A game theory approach to measuring the performance reliability of transport networks

Establishing the performance reliability of a transport network is an important practical problem for engineers and planners involved in network design. Methods proposed hitherto have assumed knowledge of link performance frequency distributions (usually delay, travel time or capacity distributions), information that is in many cases absent. In this paper, a two-player non-cooperative game is envisaged between on the one hand the network user seeking a path to minimise the expected trip cost and on the other hand an ‘evil entity’ choosing link performance scenarios to maximise the expected trip cost. At the Nash mixed strategy equilibrium, the user is unable to reduce the expected trip cost by changing his path choice probabilities while the evil entity is unable to increase the expected trip cost by changing the scenario probabilities, without cooperating. The Nash equlibrium measures network performance when users are extremely pessimistic about the state of the network and may therefore be used as a basis for a cautious approach to network design.