Network Creation Games model the construction of a communication network by selfish agents without any external coordination. These games became popular as a means to study the structure of complex networks like the Internet or social networks. Agents of the game are nodes in a network which can buy incident edges to connect to other nodes. Each agent tries to occupy a central position in the network at minimum cost for building edges. Intensive research has shed light on many aspects of these games. However, despite all those efforts there are still many intriguing open problems left - most prominently settling the Price of Anarchy.
In my talk I will summarize recent research on the Price of Anarchy question and I will discuss two promising extensions of the model: A version which incorporates locality and a version which introduces a robustness aspect to the game.