Multi-Product Duopoly with Cross-Product Cost Interdependencies

Abstract

Many multi-product firms incur a complexity fixed cost when offering different product lines in different quality tiers relative to the case when offering all products lines in the same quality tier (high or low). Such fixed costs create an interdependency between firms' choices of quality tiers across different product lines, even when demands are independent. We investigate the effects of this interdependency on equilibrium profits in a Stackelberg duopoly game. Both firms' profits are (weakly) higher when the complexity cost is infinite than when it is 0. The Stackelberg leader's profits are always (weakly) higher with a positive complexity fixed cost, but its profits can be non-monotonic in the magnitude of this cost. The Stackelberg follower's profits can be lower when the complexity fixed cost is positive than when it is equal to 0.