On existence of $\varepsilon$-equilibrium in Volterra functional operator games without discrimination

The paper is continuation of author's research on the question of existence of $\varepsilon$-equilibrium in the sense of piecewise program strategies on Volterra chain in antagonistic games associated with nonlinear controlled functional operator equations. Just as in the paper published earlier on this subject, the main result consists in sufficient conditions of $\varepsilon$-equilibrium. The difference is that this time we investigate the game without discrimination of players. Application of results obtained in the paper is illustrated by example of a mixed boundary value problem associated with wave equation.