Authors Thamhain and Wilmon presented 9 ways to influence project teams in their book, Information Technology Project Management, Fourth Edition.
Here’s a brief summary:
Authority The legitimate hierarchical right to issue orders
Assignment The project manager’s perceived ability to influence a worker’s later work assignments
Budget The project manager’s perceived ability to authorize others’ use of discretionary funds
Promotion The ability to improve a worker’s position
Money The ability to increase a worker’s pay and benefits
Penalty The project manager’s ability to cause punishment
Work Challenge The ability to assign work that capitalizes on a worker’s enjoyment of doing a particular task
Expertise The project manager’s perceived special knowledge that others deem important
Friendship The ability to establish friendly personal relationships between the project manager and others