The very general problem is about when there are two players with only private information. They report their type and mechanism will decide about the action. Each player's type is drawn independently (but not i.i.d) from a uniform continuous distribution.
One technique which comes to mind for proving optimal mechanism will not have money burning is that if there is money burning one can improve upon the mechanism by a tiny perturbation. The problem is that it will mess with all ICs. Have you seen any paper trying to use that kind of perturbation technique while preserving ICs? or any other method? I understand in many mechanisms money burning is actually optimal and hence I'm just looking for any paper or method which has tried to prove there is no money burning in their specific problem. The hope is that I might be able to use their technique for my own problem.
I know this is a very general question and I'm sorry if that's vague. I've deliberately made it general to know about any technique which is remotely relevant for the specific problem I'm solving. I don't think anybody would like to think about the specific problem I'm trying to solve as it's too boring and long ha ha. But I can be more specific if needed.