How a Game Theoretic Approach Can Minimize the Cost of Train Passenger Services: An Intermodal Competition between Rail and Road Transport




Game theory, Dual linear programming, Hurwicz criterion, Minimum costs


Game theory models provide very powerful tools for evaluating strategies that are beneficial to both rail and road operators competing for passengers on parallel routes. This study examines how game theory can help rail operators who are incurring losses on passenger transport to identify strategies that can minimise costs, using the methodology of dual linear programming to analyse strategies. In identifying the best strategies for minimising costs for the railway operator, the best strategies for maximising profits for the road operators are also identified. The game model is set up between two passenger transport operators (rail and road) and is based on the income earned by the road operators from passengers. This study illustrates the following: how the strategies of the two competitors (rail and road) are determined; the formation of the payoff matrix and the presentation of the mathematical problem for the two competitors; and the results and verification of the best strategies for both competitors. The Leonid Hurwicz criterion was used to verify the optimal strategies.


National Assembly of Zambia: Committee on parastatal bodies on the examination of the annual reports for the tanzania zambia railway authority (2017). URL

Plumer, B.: Amtrak loses a ton of money each year. it doesn’t have to. URL

Kurosaki, F., Alexandersson, G.: Managing unprofitable passenger rail operations in japan-lessons from the experience in sweden. Research in Transportation Economics 69, 460-469 (2018). doi:10.1016/j.retrec.2018.07.019

Sharma, Y.S.: Railways see a revenue loss of rs 35,000 crore from passenger segment due to covid-19. URL

Glimcher, P.W., Fehr, E.: Neuroeconomics: Decision making and the brain. Academic Press (2013). URL

Tryson, Y.: The mediating effect of customer focus on the relationship between strategic planning and competitive advantage in railway sector. Journal of Operations and Strategic Planning 5(1), 59-81 (2022). doi:10.1177/2516600X221097756

Yangailo, T., Kaunda, M.: Total quality management a modern key to managerial effectiveness. LBS Journal of Management & Research 19(2), 91-102 (2021). doi:10.5958/0974-1852.2021.00008.0

Yangailo, T.: Globalization on the railway transport sector. International Research Journal of Business Studies 15(3) (2022). doi:

Yangailo, T., Kabela, J., Turyatunga, H.: The impact of total quality management practices on productivity in the railway sector in african context. Proceedings on Engineering 5(1), 177-188 (2023). doi:10.24874/PES05.01.015

Janelle, D.G., Beuthe, M.: Globalization and research issues in transportation. Journal of Transport Geography 5(3), 199-206 (1997). doi:10.1016/S0966-6923(97)00017-3

Talib, F., Rahman, Z.: Studying the impact of total quality management in service industries. International Journal of Productivity and Quality Management 6(2), 249-268 (2010). doi:10.1504/IJPQM.2010.034408

Simon, H.A.: Theories of decision-making in economics and behavioural science. Springer (1966). doi:10.1007/978-1-349-00210-8_1

Raturi, V., Verma, A.: A game-theoretic approach to analyse inter-modal competition between high-speed rail and airlines in the indian context. Transportation Planning and Technology 43(1), 20-47 (2020). doi:10.1080/03081060.2020.1701666

Roumboutsos, A., Kapros, S.: A game theory approach to urban public transport integration policy. Transport Policy 15(4), 209-215 (2008). doi:10.1016/j.tranpol.2008.05.001

Koryagin, M.: Game theory approach to optimizing of public transport traffic under conditions of travel mode choice by passengers. Transport problems 9 (2014). URL element/bwmeta1.element.baztech-4de4a91c-57ac-4847-a24e-059022a6685d

Yang, L., Shi, Y., Hao, S., Wu, L.: Route choice model based on game theory for commuters. Promet-Traffic&Transportation 28(3), 195-203 (2016). doi:10.7307/ptt.v28i3.1727

Bell, M.G.: A game theory approach to measuring the performance reliability of transport networks. Transportation Research Part B: Methodological 34(6), 533-545 (2000). doi:10.1016/S0191-2615(99)00042-9

Pašagić Škrinjar, J., Abramović, B., Brnjac, N.: The use of game theory in urban transport planning. Tehnički vjesnik 22(6), 1617-1621 (2015). doi:10.17559/TV-20140108101820

Ighodae, M., Ekoko, P.: Game theory and its relationship with linear programming models. Journal of the Nigerian Association of Mathematical Physics 17, 377-382 (2010). URL

Thie, P.R., Keough, G.E.: An introduction to linear programming and game theory. John Wiley & Sons (2011). URL

Pavzek, K., Rozman, Č.: Decision making under conditions of uncertainty in agriculture: a case study of oil crops. Poljoprivreda 15(1), 45-50 (2009). URL

Stoilova, S.: Application of game theory in planning passenger rail and road transport on parallel routes. In: Engineering for Rural Development. Proceedings of the International Scientific Conference (Latvia). Latvia University of Life Sciences and Technologies (2020). doi:10.22616/ERDev.2020.19.TF320

Ranking Strategies for Road Transport Player




How to Cite

Yangailo, T. (2023). How a Game Theoretic Approach Can Minimize the Cost of Train Passenger Services: An Intermodal Competition between Rail and Road Transport. Collective Dynamics, 8, 1–17.