zbMATH — the first resource for mathematics

Price discrimination based on buyers’ purchase history. (English) Zbl 1391.91098
Summary: 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.
91B26 Auctions, bargaining, bidding and selling, and other market models
Full Text: DOI
[1] Acquisti, L; Varian, HR, Conditioning prices on purchase history, Market Sci, 24, 367-381, (2005)
[2] Armstrong M (2006) Recent developments in the economics of price discrimination In: Blundell R, Newey WK, Persson T (ed) Advances in economics and econometrics: theory and applications, Ninth World Congress of the Econometric Society volume 2. Econometric Society Monographs
[3] Ausubel, L; Deneckere, R, Reputation in bargaining and durable goods monopoly, Econometrica, 57, 511-531, (1989) · Zbl 0676.90006
[4] Ausubel, L; Deneckere, R, Durable goods monopoly with incomplete information, Rev Econ Stud, 59, 795-812, (1992) · Zbl 0760.90023
[5] Bagnoli, M; Salant, S; Swierzbinski, J, Durable-goods monopoly with discrete demand, J Polit Econ, 97, 1459-1478, (1989)
[6] Board S, Skrzypacz A (2010) Revenue management with forward looking buyers. Working paper
[7] Caillaud, B; Nijs, R, Strategic loyalty reward in dynamic price discrimination, Market Sci, 33, 725-742, (2014)
[8] Chen, Y, Paying customers to switch, J Econ Manag Strat, 6, 877-897, (1997)
[9] Coase, R, Durable goods monopolists, J Law Econ, 15, 143-150, (1972)
[10] Conitzer V, Taylor C, Wagman L (2010) Online privacy and price discrimination, Working paper
[11] Derman, C; Liebermann, GJ; Ross, SM, A sequential stochastic assignment problem, Manag Sci, 18, 349-355, (1972) · Zbl 0238.90054
[12] Esteves, RB; Reggiani, C, Elasticity of demand and behaviour-based price discrimination, Int J Ind Organ, 32, 46-56, (2014)
[13] Freixas, X; Guesnerie, R; Tirole, J, Planning under incomplete information and the ratchet effect, Rev Econ Stud, 52, 173-191, (1985) · Zbl 0555.90011
[14] Fudenberg, D; Levine, D; Tirole, J; Roth, A (ed.), Infinite-horizon models of bargaining with one-sided incomplete information, (1985), Cambridge
[15] Fudenberg, D; Tirole, J, Customer poaching and brand switching, RAND J Econ, 31, 634-657, (2000)
[16] Fudenberg, D; Villas-Boas, JM; Hendershott, T (ed.), Behavior based price discrimination and customer recognition, (2007), Amsterdam
[17] Gershkov, A; Moldovanu, B, Dynamic revenue maximization with heterogeneous objects: a mechanism design approach, Am Econ J Microecon, 1, 168-198, (2009)
[18] Gershkov, A; Moldovanu, B, Efficient sequential assignment with incomplete information, Games Econ Behav, 68, 144-154, (2010) · Zbl 1197.90277
[19] Gul, F; Sonnenschein, H; Wilson, R, Foundations of dynamic monopoly and the coase conjecture, J Econ Theory, 39, 155-190, (1986) · Zbl 0605.90037
[20] Hart, O; Tirole, J, Contract renegotiation and Coasian dynamics, Rev Econ Stud, 55, 509-540, (1988) · Zbl 0649.90024
[21] Hörner, J; Samuelson, L, Managing strategic buyers, J Polit Econ, 119, 379-425, (2011)
[22] Jing, B, Pricing experience goods: the effects of customer recognition and commitment, J Econ Manag Strat, 20, 451-473, (2011)
[23] Krishna V (2010) Auction theory, 2nd edn. Academic Press, Elsevier, Amsterdam
[24] Li KJ, Jain S (2015) Behavior-based pricing, an analysis of the impact of peer-induced fairness, working paper · Zbl 0649.90024
[25] Myerson, R, Optimal auction design, Math Operat Res, 6, 58-73, (1981) · Zbl 0496.90099
[26] Schmidt, K, Commitment through incomplete information in a simple repeated bargaining game, J Econ Theory, 60, 114-139, (1993) · Zbl 0803.90141
[27] Shin, J; Sudhir, K, A customer management dilemma: when is it profitable to reward one’s own customers?, Market Sci, 29, 671-689, (2010)
[28] Shin, J; Sudhir, K; Yoon, D, When to “fire” customers: customer cost-based pricing, Manag Sci, 58, 932-947, (2012)
[29] Skreta, V, Sequentially optimal mechanisms, Rev Econ Stud, 73, 1085-1111, (2006) · Zbl 1201.91085
[30] Sobel, J, Durable goods monopoly with entry of new consumers, Econometrica, 59, 1455-1485, (1991) · Zbl 0781.90026
[31] Sobel, J; Takahashi, I, A multistage model of bargaining, Rev Econ Stud, 50, 411-426, (1983) · Zbl 0515.90085
[32] Stokey, N, Intertemporal price discrimination, Quart J Econ, 93, 355-371, (1979) · Zbl 0426.90005
[33] Stokey, N, Rational expectations and durable goods pricing, Bell J Econ, 12, 112-128, (1981)
[34] Villas-Boas, JM, Dynamic competition with customer recognition, RAND J Econ, 30, 604-631, (1999)
[35] Villas-Boas, JM, Price cycles in markets with customer recognition, RAND J Econ, 35, 486-501, (2004)
[36] Zhang, J, The perils of behavior-based personalization, Market Sci, 30, 170-186, (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.