In China, logistics platforms are an effective way to solve vehicle capacity utilization using information sharing. However, most logistics platforms do not possess operational sustainability due to excessive profit-seeking. To address this problem, conflicts of interest among freight transportation participants are discussed using a stakeholder approach. A three-player evolutionary game model (TEGM) is developed to analyze the interactions among freight carriers, freight shippers, and logistics platforms. Then, the asymptotic equilibrium and evolutionary stability strategies of the three-player game are analyzed. The results indicate that a high-level positive network externality is the driving force behind the logistics platform’s “high-level service”. A fairness payment incentive guarantees a “sharing” strategy for freight carriers and shippers. When the high-level positive network externality is limited and lower than a threshold value, there is no stable equilibrium point in the TEGM. A government tax incentive cannot change the freight carriers’ and shippers’ strategy to participate in this horizontal collaboration system, except for the logistics platform’s probability of providing “high-level service”. However, the behavioral strategies of the freight transportation participants can be changed to achieve the sustainability of freight transportation by reducing the value-added tax rate through the logistics platform and increasing the high-level positive network externality of the logistics platform and other participants’ perceived fairness through a payment incentive. Finally, suggestions for regulating the behaviors of freight transportation participants and promoting the sustainability of freight transportation are discussed.