To enforce the long-term cooperation in a multistage multicriteria game we use the imputation distribution procedure (IDP) based approach. We mainly focus on such useful properties of the IDP like “reward immediately after the move” assumption, time consistency inequality, efficiency and non-negativity constraint. To overcome the problem of negative payments along the optimal cooperative trajectory the novel refined A-incremental IDP is designed. We establish the properties of the proposed A-incremental payment schedule and provide an illustrative example to clarify how the algorithm works.