Availability and policy-compliance of many communication networks must be guaranteed at any time, even during updates. Accordingly, over the last years, the problem of how to update networks in a manner which transiently preserves desirable properties, has received much attention, especially in the context of Software-Defined Networks (SDNs). While important insights have been obtained for many different problem variants, in general, the design of efficient network update algorithms remains challenging, and usually new algorithms have to be developed on a case-by -case basis. This paper is motivated by the vision of fully automated communication networks in which consistent update schedules are synthesized automatically. In particular, we propose a game approach to the network update synthesis problem, and present NetStack, a tool based on Stackelberg games which transiently ensures fundamental properties such as reachability, loop-freedom, and waypointing. Our approach features a high flexibility. For example, with a simple extension, NetStack can also support concurrent updates, where in each round multiple routers are updated simultaneously. Our empirical evaluation shows that NetStack scales to realistic network sizes, and can compute optimal concurrent schedules.