A multimodal multi-provider market equilibrium model: A game-theoretic approach

Document Type

Journal Article

Publication Date


Subject Area

policy - congestion, policy - environment, technology - alternative fuels, technology - emissions, economics - pricing, economics - operating costs, economics - benefits, planning - methods, planning - travel demand management


Multimodality, Transport planning, Complementarity formulation, Ride-sourcing, Ridesharing, Equilibrium


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.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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