# Intertemporal price discrimination with forward-looking consumers: Application to the US market for console video-games

## Abstract

Firms in durable good product markets face incentives to intertemporally price discriminate, by setting high initial prices to sell to consumers with the highest willingness to pay, and cutting prices thereafter to appeal to those with lower willingness to pay. A critical determinant of the profitability of such pricing policies is the extent to which consumers anticipate future price declines, and delay purchases. I develop a framework to investigate empirically the optimal pricing over time of a firm selling a durable-good product to such strategic consumers. Prices in the model are equilibrium outcomes of a game played between forward-looking consumers who strategically delay purchases to avail of lower prices in the future, and a forward-looking firm that takes this consumer behavior into account in formulating its optimal pricing policy. The model outlines first, a dynamic model of demand incorporating forward-looking consumer behavior, and second, an algorithm to compute the optimal dynamic sequence of prices given these demand estimates. The model is solved using numerical dynamic programming techniques. I present an empirical application to the market for video-games in the US. The results indicate that consumer forward-looking behavior has a significant effect on optimal pricing of games in the industry. Simulations reveal that the profit losses of ignoring forward-looking behavior by consumers are large and economically significant, and suggest that market research that provides information regarding the extent of discounting by consumers is valuable to video-game firms.

## Keywords

Durable-good pricing Forward-looking consumers Markov-perfect equilibrium Numerical dynamic programming Video-game industry## JEL Classification

C25 C61 D91 L11 L12 L16 L68 M31## Notes

### Acknowledgement

I thank my dissertation committee, Pradeep Chintagunta, Jean-Pierre Dubé, Günter Hitsch, and Peter Rossi for their guidance. I am grateful to Ester Han, Karen Sperduti and Sima Vasa of the NPD group, and R. Sukumar of IPSOS-Insight for their help in making available the data used in this research. I thank Dan Alderman of the Microsoft Xbox group, and Norman Basch of Reservoir Labs for sharing with me their insights on the video-game industry. I also received useful feedback from Tim Conley, Ulrich Doraszelski, Liran Einav, Wes Hartmann, Puneet Manchanda, Peter Reiss, Alan Sorensen two anonymous referees and seminar participants at Berkeley, CMU, Columbia, Cornell, Dartmouth, HKUST, ISB, MIT, Northwestern, Purdue, Stanford, UCLA, UConn, UMaryland, UPenn, UToronto, UWisconsin, Washington St. Louis and Yale.

## References

- Balachander, S., & Srinivasan, K. (1998). Modifying customer expectations of price decreases for a durable product.
*Management Science, 44*(6), 776–786.Google Scholar - Bass, F. (1969). A new-product growth model for consumer durables.
*Management Science, 15*, 215–227.Google Scholar - Benýtez-Silva, H., Hall, G., Hitsch, G., Pauletto, G., & Rust, H. (2000).
*A comparison of discrete and parametric approximation methods for continuous-state dynamic programming problems*. Working paper, SUNY-Stony Brook.Google Scholar - Benkard, L. (2004). A dynamic analysis of the market for wide-bodied commercial aircraft.
*Review of Economic Studies, 71*, 581–611.CrossRefGoogle Scholar - Berry, S. (1994). Estimating discrete choice models of product differentiation.
*Rand Journal of Economics, 25*(2), 242–261.CrossRefGoogle Scholar - Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile prices in market equilibrium.
*Econometrica, 60*(4), 841–890.CrossRefGoogle Scholar - Besanko, D., Dubé, J. P., & Gupta, S. (2003). Competitive price discrimination strategies in a vertical channel with aggregate data.
*Management Science, 49*(9), 1121–1138.CrossRefGoogle Scholar - Besanko, D., & Winston, W. (1990). Optimal price skimming by a monopolist facing rational consumers.
*Management Science, 36*(5), 555–567.CrossRefGoogle Scholar - Bulow, J. (1982). Durable goods monopolists.
*Journal of Political Economy, 90*, 314–332.CrossRefGoogle Scholar - Chevalier, J., & Goolsbee, A. (2005).
*Are durable good consumers forward looking*?*Evidence from college textbooks*. Working paper, University of Chicago.Google Scholar - Ching, A. (2005).
*Consumer learning and heterogeneity: Dynamics of demand for prescription drugs after patent expiration*. Working paper, Rotman School of Management, University of Toronto.Google Scholar - Chintagunta, P. (1999).
*A flexible aggregate logit model*. Working paper, University of Chicago.Google Scholar - Chintagunta, P., Dube, J.-P., & Goh, K.-Y. (2005). Beyond the endogeneity bias: The effect of unmeasured brand characteristics on household-level brand choice models.
*Management Science, 51*(2).Google Scholar - Coase, R. (1972). Durability and monopoly.
*Journal of Law and Economics, 15*, 143–149.CrossRefGoogle Scholar - Conlisk, J. Gerstner, E., & Sobel, J. (1984). Cyclic pricing by a durable good monopolist.
*Quarterly Journal of Economics, 99*(3), 489–505 (August).CrossRefGoogle Scholar - Coughlan, P. (2001).
*Competitive dynamics in home video-games*. J, K: Harvard Business School Cases.Google Scholar - Desai, P., & Purohit, D. (1999). Competition in durable goods markets: The strategic consequences of leasing and selling.
*Marketing Science, 18*(1), 42–58.Google Scholar - Dolan, R., & Jeuland, A. (1981). Experience curves and dynamic demand models: Implications for optimal pricing strategies.
*Journal of Marketing, 45*, 52–62.CrossRefGoogle Scholar - Dubé, J. P., Hitsch, G., & Manchanda, P. (2005). An empirical model of advertising dynamics.
*Quantitative Marketing and Economics, 3*(2), 107–144.CrossRefGoogle Scholar - Einav, L. (2006). Seasonality in the U.S. motion picture industry.
*RAND Journal of Economics*, (forthcoming).Google Scholar - Erdem, T., Keane, M. P., & Strebel, J. (2005). Learning about computers: An analysis of information search and technology choice.
*Quantitative Marketing and Economics, 3*(3), 207–247.CrossRefGoogle Scholar - Godfrey, L. G. (1978). Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables.
*Econometrica, 46*, 1293–1302.Google Scholar - Gowrisankaran, G., & Rysman, M. (2006).
*Dynamics of consumer demand for new durable goods*. Working paper, Washington University at St. Louis.Google Scholar - Gul, F., Sonneenschein, H., & Wilson, R. (1986). Foundations of dynamic monopoly and the coase conjecture.
*Journal for Economic Theory, 39*, 155–190.CrossRefGoogle Scholar - Hitsch, G. (2006). An empirical model of optimal dynamic product launch and exit under demand uncertainty.
*Marketing Science, 25*(1), 25–50.CrossRefGoogle Scholar - Horsky, D. (1990). A diffusion model incorporating product benefits, price, income, and information.
*Marketing Science, 9*(Fall), 342–365.Google Scholar - Interactive Digital Software Association (IDSA) (2001).
*State of the Industry Report: 2000–2001*. http://www.idsa.com/pressroom.html, accessed July 21, 2004. - Judd, K. (1998).
*Numerical methods in economics*. Cambridge: MIT Press.Google Scholar - Kahn, C. (1986). The durable good monopolist and consistency with increasing costs.
*Economterica, 54*, 275–294.CrossRefGoogle Scholar - Kalish, S. (1983). Monopolistic pricing with dynamic demand and production cost.
*Marketing Science, 2*, 135–160.Google Scholar - Kalish, S. (1985). A new product adoption model with pricing, advertising and uncertainty.
*Management Science, 31*, 1569–1585.Google Scholar - Kamakura, W. A., & Russell, G. (1989). A probabilistic choice model for market segmentation and elasticity structure.
*Journal of Marketing Research, 26*, 379–390.CrossRefGoogle Scholar - Keane, M. P., & Wolpin, K. I. (1994). The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte Carlo evidence.
*Review of Economics and Statistics, 76*, 648–672.CrossRefGoogle Scholar - Krishnan, T., Bass, F., & Jain, D. (1999). Optimal pricing strategy for new products.
*Management Science, 45*(12), 1650–1663.Google Scholar - Landsberger, M., & Meilijson, I. (1985). Intertemporal price discrimination and sales strategy under incomplete information.
*Rand Journal of Economics, 16*(3), 424–430.CrossRefGoogle Scholar - Lazear, E. (1986). Retail pricing and clearance sales.
*American Economic Review, 76*(1), 14–32.Google Scholar - Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models.
*Biometrika, 65*, 297–303.CrossRefGoogle Scholar - Mahajan, V., Muller, E., & Kerrin, R. A. (1984). Introduction strategy for new products with positive and negative word-of-mouth.
*Management Science, 30*, 1389–1404.Google Scholar - Melnikov, O. (2000).
*Demand for differentiated durable products: The case of the U.S. computer printer market*. Working paper, Yale University.Google Scholar - Moorthy, K. S. (1988). Consumer expectations and the pricing of durables. In T. Devinney (Ed.),
*Issues in pricing*. Lexington, MA: Lexington Books.Google Scholar - Narasimhan, C. (1989). Incorporating consumer price expectations in a diffusion model.
*Marketing Science, 8*(4), 343–357.Google Scholar - Pashigian, B. P. (1988). Demand uncertainty and sales: A study of fashion and markdown pricing.
*American Economic Review, 78*, 936–953.Google Scholar - Petrin, A., & Train, K. (2004).
*Omitted product attributes in discrete choice models*. Working paper. Graduate School of Business, University of Chicago.Google Scholar - Robinson, B., & Lakhani, C. (1975). Dynamic pricing models for new product planning.
*Management Science, 10*, 1113–1122.Google Scholar - Rust, J. (1987). Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher.
*Econometrica, 55*(5), 999–1033.CrossRefGoogle Scholar - Rust, J. (1996). Numerical dynamic programming in economics. In H. Amman, D. Kendrick, & J. Rust (Eds.),
*Handbook of computational economics*. North Holland: Elsevier.Google Scholar - Serlin, J. (1998).
*“FuncoLand Inc.,” Cornell Equity Research*. Johnson School of Management, Cornell University. http://parkercenter.johnson.cornell.edu/docs/other_research/1998_fall/fnco.pdf, July 2004. - Song, I., & Chintagunta, P. (2003). A micromodel of new product adoption with heterogeneous and forward-looking consumers: Application to the digital camera category.
*Quantitative Marketing and Economics, 1*(4), 371–407.CrossRefGoogle Scholar - Stokey, N. (1979). Intertemporal price discrimination.
*Quarterly Journal of Economics, 93*(3), 355–371.CrossRefGoogle Scholar - Stokey, N. (1981). Rational expectations and durable goods pricing.
*Bell Journal of Economics, 12*, 112–128.CrossRefGoogle Scholar - Tirole, J. (1988).
*The theory of industrial organization*. Cambridge: MIT Press.Google Scholar - Villas-Boas, M., & Winer, R. (1999). Endogeneity in brand choice models.
*Management Science*(45), 1324–1338.Google Scholar - Williams, D. (2002). Structure and competition in the U.S. home video game industry.
*International Journal on Media Management, 4*(1), 41–54.Google Scholar - Yang, S., Chen, Y., & Allenby, G. M. (2003). Bayesian analysis of simultaneous demand and supply.
*Quantitative Marketing and Economics, 1*, 251–304.CrossRefGoogle Scholar