Unveiling coopetition dynamics between shared mobility and public transport: A game-theoretic approach

The liberalization of the transport market and advancements in real-time information technologies have prospered various shared mobility services, such as ridesourcing and carsharing. The emergence of these services complicates the relationships between them and public transport, as they often compete and cooperate simultaneously. This study develops a game-theoretic model to unveil these interactions using a multi-leader single-follower framework. In this framework, operators set their service rates as leaders, while travelers are assigned to services based on a logit model, which influences the profitability of both operators. The public transport operator may also subsidize travelers who use shared mobility service to access first- or last-mile trips, referring to as the bundle services. We reformulate the resulting nonlinear, nonconvex problem into a standard convex bilevel model by using outer linear approximations and applying KKT conditions to replace the lower-level problem. An iterative algorithm is developed to solve the game-theoretical model, complemented by an optimization-based bound tightening technique to enhance solution efficiency and accuracy. Our findings show that smaller operators, limited by budget constraints, are more likely to cooperate in bundle services for longer distances but tend to compete for shorter distances. In contrast, larger operators strategically alternate between competition and cooperation based on market conditions. Furthermore, well-designed subsidies in the bundle services can incentivize cooperation between shared mobility and public transport, benefiting both operators and travelers.