The guy who responded too mentioned the "network effect".
I'm quite baffled by what is exactly the problem?
What, you are afraid that your babysitters will decide to dump your platform because one single individual is offering them more money?
What is stopping you from making your logistics work in a way that a preferred babysitter comes every time? Of course, that would make your logistics problem a bit harder, but that is exactly the point I'm making.
Network effect exists because of incapability of the system to create a situation where your workers would make more if they left your service. But, if you allowed the clients to have the same babysitter, same chef, and at the same time have an algorithm that is superior to everything else on the market, yes, the "Uber for Babysitting" idea is a stupid one, an obvious one, but execution is far above a "common guy" startup.