Imperfect competition with complements and substitutes

I study price competition in settings where end products are combinations of components supplied by different monopolists, nesting standard models of perfect complements and imperfect substitutes. I show sufficient conditions for a discrete-choice demand system to yield demand for each product which is log-concave in price, and has log-increasing differences in own and another product's price, leading to strong comparative statics results. Many results familiar from simple models, like the price effects of mergers or changes in marginal costs, extend naturally to this more complex setting.