A question! Of grammar!

[desperance]

Huh. Can two people share one behalf, or must it be always individual? Specifically, when an adult allows two children to do something, does she accept on their behalf or on their behalves? I am not sure I have ever seen "behalves", but my fingers tripped over "their behalf", so I thought I'd ask. I suppose they have common purpose, which might incline towards the singular - but on the other hand, the benefit falls to each of them individually, even if they undertake the action collectively, so...