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 1/(1-delta), 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 discount 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 unstaggered 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.