On Convergence of a Stochastic Quasigradient Algorithm of Quantile Optimization

For the nonantagonistic two-person game which is equivalent to the problem of minimizing the quantile function, a modification of the stochastic quasigradient algorithm to seek the Nash point was proposed. The Nash point defines both the optimal strategy minimizing the quantile function and the minimum value of this function. Convergence of the algorithm with the probability 1 was proved. The question of choosing the starting point was discussed.