Deteriorating bridge networks are potentially exposed to extreme events, such as earthquakes and tsunamis, during their service life, posing significant social, economic and environmental threats. Traditionally, life-cycle assessment of bridge networks primarily focuses on vulnerability and risk. However, bridge aging and degradation impact not only structural reliability but also results in additional energy consumption and carbon dioxide emissions, thereby affecting infrastructure sustainability. This paper presents a novel life-cycle-oriented probabilistic framework for sustainability assessment of bridge networks under uncertainty using cooperative game theory to comprehensively evaluate social, economic, and environmental impacts. The proposed framework treats each bridge in the network as a player in a cooperative game and uses the weighted Shapley value to fairly allocate the network's overall sustainability based on each bridge's marginal contribution to different coalitions. In bridge networks, the Shapley value helps to identify the importance and contribution of each bridge throughout its life-cycle, factoring in sustainability indicators such as social, economic, and environmental losses. The weighted Shapley value enhances the traditional Shapley approach by incorporating weights that reflect the time-variant uncertainties involved in the problem. The effectiveness of the proposed sustainability assessment framework based on a cooperative game theory approach is demonstrated by application to sustainability assessment of a bridge network over time by considering the criticality of each bridge in the network. In resource-constrained situations, the proposed framework can provide valuable insights for the prioritization of bridge maintenance and the design of re-entry routes, which are important for enhancing the overall sustainability of the bridge network.