Feasting on leftovers: Strategic use of shortages in price competition among differentiated products

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.