Dynamic competition for customer memberships

This paper analyzes a two‐period membership market with two symmetric firms charging a membership fee, allowing consumers to buy products or services at a given price. Firms can offer short‐term (ST) or long‐term (LT) memberships. When firms employ LT memberships, they have incentives to prevent their old customers from being poached by competitors and price‐discriminate them based on purchase behavior. Conversely, ST memberships lead to no unit price discrimination for old customers, but instead, they lead to membership fee discrimination, increasing the share of switchers. We find that, under general assumptions, ST memberships are offered in equilibrium. This result is robust to various extensions, including switching coupons or discounts, naive consumers, sunk costs, and asymmetric differentiation parameters. We find that firms are indifferent between ST and LT memberships only when the customer's switching coupon or discount is high relative to the transportation cost.