Suppose the government does not know the level of the marginal damages, but that the neighbors themselves can effectively petition the government to impose a Pigouvian tax of any size after a failed negotiation. What will the set of outcomes of these negotiations include? Lets say the government wanted to implement the efficient quantity but with this feedback mechanism, how might the government implement a reporting scheme (with possible fines on both sides) to insure an efficient outcome if the original model does not. What if the government has access to a costly auditing technology?