The following is a passage from an article on the idiom kill two birds with one stone:
Some people feel that this term is a bit negative, given the association with hunting and death, and they prefer more positive twists on the saying. Several organizations have even sponsored contests to come up with a new and more animal-friendly version of “to kill two birds with one stone.”
What does sponsor mean here? Is it sense #1 from OALD:
(of a company, etc.) to pay the costs of a particular event, programme, etc. as a way of advertising Sports events sponsored by the tobacco industry.
or sense #2:
to arrange for something official to take place The US is sponsoring negotiations between the two sides.