We study network protection in a decentralized setting, where nodes can protect edges (or links) incident on it against an intelligent adversary capable of attacking edges. If an edge being attacked is not being defended the edge fails with a probability 0 <; p <; 1 (no-defense attack probability); if it is defended by only a single node it fails with probability q (single-defense attack probability), 0 ≤ q ≤ p; and, if it is defended by both the nodes the attack is successfully thwarted. We model the interaction between protecting nodes and the adversary as a game and study their equilibrium strategies. We note that in general the probability of an important link being defended by both of the nodes is higher compared to a less important link, such that a more important link fails with a lower probability. We also observe that the behavior of the adversary is radically different for the two different ranges of values of single-defense attack probability: 0 ≤ q ≤ p/2 and p/2 ≤ q ≤ p. We study the special scenarios of trees and connected communities and observe that in general the nodes will defend important links (such as cut edges) with high probability, while the adversary, in contrast to a centralized protection setting will attack less important links with a higher probability only in special scenarios.