Welfare Implications of Competing Two-Sided Platforms

We study the welfare implications of two-sided (decentralized) markets involving multiple intermediaries between buyers and sellers. For the analysis, we employ a stylized model where the intermediary sets the quantities of ad slots to purchase and sell, and the prices are a consequence of a Cournot model. The mathematics associated with the model is generic enough that it carries forward to other platform markets as well. Our analysis points to two main results. First, we find that with Cournot submarkets, the social welfare does not monotonically change with the number of competing intermediaries. This result is different from the standard Cournot models. Second, for various interconnected structures of the platform markets, we compute the price of anarchy as the ratio between social welfare generated in the market and the optima. We show that when when the marginal cost and marginal value functions are linear, the price of anarchy is at least 2/3. Lastly, we also present some analysis on network structure and its implication on the price of anarchy.