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Many link formation mechanisms for the evolution of social networks have been successful to reproduce various empirical findings in social networks. However, they have largely ignored the fact that individuals make decisions on whether to create links to other individuals based on cost and benefit of linking, and the fact that individuals may use perception of the network in their decision making. In this paper, we study the evolution of social networks in terms of perception-based strategic link formation. Here each individual has her own perception of the actual network, and uses it to decide whether to create a link to another individual. An individual with the least perception accuracy can benefit from updating her perception using that of the most accurate individual via a new link. This benefit is compared to the cost of linking in decision making. Once a new link is created, it affects the accuracies of other individuals' perceptions, leading to a further evolution of the actual network. As for initial actual networks, we consider homogeneous and heterogeneous cases. The homogeneous initial actual network is modeled by Erd\H{o}s-R\'enyi (ER) random networks, while we take a star network for the heterogeneous case. In any cases, individual perceptions of the actual network are modeled by ER random networks with controllable linking probability. Then the stable link density of the actual network is found to show discontinuous transitions or jumps according to the cost of linking. As the number of jumps is the consequence of the dynamical complexity, we discuss the effect of initial conditions on the number of jumps to find that the dynamical complexity strongly depends on how much individuals initially overestimate or underestimate the link density of the actual network. For the heterogeneous case, the role of the highly connected individual as an information spreader is discussed., Comment: 8 pages, 7 figures

How does an individual's cognition change a system which is a collective behavior of individuals? Or, how does a system affect an individual's cognition? To examine the interplay between a system and individuals, we study a cognition-based network 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, an agent decides whether to form a link in order to get better information or not. Changes in a network with newly added links affect individuals' perception accuracy, which may cause further changes in a network. We characterize the early stage of network dynamics and information dispersion. Network structures in a steady state are also examined. Additionally, we discuss local interactions and a link concentration in a frequently changing network., Comment: 32 pages, 8 figures

Human dynamics is known to be inhomogeneous and bursty but the detailed understanding of the role of human factors in bursty dynamics is still lacking. In order to investigate their role we devise an agent-based model, where an agent in an uncertain situation tries to reduce the uncertainty by communicating with information providers while having to wait time for responses. Here the waiting time can be considered as cost. We show that the optimal choice of the waiting time under uncertainty gives rise to the bursty dynamics, characterized by the heavy-tailed distribution of optimal waiting time. We find that in all cases the efficiency for communication is relevant to the scaling behavior of the optimal waiting time distribution. On the other hand the cost turns out in some cases to be irrelevant depending on the degree of uncertainty and efficiency., Comment: 4 pages, 1 figure