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• Derive an analytical framework to determine the optimal matching time interval. • Analyze demand and supply curves under immediate matching strategies. • Optimize the platform's fleet size and price strategies. • Archieve joint profit maximization, social welfare, and second-best optimum. • Illustrate properties of pricing strategies under two immediate matching strategies. Supply/demand characteristics and price strategies in the ride-sourcing market are affected by matching strategies. In particular, immediate matching strategies are widely adopted to tackle supply–demand imbalance issues. This paper studies a two-sided ride-sourcing market under two immediate matching strategies: driver-first-come-first-serve and passenger-first-come-first-serve. In the former, the system is considered over-saturated with passengers, such that any driver is matched immediately upon posting their availability. Therefore, the market would be devoid of waiting drivers. In comparison, the latter strategy is oversaturated with drivers, such that any newly arriving passenger is immediately matched, and there are no waiting passengers in the system. We first derive generalized supply and demand functions and prove that the immediate matching strategies are optimal to maximize the number of completed trips under certain conditions based on equilibrium analysis. Then, we characterize the market equilibrium and discuss the properties of the wild-goose-chase phenomenon under two immediate matching strategies. We optimize the ride-sourcing platform's strategies to achieve a joint profit of platform and driver maximization (monopoly optimum), social welfare maximization (social optimum), and second-best optimum (entailing a reservation profit for the platform). Numerical experiments are conducted to demonstrate the effects of user heterogeneity, and the properties of pricing strategies under both matching strategies on the monopolistic and social optimal solution. The gained managerial insights provide suggestions for decision-makers to coordinate supply and demand in the ride-sourcing market. [ABSTRACT FROM AUTHOR]

• A multimodal multi-provider market equilibrium model is developed. • A congestion alleviation strategy through tolls and emission pricing is modelled. • Emission tax is modelled to model the EV technology penetration. • Private vehicle, walking, public transport, ride-sourcing, and ridesharing modes are modelled. The prominent planning components of recent transport systems are multimodality, pricing, shared mobility, and bundling. These systems consist of several service providers competing for a higher benefit or a lower cost. This paper proposes a generalised multi-modal multi-provider market equilibrium model to evaluate the operation of transport systems. The model includes the modes of a private vehicle, walking, public transport, ride-sourcing, ridesharing-as-driver, and ridesharing-as-rider. The economic behaviours of the service providers and a network operator are modelled using optimisation problems, i.e. their Karush–Kuhn–Tucker (KKT) optimality conditions in combination with user equilibrium conditions of travellers, forming a complementarity formulation for the market at equilibrium. Extensive computational experiments on an abstract network in Sydney demonstrate the use of the model for handling responses of various market players to EVs technological improvements, travel demand changes, restrictions on GHG emissions, and diminishing ridesharing use cultural barriers. [ABSTRACT FROM AUTHOR]