It has the following properties: The protocol was developed by Jack M. Robertson and William A. Webb.
If all agents have the same rights, then wi = 1/n for all i, but in general the weights may be different.
It is required to partition C into n subsets, not necessarily connected, such that, for every two agents i and h:
[3] The main difficulty in designing an envy-free procedure for n > 2 agents is that the problem is not "divisible".
The Robertson–Webb protocol addresses this difficulty by requiring that the division is not only envy-free but also near-exact.
A partition of X to pieces X1, …, Xm, assigned to the m active players, such that:
[2] Use a near-exact division procedure on X and get a partition which all n players view as ε-near-exact with weights w1, …, wm.
Let one of the active players (e.g. A1) cut the pieces such that the division is exact for him, i.e. for every j: V1(Xj)/V1(X) = wj.
By cutting P to smaller pieces if necessary, we may bound the disagreement such that all players agree that: V(P)/V(X) < ε.
Let δ be the difference between the values, such that for every optimist i and every pessimist j: Vi(P)/Vi(X) – Vj(P)/Vj(X) > δ. Divide the remaining cake, X − P, into pieces Q and R, such that the division is near-exact among all n players.
At this point we have partitioned the active players to two camps, each collectively claiming complementary portions of the cake and each camp is more than satisfied with their collective portion.
It remains to divide each portion of the cake to the players in its camp.