"Modelling complex networks (e.g. the Internet or social networks) has in the past few years been a central topic in statistical physics. However, the role of game theory for network formation is still not sufficiently appreciated by physicists. Here I propose to develop a model, called the ""local network connection game"", which is inspired by the manner in which decisions are taken by agents in real social, economic and communication networks. In this game, the players' strategies and the network that results from their decisions co-evolve. The players are nodes in a network who must strategically establish links to other nodes. Each player has to find a trade-off between the cost of building links and the benefit of being connected to other players. A social dilemma arises because it is in every players interest to withhold any own investment and instead exploit the willingness of others who pay for creating connections.This fellowship will allow me to collaborate closely with experts in statistical physics who have applied evolutionary theory to games with social dilemmas (e.g. the prisoner's dilemma). As I plan to make game theory a central topic on my research agenda, this training will strengthen my position as independent researcher as intended by the fellowship's work programme. Specifically, I will perform Monte Carlo simulations of the iterated network connection game, where players are boundedly rational (i.e. they attempt to improve their payoff, but sometimes fail to find the exact optimum strategy). A temperature-like parameter will allow me to tune the degree of rationality. I will characterise stationary and metastable networks in terms of the ""price of anarchy"" (i.e. the ratio of the social cost in the equilibrium to the smallest possible social cost). I will analyse the dynamics of the game which exhibits long phases of quiescence interspersed by intense short-term activity, reminiscent of the bursty behaviour observed in real man-made networks."