Not only that, I never understand why people think it's appropriate to ask a professional working for them to give them some of their income. Why on earth should someone else pay for you to buy something?
Now, if you want to ask for a reduction in commission since they'll get both sides, that's something you probably should already have asked about - makes no difference if they are on both sides of the transaction or not (though I would question how hard they'll negotiate for you - surely, the partners will talk and surely both agents know stuff about both of you).
Either way, if they have a listing, they'll sell it to someone and won't have to give you money to do so. It's totally inappropriate to think so.