We consider n players P i , i = 1,…, n, that are involved in a so called dynamical game. We assume that every player is assigned a state vector function x i : ℕ0 → ℝ ni and has at his disposal a control vector function u i : ℕ0 → ℝ mi which are dynamically coupled by a system of difference equations $$ \begin{gathered} x_i (t + 1) = g_i (x(t), u(t)), t \in \mathbb{N}_0 , \hfill \\ i = 1, \ldots ,n, \hfill \\ \end{gathered} $$ (3.1) where x(t) = (x 1(t) T ,…, x n (t) T ) T , u(t) = (u 1(t) T ,…, u n (t) T ) T , and g i ∈ C(ℝ N x ℝ M , ℝ ni ), i = 1,…,n, with \( N = \sum\limits_{i = 1}^n {n_i } and M = \sum\limits_{i = 1}^n {m_i } \)