The dual carbon goals necessitate coordinated development between transportation and energy systems, yet their inherent institutional and infrastructural disparities create significant barriers to collaborative benefit allocation. This study proposes a three-stage cooperative game model to resolve conflicts arising from divergent policy priorities and technical interdependencies. First, static Shapley value analysis quantifies the marginal contributions of infrastructure investment and energy complementarity, establishing a baseline for equitable profit distribution. Second, a stochastic dynamic allocation framework integrates time-varying risks and dynamic programming to address technological evolution and policy shifts, ensuring adaptive stability. Third, a multi-objective Chebyshev optimization method harmonizes economic efficiency, energy transition targets, and social welfare considerations. Theoretical validations demonstrate that the model outperforms conventional methods by balancing conflicting objectives without relying on empirical data calibration. By formalizing the bidirectional interdependence between energy grid flexibility and transport load management, this framework provides a systematic solution to align stakeholder incentives. The results advance the understanding of institutional design in cross-sectoral synergies, offering scalable governance principles for achieving carbon neutrality in interconnected systems.