– there may be a specialised attack that works well against each defence, and vice versa – but if evolutionary games on networks behave like more traditional evolutionary games, we may expect to find some strategies that do well overall, as ‘tit for tat’ does in multi-round prisoners’ dilemma. We may also expect to gain useful insights in the process.

Defense strategy 1 – random replenishment
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Our first defensive strategy is the simplest of all, and is one of the naive defences introduced in the above section. New nodes are joined to the graph at random. We assume that each attack round removes $r$ nodes, and the replenishment round adds exactly $r$ nodes, each of which is joined to the surviving vertices with probability $p$. $r$ remains constant for each run of the simulation, while $p$ increases from $k/(N-r)$ to $k/(N-1)$ as the replenishment proceeds. In this strategy, the defender does nothing in the adaptation phase.

This models the case where new recruits to a subversive network simply contact any other subversives they can find; no attempt is made to reshape the network in response to the capture of leaders but the network is simply allowed to become more 