Harris,et al.  A Theory of Monopoly Pricing Schemes with Demand Uncertainty , 1981 .

[8]  Jeremy I. Bulow.  Durable-Goods Monopolists , 1982, Journal of Political Economy.

[9]  J. Sobel,et al.  Cyclic Pricing by a Durable Goods Monopolist , 1984 .

[10]  R. Myerson.  MULTISTAGE GAMES WITH COMMUNICATION , 1984 .

[11]  E. Lazear.  Retail Pricing and Clearance Sales , 1984 .

[12]  M. Riordan,et al.  Awarding Monopoly Franchises , 1987 .

[13]  R. McAfee,et al.  Auctions with a stochastic number of bidders , 1987 .

[14]  Barry C. Smith,et al.  Yield Management at American Airlines , 1992 .

[15]  Ruqu Wang.  Auctions versus Posted-Price Selling , 1993 .

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

[17]  Kathryn Graddy,et al.  Testing for imperfect competition at the Fulton fish market , 1995 .

[18]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[19]  Ilya Segal,et al.  Solutions manual for Microeconomic theory : Mas-Colell, Whinston and Green , 1997 .

[20]  F Thomas Bruss,et al.  Multiple buying or selling with vector offers , 1997, Journal of Applied Probability.

[21]  Hing-Man Leung,et al.  Intertemporal Price Discrimination , 2000 .

[22]  Gopal Das Varma,et al.  Optimal dynamic pricing with inventories , 2001 .

[23]  Garrett J. van Ryzin,et al.  Optimal Dynamic Auctions for Revenue Management By , 2001 .

[24]  Ilya Segal,et al.  Optimal Pricing Mechanisms with Unknown Demand , 2002 .

[25]  Cyclic pricing by a durable goods monopolist: Corrigendum , 2002 .

[26]  W. Lieberman.  The Theory and Practice of Revenue Management , 2005 .

[27]  Jérémie Gallien,et al.  Sloan School of Management Working Paper 4268-02 December 2002 Dynamic Mechanism Design for Online Commerce , 2002 .

[28]  Kathryn Graddy,et al.  Markets: The Fulton Fish Market , 2006 .

[29]  Wesley R. Hartmann.  Intertemporal effects of consumption and their implications for demand elasticity estimates , 2006 .

[30]  Robert Zeithammer.  Forward-Looking Bidding in Online Auctions , 2005 .

[31]  Renato Redondi,et al.  Pricing strategies of low-cost airlines: The Ryanair case study , 2009 .

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

[33]  Xuanming Su,et al.  Intertemporal Pricing with Strategic Customer Behavior , 2007, Manag. Sci..

[34]  Marc Rysman,et al.  Dynamics of Consumer Demand for New Durable Goods , 2007 .

[35]  Simon Board,et al.  Selling options , 2007, J. Econ. Theory.

[36]  Andrzej Skrzypacz,et al.  Bargaining with Arrival of New Traders , 2010 .

[37]  Pinar Keskinocak,et al.  Designing Optimal Preannounced Markdowns in the Presence of Rational Customers with Multiunit Demands , 2008, Manuf. Serv. Oper. Manag..

[38]  Mallesh M. Pai,et al.  Optimal Dynamic Auctions , 2008 .

[39]  L. Samuelson,et al.  Managing Strategic Buyers Managing Strategic Buyers * Managing Strategic Buyers , 2022 .

[40]  Simon Board,et al.  Durable-Goods Monopoly with Varying Demand , 2008 .

[41]  Yossi Aviv,et al.  Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers , 2008, Manuf. Serv. Oper. Manag..

[42]  Kathryn Graddy,et al.  A Dynamic Model of Price Discrimination and Inventory Management at the Fulton Fish Market , 2009 .

[43]  Alex Gershkov,et al.  Learning about the Future and Dynamic Efficiency , 2009 .

[44]  Maher Said,et al.  Auctions with Dynamic Populations: Efficiency and Revenue Maximization , 2012, J. Econ. Theory.

[45]  Alex Gershkov,et al.  Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach , 2009 .

[46]  Z. Shen,et al.  Customer Behavior Modeling in Revenue Management and Auctions: A Review and New Research Opportunities , 2007 .

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

[48]  Andrew Sweeting,et al.  Applied Economics Workshop Business 33610 Spring Quarter 2012 "dynamic Pricing Behavior in Perishable Goods Markets: Evidence from Secondary Markets for Major League Baseball Tickets" Dynamic Pricing Behavior in Perishable Goods Markets: Evidence from Secondary Markets for Major League Baseball Tick , 2022 .

[49]  R. Deneckere,et al.  Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting , 2012 .

[50]  Lakshman Krishnamurthi,et al.  Demand Dynamics in the Seasonal Goods Industry: An Empirical Analysis , 2012, Mark. Sci..

[51]  M. Said.  Auctions with Dynamic Populations: Efficiency and Revenue Maximization , 2012 .

[52]  Rakesh V. Vohra,et al.  Optimal Dynamic Auctions and Simple Index Rules , 2013, Math. Oper. Res..

[53]  Jonathan Levin,et al.  Sales Mechanisms in Online Markets: What Happened to Internet Auctions? , 2013 .

[54]  Jun Li,et al.  Are Consumers Strategic? Structural Estimation from the Air-Travel Industry , 2014, Manag. Sci..

[55]  J. C. Penney: Activist Investors and the Rise and Fall of Ron Johnson , 2014 .

[56]  Philipp Strack,et al.  Optimal Stopping with Private Information , 2014, J. Econ. Theory.

[57]  Brigitte Maier,et al.  Supermodularity And Complementarity , 2016 .

[58]  Andrzej Skrzypacz,et al.  All Revenue Management with Forward-Looking Buyers , 2016 .

[59]  Konrad Mierendorff,et al.  Optimal dynamic mechanism design with deadlines , 2016, J. Econ. Theory.

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