This is where stakholder management is part of the activities for both expectations and the contributions. Again there is a need for people management, because the people who do the work need to understand the importance and be driven to take responsibilities.
Many project managers 'lean' on the mandate of the stakeholder to achieve the goal, but how do you get people to see the necessity themselves? You can achieve a lot with personal interest and approach, while making an effort to help people to get what they are looking for.
Let them know how important they are, which is no less than the truth. And again this has to be a message that you mean.
Small rewards work, but are not decisive. Let the line managers know about the good performance of their teams and ensure they pass the compliments on to them.