Two single-product firms with different quality levels and fixed limited capacities engage in sequential price competition in an essentially deterministic model where customers have heterogeneous valuations for both products. We develop conditions under which the leader (she) can take strategic advantage of her limited capacity by pricing relatively low, purposefully creating shortages and leaving some leftovers for the follower (him) to feast on, avoiding direct competition. The extent to which the leader benefits in this Leftovers Equilibrium depends on operational variables such as the capacity levels of the two firms and the sequence in which customers arrive at the market. We spell out the details for three different known arrival sequences within a specific subset of plausible fixed-capacity levels. The follower’s strategic shadow price can be positive even when not all his capacity is used, and the leader’s can be negative when all her capacity is used. We illustrate that Leftovers Equilibria can arise when some of our assumptions are relaxed.

The window between a film’s theatrical and video releases has been steadily declining with some studios now testing day-and-date strategies (i.e., when a film is released across multiple channels at once). We present a model of consumer choice that examines trade-offs between substitutable products (theatrical and video forms), the possibility of purchasing both alternatives, and the timing of consumption; this permits a normative study of the impact of smaller release windows (0-3 months) for which there is a scarcity of relevant data. In this setting, we demonstrate that congestion externalities can drive consumers to smooth consumption over time such that their derived equilibrium behavior is consistent with empirical observations: an exponentially time decaying demand. Using this equilibrium characterization, we first study how day-and-date strategies impact consumption incentives and explore their optimality from a profit-maximizing perspective. We establish that day-and-date strategies are optimal for films with high content durability (i.e., films whose content tends to lead consumers to purchase both alternatives). Furthermore, in circumstances where content durability is low and congestion cannot be efficiently reduced, day-and-date strategies are optimal for hit films while a direct-to-video strategy is optimal for lower value films. Interestingly, even at lower levels of congestion, a studio can optimally use a day-and-date strategy for films with content durability within a medium-low range. Second, we characterize the optimal delayed release strategy as influenced by congestion, content durability, and movie quality. We find that the optimal release time is non-monotonic in content durability: within an intermediate range of content durability, the optimal release time first increases in durability, then decreases. We also illustrate that, for relatively low quality movies, an increase in quality should be accompanied by a later video release time. Surprisingly, however, we observe the opposite for relatively higher quality movies: an increase in the quality can justify an earlier release of the video.