Allocation Problem For The Platform of Platforms In A Two-Sided Service Market

We study the Allocation Problem for the Platform of Platforms (abbreviated as AP3) in a two-sided service market, where a third-party integrator tries to allocate customers to workers separately controlled by a set of online platforms in a manner that satisfies all stakeholders. AP3 is a natural Stackelberg game. The integrator, as a leader, influences the outcome of the game by pricing the service, whereas the platforms (followers) are given the freedom to accept or reject customers to maximize their own profit, given the prices set by the integrator. A set of nonlinear constraints are imposed on the leader's problem to eliminate artificial scarcity, derived from the integrator's monopoly power. We formulate AP3 as a Stackelberg bipartite matching problem, which is known to be NP-hard in general. Our main result concerns the proof that AP3 can be reduced to a polynomially solvable problem by taking advantage of, somewhat paradoxically, the "hard" requirement of ruling out artificial scarcity. Numerical experiments are conducted using the ride-hail service market as a case study. We find artificial scarcity negatively affects the number of customers served, although the magnitude of the effect varies with market conditions. In most cases, the integrator takes the lion's share of the profit, but the need to eliminate artificial scarcity sometimes forces them to concede the benefits of collaboration to the platforms. The tighter the supply relative to the demand, the more the platforms benefit from removing artificial scarcity. In an over-supplied market, however, the integrator has a consistent and overwhelming advantage bestowed by its monopoly position