  Robustness is one of the key properties of nowadays networks. However,
robustness cannot be simply enforced by design or regulation since many
important networks, most prominently the Internet, are not created and
controlled by a central authority. Instead, Internet-like networks emerge from
strategic decisions of many selfish agents. Interestingly, although lacking a
coordinating authority, such naturally grown networks are surprisingly robust
while at the same time having desirable properties like a small diameter.
  To investigate this phenomenon we present the first simple model for selfish
network creation which explicitly incorporates agents striving for a central
position in the network while at the same time protecting themselves against
random edge-failure. We show that networks in our model are diverse and we
prove the versatility of our model by adapting various properties and
techniques from the non-robust versions which we then use for establishing
bounds on the Price of Anarchy. Moreover, we analyze the computational hardness
of finding best possible strategies and investigate the game dynamics of our
model.
