The reduced game relevant for the consistency of the prekernel is used to reinterpret this solution concept in a way that makes it independent of interpersonal utility comparisons. Based on this reinterpretation, a non-cooperative model is presented that yields in stationary equilibria the prekernel (kernel) for the class of monotonic transferable utility games. Next, we apply the same non-cooperative model to more general coalitional games. For pure bargaining problems, the model yields the Nash solution. For general non-transferable utility games, a natural extension of the prekernel arises. Thus, the prekernel is obtained as the set of payoffs where the relevant bargaining range between every pair of players is split in half.Journal of Economic LiteratureClassification Numbers: C71, C72, C78.