  The game in which acts of participants don't have an adequate description in
terms of Boolean logic and classical theory of probabilities is considered. The
model of the game interaction is constructed on the basis of a non-distributive
orthocomplemented lattice. Mixed strategies of the participants are calculated
by the use of probability amplitudes according to the rules of quantum
mechanics. A scheme of quantization of the payoff function is proposed and an
algorithm for the search of Nash equilibrium is given. It is shown that
differently from the classical case in the quantum situation a discrete set of
equilibrium is possible.
