How does individuals’ cognition change a system which is a collective behavior of individuals? Or how does a system affect individuals’ cognition? To examine the interplay between a system and individuals, we study a cognition-based strategic link formation. When a network is not fully observable, individuals’ perception of a network plays an important role in decision making. Assuming that a communication link is costly and more accurate perception yields higher network utility, one decides whether to form a link in order to get better knowledge. A newly added link is a change in a network, which affects individuals’ perception accuracy back. We characterize the early stage of dynamics that a ring network is a global structure and there exists an agent who keeps the full information once a network is connected. Moreover, we discuss a local linking process which causes clusters and the influence of a positive cost of linking in the coevolution between a network and perception.