"RFPs put people in competition with each other, they do not encourage collaboration"

- panelist at a public health event I am attending

But doesn't any funding mechanism that has a fixed amount of money to give away put people in competition with each other? What are the best ways to minimize this?

Maybe by making the RFP applications or process public. 

There will still be competition to win the RFP,  but a team will easily be able to find collaborators if there are knowledge/skills gaps needed to deliver on the RFP.