Precommitments in Two-Sided Market Competition

We consider a two-sided market competition problem where two platforms compete in both supply and demand sides. We examine a variety of competition modes and study the impact of precommitment on the equilibrium outcomes. By comparing three types of competitions: simultaneous price and wage competition (with no precommitment), wage precommitment competition (followed by price competition), and price precommitment competition (followed by wage competition), we show that a precommitment made on the less competitive side has a less intensified outcome than no commitment. We show that commission precommitment, where the platforms first compete in setting their commission rates and then their prices, is less profitable than the precommitment in price or wage whichever is on the less competitive side. Moreover, commission precommitment is more profitable than no commitment when the competition intensity of one side is sufficiently higher than the other; however, when the competition intensities of both sides are sufficiently close, the commission precommitment can be less profitable than no precommitment at all. Further, we extend the celebrated Kreps-Scheinkman equivalency to the two-sided market and show that the capacity precommitment, in which the platforms first precommit to an initial matching capacity and then set price and wage simultaneously subject to the precommitted capacity, leads to the most profitable outcome among all competition modes. We then extend the comparison of various competition modes to account for demand uncertainty with positively or negatively correlated potential market sizes, reflecting weather-driven or spatial-dispersion uncertainty. We show that beyond the tradeoffs mentioned above without demand uncertainty, no commitment and commission precommitment benefit from more demand variability due to their operational flexibility in response to the market changes. Moreover, in comparison with no commitment, wage precommitment can tie the hands of platforms in responding to market changes, but can restrain cutthroat wage competition when the potential market sizes turn out to be high. The strengths of these two countervailing effects depend on the correlation of the platforms' market size uncertainties