A Model of Ride Dispatch in Informal Market under Rival Entry

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.