Truck platooning refers to coordinating a group of heavy-duty vehicles at a close inter-vehicle distance to reduce overall fuel consumption. This coordination between trucks is traditionally achieved by adjusting the schedule, velocity, and routines to increase the platooning chances, and thus improve the overall fuel efficiency. However, the data model built for the coordination problem is typically integer-constrained, making it generally hard to solve. On the other hand, the interaction among self-interested fleets that are operated by different companies is not well-studied. This thesis aims to build a distributed framework for multi-fleet truck platooning coordination to enable the coordination without a third-party service provider. The interaction among fleets is considered a non-cooperative finite game, for which we propose the best response search method, which essentially requires to solve a cooperative truck platooning optimization problem iteratively. We refer to the optimization problem as a best-response problem, which is formulated as a mixed-integer linear problem with relaxation skills. To achieve a feasible time complexity for the best-response subproblem, we propose a decentralized algorithm, distributing the computational load to connected automated vehicles within the fleet. The proposed method is examined under a real-world featured demand set to compare the performance in optimality and time complexity with previous studies. The result suggests that the decentralized algorithm delivers the optimal objective value in this case, while the best-response search does not deliver extra benefits as the dominating time costs in the cost functions eliminate the potential for improvement.