There are three important aspects to-be-taken into account when the stability problem of a long-term cooperative agreement is investigated: time consistency (dynamic stability) of the cooperative agreement, strategic stability and irrational behavior proofness. The mathematical results based on imputation distribution procedure (IDP) are developed for dealing with the above-mentioned aspects of cooperation. The authors prove that, for a special class of differential games, a time-consistent cooperative agreement can be strategically supported by a Nash equilibrium. An example is also considered, where all the three conditions are satisfied.