3-Strategy evolutionary game model for operation extensions of subway networks

With the growing demand for night travel and the development of the night-time economy, extending the operation time of metropolitan subway networks has become essential. This paper proposes a 2-population 3-strategy evolutionary game model for subway network operation extension decisions, which considers the interests of subway companies, passengers, and the government while addressing transfer failure between lines due to uncoordinated subway operation time adjustments. The study resolves the Evolutionary Equilibria (EEs) of the replicator dynamics system and identifies key factors influencing the evolutionary path using theoretical calculations and a ternary phase diagram. Additionally, an extended game model investigates the impact of adjustment minutes. To verify the models, a case study based on the Beijing subway network is conducted. We show that the rule of maximum total fitness ensures the priority of EE strategies for all lines, selecting Nash equilibrium strategies for the lines which cannot select EE in a vastly reduced network strategy profile space (from 729 to 2). The study concludes that combining subsidy measures can eliminate multiple equilibria produced by implementing only penalty measures, and combining penalty measures can have the effect of making small subsidies as effective as large subsidies. The variation of the satisfaction/loyalty affects the system equilibrium only when both game players value passenger satisfaction/loyalty. Finally, we find that the proper adjustment minutes not only can make operation extension a long-term best strategy but also increase the payoff (106,158 RMB/year) and enhance the occupancy rate (20 %) of the last train. The study provides a theoretical foundation for the government to regulate the operation extension of subway companies from multiple perspectives.