the replenishment phase is exogenous.

A further initial assumption is that the attack and defence budgets are roughly equal. By this we will mean that for each node destroyed in the attack phase, one node will be replaced in the resource addition phase. Thus the network will neither grow or shrink in absolute size and we can concentrate on connectivity effects. We will discuss other possible assumptions later, but the static budgets and global attack / local defence assumptions will get us started.

Defence Evolution – First Round
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To analyse the vulnerability of a network, the selection of network elements (nodes or edges) destroyed in each round is the attacker’s choice and constitutes her strategy. The attacker wishes to maximize the network damage caused per unit of work.

We will start off by considering a static attacker, using what we know to be a reasonable attack (vertex-order), and examine how the defence strategy can adapt. Then we will see what better attacks can be found against the best defence we found. Then we will look for a defence against the best attack we found in the last round, and so on. There is no guarantee that the process converges 