Risk-averse user equilibrium traffic assignment: an application of game theory

Transport network users frequently have to make route choices in the presence of uncertainty about route costs. Uncertainty about costs differs from variation in cost perception, since uncertainty requires network users to have a strategy toward risk. The conventional approach is to add a safety margin based on the standard deviation of link cost. However, this requires the specification of the cost distribution. An alternative approach is presented here whereby the network user ‘plays through’ all the possible eventualities before selecting his best route. A deterministic user equilibrium traffic assignment is shown to be equivalent to the mixed-strategy Nash equilibrium of an n-player, non-cooperative game. Then an n + m-player, non-cooperative game is formulated, where n network users seek their best routes and m origin–destination (OD)-specific demons penalise the network users maximally by failing links. The mixed-strategy Nash equilibrium of this game is shown to describe a risk-averse user equilibrium traffic assignment. A simple solution procedure is presented, along with an illustrative example.