Sufficient Decisions in Multi-Sided and Multiproduct Markets

We show that in many models where firms make multiple decisions, analysis can be made more tractable by re-formulating the model into one where each firm makes a single choice, which we call a sufficient decision. The transformation allows application of standard techniques in these settings, including pass-through for tax incidence and upward pricing pressure for merger analysis. The transformation works because the assumption of profit maximization links the firms' decisions together. Example include models of monopoly and oligopoly in two-sided markets, where a natural sufficient decision may be the number of transactions that the firm facilitates, and multiproduct markets.