Spoiler for An alternate approach for $11

If we lift the assumption that A and B pay the same amount, there is another option.

A and B use "Rock, Paper, Scissors" [we know that they have no coins] or other method to determine a loser. That person [say A] will pay $1 more.

So the payment is [A, B, C] pays [5, 4, 2]. THis takes care of the problem of C paying less for the $11 pizza than the $10 and the total offset is the same

A over pays by 6%, B underpays by 15% and C overpays by 27%.

The total absolute offset = 6% + 15% + 27% = 48% .... which happens to be the totla absolute offset for the [5,5,1] payment scheme described above.

A and B use "Rock, Paper, Scissors" [we know that they have no coins] or other method to determine a loser. That person [say A] will pay $1 more.

So the payment is [A, B, C] pays [5, 4, 2]. THis takes care of the problem of C paying less for the $11 pizza than the $10 and the total offset is the same

A over pays by 6%, B underpays by 15% and C overpays by 27%.

The total absolute offset = 6% + 15% + 27% = 48% .... which happens to be the totla absolute offset for the [5,5,1] payment scheme described above.