Dynamic interdiction games on PERT networks

In a PERT network interdiction game one player tries to get a project, represented as a PERT graph, finished as quickly as possible by allocating resources, expediting the project’s tasks and choosing between different technologies to use. At the same time a second player aims to maximally delay the project’s completion date by carefully choosing which tasks to disrupt. We develop a novel continuous time model of the game, showing that it can be solved as an MDP. We then implement an efficient exact dynamic programming algorithm for it and propose extensions involving implementation uncertainty and crashing with renewable resources. In addition, we demonstrate that approximate techniques for solving our models can alleviate the ‘the curse of dimensionality’.