To Commit or Not to Commit: Revisiting Quantity vs. Price Competition in a Differentiated Industry

Previous studies have shown that quantity commitment by all firms in an industry mitigates price competition. This paper shows that when firms have a choice, asymmetric outcomes can arise, with some firms choosing to commit to quantity and other firms choosing not to. To study the commitment decision, we analyze a multi-stage game within a duopoly of differentiated firms a la Hotelling. In the first stage of the game, firms choose whether or not to commit to quantity. In the second stage, each firm that chose to commit sets quantity, which represents an upper bound on how much it can sell to consumers. In the third stage, both firms set prices strategically, regardless of whether or not they committed. In the final stage, demand is allocated as consumers maximize their utilities. Firm(s) that chose not to commit to quantity in the first stage can fulfill any quantity that consumers demand at the equilibrium prices. We find that if product differentiation is sufficiently low, both firms choose to commit to quantity in equilibrium. This symmetric equilibrium allows both firms to avoid the intense price competition associated with low product differentiation. If the level of differentiation is sufficiently high, the equilibrium in quantity commitment is asymmetric such that one firm chooses to commit while its competitor chooses not to commit. Under this equilibrium, a pricing equilibrium in pure strategies does not exist, only a pricing equilibrium in mixed strategies does, and the equilibrium prices can result in a committed firm not clearing the entire quantity it chose earlier.