Path disruption games

We propose Path Disruption Games (PDGs), which consider collaboration between agents attempting stop an adversary from travelling from a source node to a target node in a graph. PDGs can model physical or network security domains. The coalition attempts to stop the adversary by placing checkpoints in intermediate nodes in the graph, to make sure the adversary cannot travel through them. Thus, the coalition wins if it controls a node subset whose removal from the graph disconnects the source and target. We analyze this domain from a cooperative game theoretic perspective, and consider how the gains can be distributed between the agents controlling the vertices. We also consider power indices, which express the influence of each checkpoint location on the outcome of the game, and can be used to identify the most critical locations where checkpoints should be placed. We consider both general graphs and the restricted case of trees, and consider both a model with no cost for placing a checkpoint and a model with where each vertex has its own cost for placing a checkpoint.