A Nash equilibrium formulation of a tradable credits scheme for incentivizing transport choices: From next-generation public transport mode choice to HOT lanes

Document Type

Journal Article

Publication Date


Subject Area

place - urban, mode - bus, mode - bus rapid transit, mode - car, technology - geographic information systems, technology - ticketing systems, planning - service quality, ridership - behaviour


Tradable credits scheme, Binary atomic game, Nash equilibria, High-occupancy toll, Choice incentives


We consider a tradable credits scheme for binary transport games where one option is faster (or more comfortable) than the other, but its quality of service suffers when usage is high. Applications can be found in mode choice (public transit versus road transport), premium (i.e., express bus) versus ordinary public transit, and fast (e.g., high-occupancy toll, or HOT) versus regular lanes on expressways. We are motivated in particular by the choice between public transport and use of the road network as a privilege to be discouraged. In a future where GPS-based time-distance-place road charging exists, such next-generation transport management strategies become realizable as the choice to drive or not can be linked to a fixed fee toll, or indeed to a tradable credits scheme. When public transport payment uses the same smart card as the road usage fee (via tolls or tradable credits) usage of the two may be linked. In this setting, a public transport vs. road-use tradable credit scheme becomes feasible. In this case, individuals wishing to choose the faster option must obtain credits from other commuters via credit trading, rather than pay a direct toll or fee. Such a scheme creates a kind of equity, in the sense that lower-income commuters have an economic incentive to resort to the slower or less comfortable choice. We study the underlying market and its effects on individuals’ utilities; we use an atomic game framework so as to model explicitly the exchange process across users. The market we define determines the quantities of users choosing each option, as opposed to the prices themselves. Using the properties of potential games, we show that under mild assumptions, efficient Nash equilibria exist and can be reached using simple learning algorithms. We show that these equilibria can satisfy the transport authority’s requirements, and thus drive the transport system to a state where a desired proportion of individuals resort to each of the two options, when the scheme’s parameters are well tuned.


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


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