On the approximate controllability of Stackelberg-Nash strategies for Stokes equations

Abstract

We study a Stackelberg strategy subject to the evolutionary Stokes equations, considering a Nash multi-objective equilibrium (not necessarily cooperative) for the “follower players” (as they are called in the economy field) and an optimal problem for the leader player with approximate controllability objective.

We will obtain the following three main results: the existence and uniqueness of the Nash equilibrium and its characterization, the approximate controllability of the Stokes system with respect to the leader control and the associate Nash equilibrium, and the existence and uniqueness of the Stackelberg-Nash problem and its characterization.