Understanding the motivations of agitators is not too difficult if you look at their behavior and then ask yourself why they are behaving that way. More to the point, what do they get out of it? Their motivations are in the payoff or what they get.
The agitator will say anything no matter who gets hurt or feels badly. What does the player get? He gets a cheap moment in the spotlight, even if it is at the expense of a co-worker. Just keep in mind that the player will say anything about anyone, including you. The agitator also gets his kicks from complaining. He is again in the spotlight. Of course, there is always a little more power in that position.
The player makes things seem bad, people seem incompetent, and everything appears worse than it is. The player gets attention, gets a little more power for a little while, and is seen as someone who is in the know and on top of things. Experienced players do this in a way that is additive over time. They also take care not to overdo it. They are very good at not giving away their game.
Given the behavior, its varieties and its motivations, what does counter play look like? Listen to what the agitator has to say and then say, "You are a trip. You can find more ways to look at things negatively than anyone I know." The strategy is to call the player on his behavior and make it clear that you have no interest in what he says. There is no power reinforcement for the behavior.
In another example, a player is agitating. He says something negative about someone. The classy response is, "I am surprised to hear you say that. I do not think it is true." The player will almost always press on with, "It is true! I . . .." He goes on to say some more negative things.
Your response is, "You probably would describe the tooth fairy as a thief." Now comes the real trick. No matter what the player says next, do not respond. The game is over.
As with most people who drive you up the wall, the trick to counter play with agitators is to do what needs to be done and then quit. Players of any type or variety can only play with people who will play. For agitators, just be sure they get minimal attention and no additional power or status from you. Quietly and calmly call them on their behavior and then let it go. When others do not play, the game gradually stops.
Also when agitating gets started in a group, it tends to be contagious. The play is hard to resist. People who just enjoy small talk - almost always about other people who are not there - inadvertently pick up the behavior. The play becomes a way to get status and attention in the group. It works for the agitator so why not for others?
Given the contagion virility of the game, it is important to stop it as quickly and completely as possible.
Locate the most vocal agitator and then do two things. First, privately ask him to tell you what problems he sees or what concerns he has. If necessary, candidly share with him what you have learned he is saying or complaining about. Once the issues are on the table, you and he can go into a problem solving mode.
Next, and this is the key, tell him that his agitating behavior is unacceptable. Let him know that you are always available to work on problems but will not tolerate agitating. He will undoubtedly act shocked and deny the behavior. Nonetheless, make your point and do not argue with him.
If necessary and after giving problem solving a chance, say to the player, "This behavior must stop. If not, I will call a meeting of the group. At that time, I will again say to you that your destructive behavior must stop. I also will caution your associates not to follow your example."
This is usually enough. You must not be bluffing, though. It may be necessary for you to follow through, especially with dyed-in-the-wool agitators.