apply ideas from evolutionary game theory developed by Axelrod and others [@Axel84; @Axel97]. This theory studies how games of multiple rounds differ from single-round games, and it has turned out to have significant explanatory power in applications from ethology to economics.

We now formalise a model in which a game is played with a number of rounds. Each round consists of attack followed by recovery. Recovery in turn consists of two phases: replenishment and adaptation.

In the [**attack phase**]{}, the attacker destroys a number of nodes (or, in a variant, of edges); this number is his budget. He selects nodes for destruction according to some rule, which is his strategy. For example, he might at each round destroy the ten nodes with the largest number of edges connected to them. He executes this strategy on the basis of information about the network topology.

In the [**replenishment phase**]{}, the defending nodes recruit a number of new nodes, and go through a phase of establishing connections – again, according to given strategies and information.

In the [**adaptation**]{} phase, the defending nodes may rewire links within each connected component of the network, in accordance with some defensive strategy. The adaptation phase is applied 