Spatial Matching under Multihoming

Abstract

In spatial matching markets, such as ride-hailing and delivery services, academics and practitioners have stressed the importance of admission controls, such as surge pricing or matching systems, that maintain a sufficiently large "buffer'' of available supply to reduce dispatch distances and utilize labor time efficiently. However, the extent to which platforms have an incentive to maintain this buffer in competitive markets, where suppliers serve multiple platforms---a phenomenon known as multihoming---remains unclear.

This paper studies this issue using a game-theoretic stochastic model, representing two platforms in a spatial market. Both platforms serve disjoint streams of customer requests, but they draw from a shared pool of suppliers, i.e., suppliers multihome. We analyze the large-market equilibria resulting from two classes of admission control policies. We find that in equilibrium, at least one platform accepts all its profitable customer requests, a strategy we term "undercutting", in a bid to gain market share. However, depending on the market characteristics, two different regimes arise.
If both platforms undercut, the supply buffer is not maintained, and inefficiencies ensue. These scale-inefficient equilibria occur in symmetric markets where supply is scarce. In contrast, if only one platform undercuts, the market achieves scale efficiencies comparable to the monopolist scenario. Our results suggest that, in certain settings, multihoming might harm the operational efficiency of spatial matching markets even if it reduces market fragmentation.

Keywords: Spatial Matching, Duopoly, Price of Anarchy, Nash Equilibrium.