  Many real-world networks, like the Internet, are not the result of central
design but instead the outcome of the interaction of local agents who are
selfishly optimizing for their individual utility. The famous Network Creation
Game [Fabrikant et al., PODC 2003] enables us to understand such processes,
their dynamics, and their outcomes in the form of equilibrium states. In this
model, agents buy incident edges towards other agents for a price of $\alpha$
and simultaneously try to minimize their buying cost and their total hop
distance. Since in many real-world networks, e.g., social networks, consent
from both sides is required to maintain a connection, Corbo and Parkes [PODC
2005] proposed a bilateral version of the Network Creation Game, in which
mutual consent and payment are required in order to create edges. It is known
that the bilateral version has a significantly higher Price of Anarchy,
compared to the unilateral version. This is counter-intuitive, since
cooperation should help to avoid socially bad states. We investigate this
phenomenon by analyzing the Price of Anarchy of the bilateral version with
respect to different solution concepts that allow for various degrees of
cooperation among the agents. With this, we provide insights into what kind of
cooperation is needed to ensure that socially good networks are created. We
present a collection of asymptotically tight bounds on the Price of Anarchy
that precisely map the impact of cooperation on the quality of tree networks
and we find that weak forms of cooperation already yield a significantly
improved Price of Anarchy. Moreover, for general networks we show that enhanced
cooperation yields close to optimal networks for a wide range of edge prices.
