Integrating equilibrium assignment in game-theoretic approach to measure many-to-many transportation network vulnerability

In transportation networks, the vulnerable links will be those which play a critical role and are therefore the most likely to be attacked. High-volume edges with few alternative paths represent obvious system vulnerabilities. Conflict between a terrorist organization and a transportation management agency can be characterized as two opponents who compete with each other to win a game. In this paper a mixed-strategy, stochastic game theoretic approach is presented to mathematically capture each player's strategy and predict the possible result. A game considering all possible origin-destination pairs is constructed between a router, which seeks to maximally ensure safety and efficiency for all travelers, and the tester, which seeks to maximally disrupt network performance by disabling links within the network. The User-equilibrium assignment is utilized for routing probabilities computing, while the Method of Successive Averages (MSA) is employed to update the link cost during the game play. The method is demonstrated on a small sample network and then applied to the Sioux Fall network and large scale city network of Anaheim, California.