Belatedly, yet another preorder: In an \\(n\\)-player non-cooperative game, outcomes live in \\(\mathbb R^n\\). Player \\(i\\) has a preference relation \\(\geq_i\\) on \\(\mathbb R^n\\) given by \\(x \geq_i y\\) iff \\(x_i \geq y_i\\), i.e. they prefer to maximise their own payoff and are indifferent about everyone else's. This makes \\(\geq_i\\) a preorder. Then \\(x \cong_i y\\) iff \\(x_i = y_i\\), which means that player \\(i\\) is indifferent between \\(x\\) and \\(y\\).