  Several notions of game enjoy a Nash-like notion of equilibrium without
guarantee of existence. There are different ways of weakening a definition of
Nash-like equilibrium in order to guarantee the existence of a weakened
equilibrium. Nash's approach to the problem for strategic games is
probabilistic, \textit{i.e.} continuous, and static. CP and BR approaches for
CP and BR games are discrete and dynamic. This paper proposes an approach that
lies between those two different approaches: a discrete and static approach.
multi strategic games are introduced as a formalism that is able to express
both sequential and simultaneous decision-making, which promises a good
modelling power. multi strategic games are a generalisation of strategic games
and sequential graph games that still enjoys a Cartesian product structure,
\textit{i.e.} where agent actually choose their strategies. A pre-fixed point
result allows guaranteeing existence of discrete and non deterministic
equilibria. On the one hand, these equilibria can be computed with polynomial
(low) complexity. On the other hand, they are effective in terms of
recommendation, as shown by a numerical example.
