Spatial Matching under Multihoming

<div> <div> <span>In spatial matching systems such as ride-hailing and delivery platforms, it is well known that monopolist platforms rely on admission controls---including surge pricing and dispatch thresholds---to maintain a buffer of idle supply, which reduces dispatch distances and improves labor utilization. However, given that suppliers often serve multiple platforms (i.e., multihoming) in competitive markets, it is unclear whether platforms still have the incentive to maintain such a buffer.</span> </div> <div> <br> </div> <div> We study this problem using a game-theoretic stochastic model of two platforms operating in a <i>d</i>-dimensional Euclidean space. Both platforms serve disjoint customer streams but draw from a shared pool of multihoming suppliers. We analyze equilibria under distance-threshold dispatch policies, where platforms serve customers only if a supplier is available within a given radius. </div> <div> <br> </div> <div> We find that in equilibrium, at least one platform accepts all profitable requests regardless of dispatch distance---a strategy we call undercutting---to gain market share. Two regimes emerge depending on market characteristics. When only one platform undercuts, the market achieves scale efficiencies comparable to a monopolist. When both undercut, which occurs in symmetric markets with scarce supply, the buffer erodes and inefficiencies arise. Hence, multihoming can harm operational efficiency in spatial matching markets, even when it reduces market fragmentation. This work gives a new justification for policies that either internalize the costs of dispatch distances to the platform or curb multi-homing---such as minimum hourly wage or loyalty incentives---to mitigate the risk of dispatch inefficiencies in spatial markets. </div> </div> <div> <br> </div>