We analyse the behaviour 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. As recent decades have seen a shift from governmental provision of public transport to provision by private firms, we test how different market structures influence public transport fares and social welfare, and how they compare with governmental provision. In particular, we analyse 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 transport network consisting of two serial segments and two parallel congestible modes of transport. Using a reduced form of the train operator’s optimal fare setting problem, we show that, even if the total travel demand is inelastic, serial Bertrand-Nash competition on the rail 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 generalised prices of all commuters, are influenced by all train 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 higher than duopolistic fares; the opposite can also occur. We also explore how different parameters influence the price differential, and how this affects welfare.