- Snap positions used for collision to cells.
- Snap movement to cells.
- Add 0.5 or something tolerance to collision.
- Add buffer to persons for pathfinding. (Not so cool, cause pathfinding won't find a path between 2 persons standing 1 cell apart.)
- Decrease size of pathfinding cells.
I'd probably use the first one and the last one - however as long as positions/pathfinding/collision do not really use the same grid you will have inconsistencies. Graphical overlapping, collisions where there should be none, no collisions where the should be, etc. - You'd just have to pick the inconsistency you would feel most comfortable with.
(Also i think you mean "he collides with a blue person.")