Public transport services under market arrangements, Part I: A model of competition between independent operators

A model of competition between public transport services operating on a single route is developed and its properties explored analytically and numerically. The passenger demand function incorporates both substitution between services, expressed through a multinomial logit model, and elastic demand for the public transport market as a whole. Each operator is assumed to maximize its net revenue. Expressions are derived for the Nash-Cournot equilibrium fares and frequencies, which determine the resultant profits to suppliers and consumer benefits to users. The sensitivity of the equilibrium configurations to changes in the parameters characterizing the demand for and cost of service provision is explored in a series of numerical studies. The equilibrium analysis allows explicit conclusions to be drawn about the determinants of market concentration and the emergence of monopolies.