Is there an expression for asking two people to perform a task, but neither do it, assuming that the other will?

Solution 1:

Everybody’s business is nobody’s business Here ‘business’ means ‘duty’ or ‘task’. When nobody is directly responsible for doing a thing, nobody does it, because everybody thinks somebody else is or will be doing it. http://proverbhunter.com/everybodys-business-is-nobodys-business/