  We investigate a non-cooperative game-theoretic model for the formation of
communication networks by selfish agents. Each agent aims for a central
position at minimum cost for creating edges. In particular, the general model
(Fabrikant et al., PODC'03) became popular for studying the structure of the
Internet or social networks. Despite its significance, locality in this game
was first studied only recently (Bil\`o et al., SPAA'14), where a worst case
locality model was presented, which came with a high efficiency loss in terms
of quality of equilibria. Our main contribution is a new and more optimistic
view on locality: agents are limited in their knowledge and actions to their
local view ranges, but can probe different strategies and finally choose the
best. We study the influence of our locality notion on the hardness of
computing best responses, convergence to equilibria, and quality of equilibria.
Moreover, we compare the strength of local versus non-local strategy-changes.
Our results address the gap between the original model and the worst case
locality variant. On the bright side, our efficiency results are in line with
observations from the original model, yet we have a non-constant lower bound on
the price of anarchy.
