Is it possible that your teammates will give their best to the project—without you giving your best when you’re with them?
It’s possible, of course. But highly unlikely. Your actions are the greatest predictor of the thinking and actions your teammates will take. Think of them as someone who doesn’t know as much as you, and they’ll respond with retreating or aggressive actions.
Conversely, treat them as an equal, and you’re far more likely to see them mirror the best of humanity.
It seems rational to wait for others to treat you the way you want to be treated before you respond in kind. But teams don’t do big things that way. (The method is too slow.)
How badly do you want to do big things? Be irrational: go first. Bring your best to your teammates, and see what they bring back to you.
(Either way, you’re rewarded.)