The network of social relations among individuals has deep effects on many economic and social processes. It is evident that acquaintances bear an important factor in conveying opportunities and information. This has already been formally recognized by sociologists in the seminal paper of Granovetter [6], who analyzes the contacts that influence the job market. However, it has been incorporated into game theoretical modelling only in the recent past, because of the technical difficulties of including graph theory in a framework of full rationality, as indicated already by some attempts as Myerson [10]. Since the 1990s there has been an increased interest, from many disciplines, in the study of complex networks, and this has led to a new branch of research in game theory, that has been steadily increasing since then. Formally, there are different ways in which the network topology can play a role in a game, either in the actions, because for example the network itself results from the strategy profiles, or through payoffs, because for example the network imposes limitations on the externalities between players.

The first works in this area applied a combination of solution concepts from cooperative and non-cooperative game theory to formal models of network formation. This stream of literature began with the seminal work of Jackson and Wolinsky [8], soon after being enriched with the adoption of dynamic approaches [7].