  In this paper, we discuss a class of two-stage hierarchical games with
multiple leaders and followers, which is called Nash-Stackelberg-Nash (N-S-N)
games. Particularly, we consider N-S-N games under decision-dependent
uncertainties (DDUs). DDUs refer to the uncertainties that are affected by the
strategies of decision-makers and have been rarely addressed in game
equilibrium analysis. In this paper, we first formulate the N-S-N games with
DDUs of complete ignorance, where the interactions between the players and DDUs
are characterized by uncertainty sets that depend parametrically on the
players' strategies. Then, a rigorous definition for the equilibrium of the
game is established by consolidating generalized Nash equilibrium and
Pareto-Nash equilibrium. Afterward, we prove the existence of the equilibrium
of N-S-N games under DDUs by applying Kakutani's fixed-point theorem. Finally,
an illustrative example is provided to show the impact of DDUs on the
equilibrium of N-S-N games.
