Long-Lived Consumers, Intertemporal Bundling, and Tacit Collusion

The level of profits that can be sustained in repeated price game is higher when consumers are long-lived and firms can intertemporally bundle their output. With short-lived consumers, it is well known that any price and profit, up to the monopoly profit, can be sustained in a subgame perfect Nash equilibrium (SPNE) as long as the number of firms does not exceed 11−δ, or equivalently, the discount factor is greater than n−1 n, and that marginal cost pricing is the unique SPNE otherwise. We show that when firms face long-lived, repeat-purchase consumers and are free to offer intertemporal bundles, strictly positive profits can be supported for any number of firms and for any strictly positive dis-count factor. One equilibrium strategy that increases profits is to temporally segment the market with staggered long-term contracts and exploit the fact that consumers anticipate future price cuts in response to current deviations. A second, potentially more profitable, equilibrium strategy is to sell unstag-gered multi-period contracts and simultaneously offer single-period discounts in the period in which the multi-period contracts are being renewed. The single-period contracts are not purchased in equilibrium, but they limit firms’ incentives to cut price. ∗We want to thank George Deltas, Scott Stern, and especially Kathryn E. Spier for helpful comments. 1