The Impact of Informed Adversarial Behavior in Graphical Coordination Games

Abstract

How does system-level information impact the ability of an adversary to degrade performance in a networked control system? How does the complexity of an adversary's strategy affect its ability to degrade performance? This paper focuses on these questions in the context of graphical coordination games where an adversary can influence a given fraction of the agents in the system. Focusing on the class of ring graphs, we explicitly highlight how both (i) the complexity of the attack strategies and (ii) the knowledge of the graph structure and agent identities can be leveraged by an adversary to degrade system performance. We study four types of adversarial influence with varying degrees of knowledge and complexity. We find these models can be ranked: complex and informed adversaries can inflict more harm to the system whereas simple and uninformed adversaries have the least ability to inflict damage. arXiv:1909.02671v2 [eess.SY]

The Impact of Complex and Informed Adversarial Behavior in Graphical Coordination Games

“…j=1 j , which reduces to (19). One can prove sufficiency in a similar manner as step 1 from the previous section -by allocating the y adversaries with a spacing of 1 kα apart, the potential of y Ly exceeds that of any other a Ly = {y Ly , x Ly }.…”

“…By dynamic, we mean that the adversary can alter its behavior based on the current network state. That is, we consider stationary policies 1 {S x (a(t)), S y (a(t))} t=1,2,... . A static policy does not allow this flexibility: S x (a(t)) = S x and S y (a(t)) = S y ∀t.…”

“…x = ( x,1 , x,2 , x,3 ), 1 y = ( y,1 , y,2 , y,3 ) and s = (s 1 , s 2 , s 3 ) with s 1 > 0 and s 2 , s 3 < 0. Hence, we can find r 1 such that (r 1 ) s 1 = 0.…”

“…A defensive y strategy is implemented on all y-segments at any given time. In property 2, defensive x strategies are applied only if α < 1 2 , and to segments that are shorter than a threshold length. Furthermore, the strategy does not "activate" until there are at most two consecutive agents playing x in the segment.…”

Risk and security tradeoffs in graphical coordination games

“…The ν i correspond to the worst-case deterministic efficiencies J * b (α i ) = 1 − R * b (α i ) of the M gains and ni di to local efficiencies of selected partitions in the graph. Fact 2 will be used to establish (22), and Fact 3 for (23) (Theorem 3). We now identify a structural property required of worst-case graphs.…”