van der Weijde, A.H., Verhoef, E. and van den Berg, V.A.C. (2013). Competition in multi-modal transport networks: A dynamic approach Transportation Research. Part B, Methodological, 53:31--44.

We analyze the behavior of market participants in a multi-modal commuter network, where roads are not priced, but public transport has a usage fee, which is set while taking the effects on the roads into account. In particular, we analyze the difference between markets with a monopolistic public transport operator, which operates all public transport links, and markets in which separate operators own each public transport link. To do so, we consider a simple dynamic transport network consisting of two serial segments and two parallel congestible modes of transport. We obtain a reduced form of the public transport operator's optimal fare setting problem and show that, even if the total travel demand is inelastic, serial Bertrand-Nash competition on the public transport links leads to different fares than a serial monopoly; a result not observed in a static model. This results from the fact that trip timing decisions, and therefore the generalized prices of all commuters, are influenced by all fares in the network. We then use numerical simulations to show that, contrary to the results obtained in classic studies on vertical competition, monopolistic fares are not always lower than duopolistic fares; the opposite can also occur. We also explore how different parameters influence the price differential, and how this affects welfare. {\textcopyright} 2013 Elsevier Ltd.