This paper presents a network-based multi-agent optimization model for the strategic planning of service facilities in a stochastic and competitive market. We focus on the type of service facilities that are of intermediate nature, i.e., users may need to deviate from the shortest path to receive/provide services in between the users’ planned origins and destinations. This problem has many applications in emerging transportation mobility, including dynamic ride-sharing hub design and competitive facility location and allocation problems for alternative fuel vehicle refueling stations. The main contribution of this paper is establishing a new multi-agent optimization framework considering decentralized decision makings of facility investors and users over a transportation network and providing rigorous analyses of its mathematical properties, such as uniqueness and existence of system equilibrium. In addition, we develop an exact convex reformulation of the original multi-agent optimization problems to overcome computational challenges brought by non-convexity. Extensive analysis on case studies showed how the proposed model can capture the complex interaction between different stakeholders in an uncertain environment. Additionally, our model allowed quantifying the value of stochastic modeling and information availability by exploring stochastic metrics, including value of stochastic solution (VSS) and expected value of perfect information (EVPI), in a multi-agent framework.