How are PIDs assigned?

For basic XvX ladder games this is pretty straight forward but there are a number of alternate game scenarios that people are bound to run into:

[This game](http://drop.sc/334281/d) is a 1v2 AI that seems to assign PIDs as follows:

```
Team 1:
Player 1 - Tzuqris
Team 2:
Player 3 - A.I. 2 (Very Easy)
Player 4 - A.I. 3 (Very Easy)
```

[This game](http://ggtracker.com/matches/3167851/replay) is a 1v2 humans that seems to assign PIDs as follows:

```
Team 1:
Player 1 - Brothus
Team 2:
Player 2 - Collision
Player 3 - goatsonfire
```

[This game](http://drop.sc/94) from 1.2.2 (didn't have a newer example on hand) is a 1v1 with 6 observers. Correctly assigning ids to observers is important for things like chat messages and is required for correctly mapping game events. The linked replay isn't a great example because there is no observer chat, maybe someone can find a better one.