  We investigate a repeated two-player zero-sum game setting where the column
player is also a designer of the system, and has full control on the design of
the payoff matrix. In addition, the row player uses a no-regret algorithm to
efficiently learn how to adapt their strategy to the column player's behaviour
over time in order to achieve good total payoff. The goal of the column player
is to guide her opponent to pick a mixed strategy which is favourable for the
system designer. Therefore, she needs to: (i) design an appropriate payoff
matrix $A$ whose unique minimax solution contains the desired mixed strategy of
the row player; and (ii) strategically interact with the row player during a
sequence of plays in order to guide her opponent to converge to that desired
behaviour. To design such a payoff matrix, we propose a novel solution that
provably has a unique minimax solution with the desired behaviour. We also
investigate a relaxation of this problem where uniqueness is not required, but
all the minimax solutions have the same mixed strategy for the row player.
Finally, we propose a new game playing algorithm for the system designer and
prove that it can guide the row player, who may play a \emph{stable} no-regret
algorithm, to converge to a minimax solution.
