Risk Averseness in 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 fundamentally from variation in cost perception, since uncertainty requires network users to have a strategy toward risk. The conventional approach to risk assignment is to associate a disutility with the standard deviation of cost by adding the standard deviation multiplied by an appropriate factor to the cost function for the link or route. However, this requires the specification of the cost distribution, which is more information than most network users possess. An alternative approach will be presented whereby the network user "plays through" all the possible eventualities before selecting his best route, on the assumption that "what might go wrong will go wrong". This is formulated as a n+m person, zero sum, non-cooperative game, where n players are network users who seek their best routes and m players are OD-specific demons who set out to penalise the network users as much as possible. The mixed strategy Nash equilibrium of this problem is shown to describe a risk averse traffic assignment. A simple solution procedure will be presented, along with an illustrative example.