Sufficient Decisions in Multi-Sided and Multi-Product Markets

We show that in many applied economic models, it is possible to reduce the dimensionality of the space of actions to what we call sufficient decisions. We find that for monopoly and oligopoly in multi-sided markets and multi-product markets, the market equilibrium can be transformed into an equivalent market equilibrium in which each firm makes a single decision -- the volume of transactions. The transformation works because profit maximization connects a firm's decisions to each other, and it is often possible to introduce a constraint linking the firm's decisions. For example, the number of facilitated transactions is a sufficient decision for a monopolist in a two-sided market. We also analyze a related distortion, akin to the quality choice distortion by a profit maximizing firm. Our approach is useful for addressing economic questions in multi-sided and multi-product markets using standard intuition, comparative statics, and empirical tools developed for one-dimensional economic models.