Exploring the congested parallel route problem with variable substitutability

Many transport and other service problems come down to simple network choices: what mode and/or route to take, when some of the routes and modes are congested and their use can be priced or not priced by different operators. The operators can have different objectives and face different market environments: public or private monopoly, private duopoly, etc.. This standard problem has been studied in many variants, mostly using the assumption of perfect substitutability between alternatives, so that in the deterministic Wardrop equilibrium, all routes that are used have the same generalized cost. This paper examines in more detail the role of the substitutability assumption using varying degrees of unobserved individual heterogeneity. Users of a network consume transport services, which are differentiated in two ways. There are objective differences in quality (length of route, congestion level) perceived in the same way by all users but there are also individual idiosyncratic preferences or unobserved heterogeneity (e.g. in modal choice) for transport services. The resulting stochastic equilibrium is analysed on a simple parallel network for four types of ownership regimes: private ownership, coordinated public ownership, mixed public-private and public Stackelberg leadership. First we synthesize the literature and prove rigorously that when total demand is fixed and there is congestion, then by controlling one route a government can achieve the First Best allocation, irrespective of whether the second route is privately operated or unpriced. This result holds whatever the level of substitutability and whatever the levels of congestion on the two routes. Secondly, we rank ownership regimes when the government cannot control the pricing of any route. If there is no congestion, no pricing is obviously best and second best is to have only the inferior route privately priced. If there is congestion and the heterogeneity in the preferences is limited, it is still best to have the more congestible route privately tolled.