Design of an Optimal Frequency Reward Program in the Face of Competition
We optimize the design of a frequency reward program against traditional pricing in a competitive duopoly, where customers measure their utilities in rational economic terms. We assume two kinds of customers: myopic and strategic . Every customer has a prior loyalty bias  toward the reward program merchant, a parameter drawn from a known distribution, indicating an additional probability of choosing the reward program merchant over the traditional pricing merchant. Under this model, we characterize the customer behavior: the loyalty bias increases the switching costs  of strategic customers until a tipping point, after which they strictly prefer and adopt the reward program merchant. Subsequently, we optimize the reward parameters to maximize the revenue objective of the reward program merchant. We show that under mild assumptions, the optimal parameters for the reward program design to maximize the revenue objective correspond exactly to minimizing the tipping point of customers and are independent of the customer population parameters. Moreover, we characterize the conditions for the reward program to be better when the loyalty bias distribution is uniform - a minimum fraction of population needs to be strategic, and the loyalty bias needs to be in an optimal range. If the bias is high, the reward program creates loss in revenues, as customers effectively gain rewards for “free”, whereas a low value of bias leads to loss in market share to the competing merchant. In short, if a merchant can estimate the customer population parameters, our framework and results provide theoretical guarantees on the pros and cons of running a reward program against traditional pricing.
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