A balance method for solving matrix games with constraints (Q1975117)

The author considers antogonistic matrix games, in which additional losses are assigned to pure strategies of one or both players. If mixed strategies are used, the mean value of these losses must not exceed a sertain number. A balance method is suggested that takes these constraints into account and thus reduces matrix games with constraints to equivalent unconstrained games, which makes it possible to apply known methods for solving games. Typically, such losses must be allowed for in problems of control under conflicting conditions when the expendable resource is limited. An example of application of the balance method is given.