 The next example reveals that in some cases not even first-order knowledge is sufficient to trigger action, and higher levels of knowledge are necessary. Consider four players, each with threshold 3, in the two different networks represented in figure 3.6 (‘square’, in figure 3.6a, and ‘kite’, in figure 3.6b.) In the square network, player 1 knows that both 2 and 4 have threshold 3. However, she does not know about player 3’s threshold. If player 3 has threshold 5, then player 2 will never revolt, since he does not know about player 4’s threshold and it is then possible for him that player 4 has threshold 5 as well. Player 1’s uncertainty about player 3 together with player 1’s knowledge of player 2’s uncertainty about player 4 force her not to revolt, although she has threshold 3 and two neighbors with threshold 3 as well. Similar reasoning applies to all other players, hence in the square no one revolts. Consider now the kite network. Player 4 ignores player 1’s and player 2’s thresholds, hence he does not revolt. However, player 1 knows that players 2 and 3 have threshold 3, that they know that they do, and that they know that player 1 knows that they do. This is enough to trigger action \(r\) for the three of them, and indeed if players 1, 2 and 3 all revolt in all states in \(\{3331, 3332, 3333, 3334, 3335\}\), this is an equilibrium since in all states at least three people revolt each with threshold three.