For one bar to track two numbers, a total of three colors are used: 1) to show where the values overlap, 2) to show how much larger the first value is than the second, and 3) to show how much larger the second is than the first. This isn't a problem when one has many colors available. However, I need three bars with two percentages per bar, and the three bars are Red, Green, and Blue; so instead of different colors, I need three different shades of red, green, and blue. What colors would work in this situation or how do I determine for myself the optimum colors so that all values are easily distinguished? Also, the three bars are right next to each other.

Can you elaborate more on what exactly you're doing? I have zero idea what you're doing beyond looking for safe color ideas.

I don't really see the problem...
Take your blue gauge.
Have a background colour, say black.
Then your first value is represented by dark blue. Then on top of that your second value is represented by light blue.
If light blue value is inferior to dark blue value, then light blue is on top.
If dark blue is lower, then dark blue is on top...
In fact, you could have more than two. Simply render the smaller values on top of the higher values...

here is some ASCII art (with # being dark blue, % light blue):

+---------------+  +---------------+|########%%%%...|  |%%%%%%####.....|+---------------+  +---------------+0              100 0              100

Darklands used such a system to show what the max stat could be and the current stat, all out of a 100%.

this sounds more like a programming issue.

criteria 2 and 3 are the same thing.
i'm not seeing why you would make them separate.
if the first bar is greater than the second then you wouldn't need to show how the second bar is greater than the first. cuz that's impossible.

why are they overlapping? if one bar is representing two bars then it stands to reason that if for instance: you have a bar one side midnight blue (dark) and the other side sky blue (light) split evenly in the middle. when the player 1 (represented by midnight blue bar) attacks player 2 (represented by sky blue bar) and damages by 10%, player 1's bar will move by 10% (to the right) and player's 2 bar will by 10% (to the right).

most likely i'm missing what you're saying, but it sounds you're making a energy bar to me.

Consider using different patterns instead of different colors. This can look really nice if it fits with your GUI scheme.