We model a platooning system including trucks and a third-party service provider that performs platoon coordination, distributes the platooning profit within platoons, and charges the trucks in exchange for its services. This paper studies one class of pricing rules, where the third-party service provider keeps part of the platooning profit each time a platoon is formed. Furthermore, we propose a platoon coordination solution based on distributed model predictive control in which the pricing rule is integrated. To evaluate the effect of the pricing on the platooning system, we perform a simulation over the Swedish road network. The simulation shows that the platooning rate and profit highly depend on the pricing. This suggests that pricing needs to be set carefully to obtain a satisfactory platooning system in the future.