Solving non-zero sum multiagent network flow security games with attack costs

Moving assets through a transportation network is a crucial challenge in hostile environments such as future battlefields where malicious adversaries have strong incentives to attack vulnerable patrols and supply convoys. Intelligent agents must balance network costs with the harm that can be inflicted by adversaries who are in turn acting rationally to maximize harm while trading off against their own costs to attack. Furthermore, agents must choose their strategies even without full knowledge of their adversaries' capabilities, costs, or incentives. In this paper we model this problem as a non-zero sum game between two players, a sender who chooses flows through the network and an adversary who chooses attacks on the network. We advance the state of the art by: (1) moving beyond the zero-sum games previously considered to non-zero sum games where the adversary incurs attack costs that are not incorporated into the payoff of the sender; (2) introducing a refinement of the Stackelberg equilibrium that is more appropriate to network security games than previous solution concepts; and (3) using Bayesian games where the sender is uncertain of the capabilities, payoffs, and costs of the adversary. We provide polynomial time algorithms for finding equilibria in each of these cases. We also show how our approach can be applied to games where there are multiple adversaries.