Game Theory and Why Nobody Does Their Job

I have a very specific problem at work: the power engineers refuse to assist me. Well I can't say refuse, more like "only help me begrudgingly and only if they absolutely have to and even then very little." Why? It's their task to work on the power circuits of my boards. And why not? The problems on my board are relatively small compared to other problems (e.g. bugs and such). Well, part of the problem is management, and the other part is time.

They're busy. Really busy. Basically the power engineers have about ten boards to work on. Two of them have huge issues and they need rectification quickly. The rest remain ignored. I understand their priorities, but I also understand that they have deadlines and all of their boards must be working by the deadline or else.

So I sought to understand the problem using a general sum game. Each player (i.e. myself v power team) gets a certain amount of points based on a finite set of circumstances. The way each player "plays their cards" depends on how good their payoff is for each circumstance.

If I ignore my boards I am heavily penalized by my manager and the team. If I do work on my boards I am rewarded. If the Power Team works on my board the are rewarded, but because of a lower priority set by their manager and the team, they don't get much. If they ignore my board there is no reward or penalty, because they are excused because of the two priority boards. As a result we have the following table:

                                     Power Team
                         Work on My Board   Ignore My Board
me   Work on My Board           (10,5)           (10,0)
     Ignore My Board            (-5,-5)          (-5,5)

If you calculate the minimax values, we arrive at these two probabilities:

1. I should always work on my board. This seems to be the case.
2. The power engineer only has incentive to work on my board 1/3 of the time. The rest their are off doing other things.

In retrospect it would seem that the reward for working on the priority boards is far higher than I suggested, because I don't think the Power Team would (or need) to contribute 1/3 of their time. In addition, depending on priorities set by their manager, they might even be penalized for working on it.