Precommitments in two-sided market competition

Abstract

Problem definition: We consider a two-sided market competition problem where two platforms, such as Uber and Lyft, compete on both supply and demand sides and study the impact of precommitments in a variety of practically motivated instruments on the equilibrium outcomes. Academic/practical relevance: We extend a set of classic oligopoly pricing results to account for two-sided competition under demand uncertainty. Methodology: We investigate multi-stage competition games. Results: We start with a sufficiently low demand uncertainty. First, we show that a precommitment made on the less competitive (demand or supply) side (on price or wage) has a less intense outcome than no commitment (i.e., spot-market price and wage competition). Then we show that, somewhat surprisingly, if the competition intensities of both sides are sufficiently close, the commission precommitment, where the platforms first compete in setting their commission rates and then their prices, is less profitable than no precommitment at all, and vice versa. Furthermore, we show that the capacity precommitment, in which the platforms first commit to a matching capacity and then set price and wage simultaneously subject to the precommitted capacity, leads to the most profitable outcome of all competition modes and extends the celebrated Kreps-Scheinkman equivalency to the two-sided market (without demand uncertainty). Then we extend the comparisons of various competition modes to account for a relatively high demand uncertainty. We show that the comparison between the spot-market price and wage competition and the commission precommitment stays the same as that with a sufficiently low demand uncertainty. In addition, the more flexible competition modes, such as no commitment and commission precommitment, benefit from higher demand uncertainty (with a fixed mean demand) because of their operational flexibility in response to the market changes. Further, a relatively high demand uncertainty may undermine or enhance the value of the wage precommitment, as opposed to no commitment. Finally, we also account for platforms with asymmetric parameters and matching friction and find that our main insights tend to be robust. Managerial implications: Our results caution platforms that a precommitment to the wrong instrument can be worse than no commitment at all. Moreover, the regulation of classifying gig workers as employees, despite many of its benefits to workers, may lead to a less competitive market outcome and, surprisingly, hurt gig workers by paying them lower wages.