This paper considers a multiactor decision process, where each actor chooses a sequence of actions over time, in order to maximize his utility, subject to a random noise in the utility evaluation. The pool of alternative actions is limited, and all actors compete to use these alternatives, thus generating mutual externalities due to shortages. This process, which has a direct formulation in terms of a nested random utility model, is shown to be equivalent to a suitably built optimal control problem, whose Hamiltonian can be interpreted as a total benefit. A continuous time formulation is outlined, and an application to modelling residential mobility is discussed.