Network Formation Game with Different Cost Value for Players

In Social Networks, it is often interesting to study type of networks formed, its efficiency with respect to social objective and which networks are stable. Many work have already been there in this area. Players in network formation game will incur some cost to form a link. In previous work, all player will have same cost for forming a link int he network. Here we will the study the optimal network and Nash equilibrium network when each player have different cost value for forming the link in the social network.