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Application of game theory in planning passenger rail and road transport on parallel routes

The game theory provides powerful tools for analysing transport systems and making decisions in situations, where there are opposite interests between the participants. This study proposes a methodology based on the game theory for selection the strategy of passenger transport planning on parallel routes for railway and road transport. The game theory presents the behaviour of the railway and road operators in conflict situations. The methodology uses dual linear programming to assess the strategies. The game is formulated between two transport operators (road and railway) that are competitors in passenger transportation. Two game models have been developed, one based on the profit of the road operator and the other based on the number of passengers. The road operator determines the profit, which is proportional to the flow of passenger traffic through the route. Its purpose is to maximize the overall transport profit. The aim of the railway operator is to minimize the overall transport costs. The research includes four steps. In the first step, the strategies of transportation for railway and road operators are determined. The second step includes formation of the decision matrix and mathematical representation of the problem for both transport operators. The third step gives the optimal strategies for both transport operators. The fourth step verifies the results by using the Hurwitz’s coefficient for decision making. The methodology has been approbated for the route Sofia-Burgas from the railway and road network of Bulgaria, which is a part of the Trans-European Transport Network. The strategies for both transport operators have been determined. The game-theoretic formalization presented in the study allows modelling strategies and decision making for both railway and road operators in the case of different interests.