Multiproduct Oligopoly and Bertrand Supertraps

Abstract

We study oligopoly price competition between multiproduct firms, firms whose products interact in the pro¯t function. Specifically, we focus on the impact of intra firm product interactions on the level of equilibrium prices and pro¯ts. This impact is divided into two effects: a direct effect and a strategic effect (i.e., through the competitors' actions). We derive conditions such that, if intra-firm product interactions cause prices to decrease (increase) while holding competitors' prices fixed, then the strategic effect hurts (benefits) the ¯rm. We also show that, under reasonable general assumptions, the strategic effect more than outweighs the direct effect, so that equilibrium pro¯ts vary in the direction opposite of the direct effect (Bertrand supertrap). Several instances of Bertrand supertraps are developed. For example, stronger demand complementarity or economies of scope lead to tougher price competition to an extent that may decrease profitability (even when the direct profit effect is positive). We present a number of applications of the general results, including learning curves, network effects, systems competition, bundling, switching costs, and internet cross-referencing.