In this paper, we consider a sequential allocation problem with n individuals. The first individual can consume any amount of a resource, leaving the remainder for the second individual, and so on. Motivated by the limitations associated with the cooperative or non-cooperative solutions, we propose a new approach from basic definitions of representativeness and equal treatment. The result is a unique asymptotic allocation rule for any number of individuals. We show that it satisfies a set of desirable properties. Keywords: Sequential allocation rule, River sharing problem, Cooperative and non-cooperative games, Dictator and ultimatum games. JEL classification: C79, D63, D74.