Erratum - A contract and balancing mechanism for sharing capacity in a communication network

In a recent paper, the first three authors proposed a method for determining how much to charge users of a communication network when they share bandwidth, and studied the existence and form of Nash equilibria for players' choices of capacity. However, the proof of one of the propositions in that paper contained a flaw. In this note, we prove that the original proposition is true under an additional condition, and provide two examples to show that this condition is necessary.