In the benchmark model of Bala and Goyal (2000) on network formation, the equilibrium network is asymmetric and unfair as agents have different payoffs. While they are prominent in reality, asymmetric networks do not emerge in the lab mainly because of fairness concerns. We extend this model with a sequential linking decision process to ease coordination and with heterogeneous agents. Heterogeneity is introduced with the presence of a special agent who has either a higher monetary value or a different status. The equilibrium is asymmetric and unfair. Our experimental results show that thanks to sequentiality and fairness concerns, individuals coordinate on fair and efficient networks in homogeneous settings. Heterogeneity impacts the network formation process by increasing the asymmetry of networks but does not decrease the level of fairness nor efficiency.