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

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## 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.

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