They could do it dutch auction style. Suppose there are five drivers and three rides. The drivers bid per-mile rates of $.75, $1, $1.25, $1.50 and $1.75. The rides go to the three lowest bidding drivers and they all get $1.25, i.e. the highest rate of the drivers who get rides.

It gives everyone the incentive to bid their actual threshold past which they wouldn't want the ride, because if you bid too high you don't get any rides, but if you bid lower you may still get paid more than that unless bidding that low was actually necessary to get the ride. And at any given time all the riders pay the same rate as each other.