Bertrand Supertraps - Cabral, Luís M. B.; Villas-Boas, Miguel (Management Science, 2005)
We study oligopoly price competition between multiproduct firms—firms whose products interact in the profit function. Specifically, we focus on the impact of intrafirm product interactions on the level of equilibrium profits. This impact may be decomposed in two different ways: (a) a direct effect (keeping the competitors’ actions fixed) plus a strategic effect (i.e., through the competitors’ actions); or, alternatively, (b) a competitive advantage effect (change in firm i only) plus an imitation effect (change in all other firms). We derive conditions such that (a) the strategic effect more than outweighs the direct effect, and conditions such that (b) the imitation effect more than outweighs the competitive advantage effect: Bertrand supertraps. For example, an increase in the degree of economies of scope would increase profits if prices were fixed or if the change were limited to firm i’s cost function. However, if all firms increase the degree of economies of scope then all firms receive lower profits. A variety of other applications is considered, including learning curves, core competencies, demand synergies, systems competition, compatibility, bundling, network effects, switching costs, durable goods, long-term contracts.