A two-level bimatrix game with a control of payoff (Q2713945)

A two-level bimatrix game is under study where the player of the upper level can both choose a mixed strategy and change entries of payoff matrices. The low level player constructs his optimal strategy taking into account the strategy chosen on the upper level and changes at the payoff matrices. In the cooperative case, i.e. when the interests of the lower level do not contradict the interests of the upper level, it is shown that the game can be reduced to a series of linear programming problems. In the noncooperative case, the existence of \(\varepsilon\)-optimal solutions is proved.