A direct-straightforward method for solving linear discrete-time optimal control problem is applied to solve the control problem of a linear discrete-time system as a mixture of multi-criteria Stackelberg and Nash games. For simplicity, the exposition starts with the simplest case of linear discrete-time optimal control problem and, by sequential considering of more general cases, investigation finalizes with the highlighted Pareto-Nash-Stackelberg and set valued control problems. Different solution principles are compared and their equivalence is proved. We need to remark that there are other possible title variants of the considered models like, e.g., a multi-agent control problem of the Pareto-Nash-Stackelberg type. There is an appropriate approach in (Leitmann, Pickl and Wang Dynamic Games in Economics, Springer, Berlin, 205–217, 2014), [1]. A more simple and largely used title for such games is dynamic games, see e.g. (Başar, Olsder, Society for Industrial and Applied Mathematics, Philadelphia, 536, 1999), [2], (Long, A Survey of Dynamic Games in Economics, World Scientific, New Jersey, XIV–275, 2010), [3]. We insist on the above title in order to highlight both the game and control natures of the modelled real situations and processes. More the more we can refer in this context a Zaslavski’s recent monograph (Zaslavski, Discrete-Time Optimal Control and Games on Large Intervals, Springer, Switzerland, X+398, 2017, [4]) that uses an appropriate approach to the names of considered mathematical models.