Horizontal cooperation in a multimodal public transport system: the profit allocation problem

We analyse the situation involving several transport companies in an intermodal public transport system. It is assumed that they cooperate by offering travel cards which can be used on all available means of transport. In order to solve the problem of profit allocation among the companies involved, we first introduce a coloured graph which describes the transport network and then propose a game theoretical approach to share the profit among the companies. Two new allocation rules, called the Coloured Egalitarian Solution and the Coloured Cost Proportional Solution, are introduced and axiomatically characterised. Furthermore, it is shown that both solutions provide stable allocations in the sense that they cannot be improved upon by any coalition of players.