The vulnerability of a transportation network is strongly correlated with the ability of the network to withstand shocks and disruptions. A robust network with strategic redundancy allows traffic to be redistributed or reassigned without unduly compromising system performance. High-volume edges with limited alternative paths represent system vulnerabilities—a feature of transportation networks that has been exploited to identify critical components. A mixed-strategy, stochastic game-theoretic approach is presented for the measurement of network vulnerability. This method is designed to incorporate all origins and destinations in a network in a computationally efficient manner. The presented method differs from previous efforts in that it provides a many-to-many measure of vulnerability and edge-based disruptions that may not reside on a common path. A game that considers all possible origin–destination pairs is constructed between a router, which seeks minimum cost paths for travelers, and a network tester, which maximizes travel cost by disabling edges within the network. The method of successive averages is used for routing probabilities, and a weighted entropy function is employed to compute edge-disruption probabilities. The method is demonstrated on a small example network and then applied to the Sioux Falls, South Dakota, network. Results indicate good correspondence with a previous method that used equilibrium assignment and rapid solution convergence.