A Model of Ride Dispatch in Informal Market under Rival Entry

TL;DR

This paper models how an incumbent ride service provider optimally dispatches vehicles in a competitive environment with an entrant, balancing load, frequency, and customer patience, revealing strategic behaviors under competition and demand dynamics.

Contribution

It introduces a continuous-time model capturing incumbent dispatch strategies under rival entry, incorporating stochastic demand, customer tolerance, and competitive effects, which advances understanding of ride dispatch behavior.

Findings

Increased competition reduces dispatch thresholds, leading to more frequent, smaller loads.

Longer travel times raise the optimal dispatch threshold, but demand sensitivity affects actual behavior.

Demand decreases with waiting time, explaining partial loads and mid-route pickups.

Abstract

I develop a continuous-time model in which an incumbent batch-service provider faces stochastic passenger arrivals and must decide when to dispatch under the threat of customer defection to a faster entrant. The incumbent's problem is formalized as a trade-off between departure frequency and load maximization, with the option to accept mid-route pickups. I characterize the equilibrium dispatch strategy and show that increased competitive pressure strictly reduces the feasible departure threshold, leading to more frequent departures with smaller passenger loads. Longer travel times tend to raise the unconstrained optimal threshold, but realized dispatch behavior also depends on passenger tolerance for delay. Endogenizing demand by letting the arrival rate fall with expected waiting time yields an interior optimum, rationalizing why incumbents now (i) depart partially full and (ii) accept mid-route riders. Comparative statics show that the optimal threshold tends to increase with travel time under a mild regularity condition and decreases with competitive intensity.