On-the-track competition is a new phenomenon on the railway market, where operators compete on the same line for passengers. Similar reforms on the bus market have in some situations unleashed fierce, unsustainable competition and eventual return to monopoly; concerns have thus been raised over how prices, frequencies, travelvolumes and overall social welfare will develop. In particular, the existence of stable equilibrium with more than one player is questioned. The regulator plays a crucial role in this respect. Because of capacity constraints, it is by necessity involved in decisions regarding departure times and frequencies of service. Tweaks to regulatory proceedings alter the optimal strategies of market participants, and in turn social welfare and other outcomes. Assuming that the regulator strives to achieve a stable market equilibrium and high social welfare through the means of on-rail competition, what policies should be adopted? We suggest a simulation model with realistic parameters where operators compete on frequency and price. The model is built to facilitate comparison between different regulatory settings, including a duopoly market where the regulator allocates departure times; a profit-maximising monopoly; a large number of competitors; and others. It also includes bench-mark scenarios, such as welfare maximisation with a no subsidies constraint. The model allows for individual prices to be set for each departure, and it takes account of each departure’s relative position in time. In this way it builds explicitly on the hypothesis that competition occurs not only between operators but between departures that are close in time. This makes it possible to study how prices vary over the day, depending on the relative intensity of competition at certain times. Possible operator strategies to lessen the pressure of price competition are explored.