In this paper we introduce an extension of the concept of Equilibrium in Secure Strategies, which takes into account non-uniform attitudes of players to security in non-cooperative games. In particular, we examine an asymmetric attitude of players to mutual threats in the simplest case, when all players are strictly ordered by their relation to security. Namely, we assume that players can be reindexed so that each player i in their behavior takes into account threats posed by players j>i and ignores threats of players j