The adaptation of water resource systems to the potential impacts of climate change requires mixed portfolios of supply and demand adaptation measures. The issue is not only to select efficient, robust, and flexible adaptation portfolios but also to find equitable strategies of cost allocation among the stakeholders. Our work addresses such cost allocation problems by applying two different theoretical approaches: social justice and cooperative game theory in a real case study. First of all, a cost-effective portfolio of adaptation measures at the basin scale is selected using a least-cost optimization model. Cost allocation solutions are then defined based on economic rationality concepts from cooperative game theory (the Core). Second, interviews are conducted to characterize stakeholders' perceptions of social justice principles associated with the definition of alternatives cost allocation rules. The comparison of the cost allocation scenarios leads to contrasted insights in order to inform the decision-making process at the river basin scale and potentially reap the efficiency gains from cooperation in the design of river basin adaptation portfolios.