Network connectivity under node failure

- A model of network formation with the possibility of node failure has been analysed.
- Players receive benefits from connecting directly and indirectly through costly links.
- Conditions are identified for Nash and efficient networks.
- The conditions involve notion of k-Node Super Connectivity.

We examine a non-cooperative model of network formation where players may stop functioning. We identify conditions under which Nash and efficient networks will remain connected after the loss of k nodes by introducing the notion of k-Node Super Connectivity.