You have a well-maintained workflow where the agents need to work on the tickets that are assigned to them. This is why you would like to prevent the reassignment of tickets. This generally cannot be prevented with the roles and permissions given to an agent, however with the aid of a feature called "Roles" which is available from the Estate Plan onwards. 


Please navigate to Admin -> Roles and choose the appropriate actions for an agent role - while checking the boxes - please leave out the box that says, "Edit ticket properties." This would disable the agent from changing any of the ticket properties which includes agent as well.