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A little-understood phenomenon of customer reward programs is the prevalent use of finite reward expiration terms. We develop a theoretical framework to investigate the economic rationale behind this phenomenon and the trade-off between short and long expiration terms. In our model, a monopolistic firm sets the expiration term, along with the price and reward size, and interacts with consumers over an infinite horizon. Consumers are heterogeneous in shopping probabilities and product valuations and forward-looking in making purchase decisions. We find that a customer reward program with a finite expiration term can increase firm profits when (i) the valuation difference within the consumer population is intermediate and (ii) the shopping probabilities and valuations are negatively correlated among consumers. Several model extensions confirm the robustness of these results. Finally, we conduct an empirical investigation on the reward program practice of the top 100 U.S. retailers, which provides directional support for several key theoretical predictions.

Sun, Y., & Zhang, D. (2019). A model of customer reward programs with finite expiration terms. Management Science, doi:10.1287/mnsc.2018.3115