 Group knowledge is importantly different from common knowledge (Lewis 1969; Fagin et al. 1995). Common knowledge is the condition of the group where everybody knows that everybody knows that everybody knows … that \(\phi\). In other words, common knowledge concerns the hard information that each agent in the group possesses about the hard information possessed by the other members of the group. That everybody in \(G\) possesses the hard information that \(\phi\) does not imply that \(\phi\) is common knowledge. With group knowledge each agent in the group may possess the same hard information (hence achieving group knowledge) without necessarily possessing hard information about the hard information possessed by the other agents in the group. As noted by van Ditmarsh, van der Hoek, and Kooi (2008: 30), “the number of iterations of the \(E\)-operator makes a real difference in practice”. \(C_G\phi\)—the common knowledge that \(\phi\) for members of \(G\), is defined as follows: 