 For a game in which all players have sufficiently low thresholds, the complete network is clearly sufficient. Is the complete network necessary to obtain an equilibrium in which all players revolt? It turns out that it is not. A crucial role is played by structures of the same kind as the ‘triangle’ group in the kite network, called cliques. In such structures, ‘local’ common knowledge (that is, limited to the players part of the structure) arises naturally. In a complete network (that is, a network in which there is sufficient but not superfluous communication for it to fully revolt) in which cliques cover the entire population, if one clique speaks to another then every member of that clique speaks to every member of the other clique. Moreover, for every two cliques such that one is talking to the other, there exists a ‘chain’ of cliques with a starting element. In other words, every pair of cliques in the relation are part of a chain (of length at least 2) with a starting element (a leading clique.) Revolt propagates in the network moving from ‘leading adopters’ to ‘followers’, according to the social role hierarchy defined by the cliques and their relation. Consider the following example, in which cliques are represented by circles and numbers represent the thresholds of individual players: