3-Strategy Evolutionary Game Model for Operation Extensions of Subway Networks

Abstract

The increasing demand for night travel and the development of the night-time economy urge operation time extension of metropolitan subway networks. This paper proposes a 3-strategy evolutionary game model for the subway network operation extension decisions, which considers the interests of subway companies, passengers and the government as well as effectively relieves the transfer failure between lines caused by the uncoordinated adjustment of subway operation time. We resolve the Evolutionary Equilibrium of the replicator dynamics system under different situations, thereby clarifying the key factors affecting the evolutional path by theoretical calculation and a ternary phase diagram. Meanwhile, an extended game model is established to investigate the effect of the extended duration of service on subway company decisions. To verify the above models, a case study based on the Beijing Subway Network is conducted. The main conclusions suggest that: (1) Reversing incentives from the government would fail the subway companies to extend their service time, and result in an inertia-dependency. Hence, positive incentives/subsidies are required to escape the dilemma. (2) The system equilibrium will not be affected by the change of satisfaction coefficient once only one player values passenger satisfaction. When both two players value passenger satisfaction to a certain degree, the operation extension strategy can become the only equilibrium of the system. (3) Changing the extended duration can shift the system equilibrium, and the appropriate extended duration can ensure the last train of one subway line serve nearly 26% more passengers without any additional total cost. The results provide a theoretical basis for the government to regulate the operation extension of subway companies from multiple perspectives.

Keywords: Subway networks, Operation extension strategy, 3-Strategy evolutionary game, Passenger satisfaction, Replicator dynamics