Fair Dice

There are three six-sided dice, with the numbers 1 to 18 on their faces.  If you roll any two of the dice against each other, each one is equally likely to "win" by rolling the higher number.  If you roll all three dice, they are equally likely to win.  No ties are possible.

One die has the numbers:

1, 5, 10, 11, 13, 17

Can you figure out the numbers on the other two dice?

This puzzle was inspired by a much harder puzzle submitted by Eric Harshbarger to MathPuzzle in April 2012, where there were four twelve-sided dice.