Optimal choices of fare collection systems for public transportations: Barrier versus barrier-free

The present study focuses on two major types of fare collection systems for public transportations, barrier and barrier-free, and provides a mathematical framework to evaluate optimal choices between them, i.e., which system can be more profitable for a transit agency. In particular, we consider game-theoretic interactions between the transit agency and passengers for the barrier-free system and suppose that frequencies of free rides of passengers as well as inspections of the transit agency are given as a Nash equilibrium. Then the optimal choice of fare collection system is described as a subgame perfection solution in an extensive form game. We also conduct a comparative static analysis and examine how each parameter can affect the choice. As an application, we use the framework to explain various choices of fare collection systems in our society depending on local circumstances or transportation types.