Currently bbPress only supports moderators and keymasters who can “close” topics.
I sort of see why you ‘may’ want to offer this functionality but I also don’t know of any forum software that does allow this.
I am setting up a timebank where ppl can ask or offer services.
example “who can babysit my 3 yr boy for the next 3 weeks on mondaynights”
once this application is fulfilled i want the author to be able to close this topic so he/she will not get more offers.
maybe someone can point me out what needs to be set to enable “closing topics” for participants.
any other thought is welcome as well!

thanks
I actually took a peek at the code to see if there was an easy to do this, if we could override or add a custom function or filter to achieve this. No was the result 
We have some moderation changes coming in bbPress 2.6 in that individual users can be assigned a single forum (or multiple forums) to be a moderator rather than the current behaviour where if they are a moderator they can moderate all forums.
I have note scribbled down for when I next checkout this feature to check what if how we can add/modify bbPress to allow what you have asked above 