In their model of network formation, Berninghaus et al. (Exp Econ 9:237---251, 2006; J Evol Econ 17:317---347, 2007) showed that a periphery-sponsored star network is a strict Nash equilibrium. To examine the validity of their result, they also performed a laboratory experiment with human subjects, and they found that a periphery-sponsored star network can be formed, but when broken down, a different star network forms. In this paper, after considering some factors explaining this phenomenon, we develop a simulation system involving these factors with artificial autonomous agents. Through simulations using this system, we try to explain the behavior of human subjects in the network formation experiment, i.e., the fact that a strict Nash equilibrium periphery-sponsored star network is broken down and a different periphery-sponsored star network is formed.