Price Discrimination Based on Buyers’ Purchase History

We consider a repeated sales situation in which a seller sells one unit of a good each period to the same buyer. Having incomplete information about the buyer’s valuation, the seller responds to the buyer’s behavior, meaning, whether she bought previous units and at what price. We characterize the equilibrium of the no-commitment game for a uniform distribution and show that the seller discriminates between buyers based on their purchase history. Moreover, we show that the buyer’s ex-ante expected payoff is higher in the no-commitment game than in a game in which the seller can commit in advance to the prices he will charge (the commitment game). We also demonstrate that the buyer’s ex-post payoff is higher for each type of buyer in the no-commitment game. Social welfare is also higher in the no-commitment game. As the number of periods (units) increases, the opening prices decline, but fewer types of buyers accept the opening price.

[1]  Jiwoong Shin,et al.  A Customer Management Dilemma: When Is It Profitable to Reward One's Own Customers? , 2010, Mark. Sci..

[2]  Dae-Hee Yoon,et al.  When To Fire Customers? Customer Cost Based Pricing , 2011 .

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

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

[5]  J. Miguel Villas-Boas,et al.  Price Cycles in Markets with Customer Recognition , 2004 .

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

[7]  J. Tirole,et al.  Contract Renegotiation and Coasian Dynamics , 1988 .

[8]  Bernard Caillaud,et al.  Strategic Loyalty Reward in Dynamic Price Discrimination , 2014, Mark. Sci..

[9]  Raymond Deneckere,et al.  Durable Goods Monopoly with Incomplete Information , 1992 .

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

[11]  Robert B. Wilson,et al.  Foundations of Dynamic Monopoly and the Coase Conjecture , 1986 .

[12]  D. Fudenberg,et al.  Infinite-Horizon Models of Bargaining with One-Sided Incomplete Information , 1985 .

[13]  Nancy L. Stokey.  Rational Expectations and Durable Goods Pricing , 1981 .

[14]  D. Fudenberg,et al.  Behavior-Based Price Discrimination and Customer Recognition , 2007 .

[15]  Carlo Reggiani,et al.  Elasticity of demand and behaviour-based price discrimination , 2014 .

[16]  Lawrence M. Ausubel,et al.  REPUTATION IN BARGAINING AND DURABLE GOODS MONOPOLY , 1989 .

[17]  J. Sobel.  DURABLE GOODS MONOPOLY WITH ENTRY OF NEW CONSUMERS , 1991 .

[18]  J. Tirole,et al.  Planning Under Incomplete Information and the Ratchet Effect. , 1985 .

[19]  Vincent Conitzer,et al.  Online Privacy and Price Discrimination , 2010 .

[20]  J. Miguel Villas-Boas,et al.  Dynamic Competition with Customer Recognition , 1999 .

[21]  J. Sobel,et al.  A Multistage Model of Bargaining , 1983 .

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

[23]  H. Varian,et al.  Conditioning Prices on Purchase History , 2005 .

[24]  Klaus M. Schmidt.  Commitment Through Incomplete Information in a Simple Repeated Bargaining Game , 1993 .

[25]  Yongmin Chen,et al.  Paying Customers to Switch , 1997 .

[26]  Nancy L. Stokey.  Intertemporal Price Discrimination , 1979 .

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

[28]  Vasiliki Skreta.  Sequentially Optimal Mechanisms , 2000 .

[29]  R. Coase.  Durability and Monopoly , 1972, The Journal of Law and Economics.

[30]  M. Armstrong.  Recent developments in the economics of price discrimination , 2006 .

[31]  Juanjuan Zhang,et al.  The Perils of Behavior-Based Personalization , 2011, Mark. Sci..

[32]  D. Fudenberg,et al.  Customer Poaching and Brand Switching , 2000 .

[33]  Bing Jing,et al.  Pricing Experience Goods: The Effects of Customer Recognition and Commitment , 2011 .

[34]  Stephen W. Salant,et al.  Durable-Goods Monopoly with Discrete Demand , 1989, Journal of Political Economy.

[35]  Benny Moldovanu,et al.  Efficient sequential assignment with incomplete information , 2010, Games Econ. Behav..