This is not a topic I know much about but I wonder if the whole issue is too vague to be meaningful. I mean, the theorem says that an efficient outcome will ALWAYS come about, but I here I give counterexamples:
A: there is benefit to causing run-off for neighbour #1. Now neighbour #2 must pay #1 the difference, plus some profit. Only if #2's gain plus incentivizing profit plus wall cost is cheap enough will the wall be built. In fact, #1 can now refuse to build a wall on principle, preferring monthly installments to avoiding run-off.
B: causing run-off or not is cost-neutral for neighbour #1. There is an economic case for him to cause run-off anyway, to charge #1 for the service of avoiding run-off.
So I don't know what is meant by "efficient outcome". The outcome can only be seen to be efficient from the point of view of neighbour #1, insofar as run-off is economically useful, and if leveraged can derive profit.
I am making the argument that example 3 is not necessarily true, and bargaining under the Coase theorem may not lead to the most efficient outcome.
On the one hand, one could count the damage twice because there are two sources of run-off and building a wall can only counter one source. Each wall is preventing $100 of damage, so $200 of damage is being prevented by the two walls.
On the other hand, building only one wall adds no protection. It is only the second wall that protects against run-off. So the first wall is preventing no damage whatsoever; only $100 of damage is being prevented by both walls.
The second analysis seems more sensible. One should view both walls together as one remedy and add up the costs.
If, after the first wall is built, #3 starts producing run-off, there is damage being done anew and the situation can be viewed on its own as another instance of the same problem, that $100 damage is being caused and a wall is needed. But clearly there is interaction between the two cases because the previous wall has been neutralized, and whatever it cost has now been lost. So I think more than $100 dollars damage has been done by this second neighbour. It is now worth more than $100 dollars to neighbour #2 to build the next wall because he already has the other wall. Building the second wall is an easier decision.
But if both produce run-off simultaneously then building two walls is one remedy and the costs will be added and weighed against the $100 dollars. So it may happen that building two walls is not worthwhile but building a second is, for the same damage amount.
On the other hand, the court system may not agree that the damage is the same; it is perhaps different damage to the same value and the original wall is still preventing the run-off it was intended to prevent. It has therefore not been neutralized, it is effective (but not economically effective). This is a political matter though, although relevant.