On the existence of efficient and fair extensions of communication values for connected graphs

- We study values for TU games with a communication graph (CO-values).
- We study CO-values for connected graphs that are fair and efficient.
- There exists a unique efficient and fair extension to the whole domain.

We study values for TU games with a communication graph (CO-values). In particular, we show that CO-values for connected graphs that are fair and efficient allow for a unique efficient and fair extension to the full domain.