Network games play a fundamental role in understanding behavior in many domains, ranging from communication networks through markets to social networks. Such networks are used, and also evolve due to selfish behavior of the users and owners. In light of these competing forces, it is surprising how efficient these networks are. It is an exciting challenge to understand the operation and success of these networks in game theoretic terms: what principles of interaction lead selfish participants to form such efficient networks? We study the degradation of quality of solution caused by the selfish behavior of users.