This paper demonstrates an example of successful analysis of reflexive network’s influence on equilibria in certain network game, which all nonreflective equilibria are known and have been found in [2,3]. It has been proved several statements on the assumption that the set of admissible
decision rules in this game has the following properties: the players who know each other’s attributes, play a Nash equilibrium in pure strategies,
and the actions of players whose attributes are unknown to them, they predict, based on the criteria for acceptance Hurwitz solutions with the parameter equal to the optimism either zero or one. It was also constructed optimal control by reflexive network for some cases of different distributions
of optimism among the players to prevent any non-zero equilibrium in the given network game.