 If the state \(\omega\) were common knowledge, then the conditional strategy profile \((A, A)\) if \(\omega = \omega_1\) and \((B, B)\), if \(\omega = \omega_2\) would be a strict Nash equilibrium at which each would achieve a payoff of 2. So the obvious remedy to their predicament would be for Lizzi to tell Joanna Aldo’s location in a face-to-face or telephone conversation and for them to agree to go where Aldo is, which would make the state \(\omega\) and their intentions to coordinate on the best outcome given \(\omega\) common knowledge between them. Suppose for some reason they cannot talk to each other, but they prearrange that Lizzi will send Joanna an e-mail message if, and only if, \(\omega_2\) occurs. Suppose further that Joanna’s and Lizzi’s e-mail systems are set up to send a reply message automatically to the sender of any message received and viewed, and that due to technical problems there is a small probability, \(\varepsilon \gt 0\), that any message can fail to arrive at its destination. Then if Lizzi sends Joanna a message, and receives an automatic confirmation, then Lizzi knows that Joanna knows that \(\omega_2\) has occurred. If Joanna receives an automatic confirmation of Lizzi’s automatic confirmation, then Joanna knows that Lizzi knows that Joanna knows that \(\omega_2\) occurred, and so on. That \(\omega_2\) has occurred would become common knowledge if each agent received infinitely many automatic confirmations, assuming that all the confirmations could be sent and received in a finite amount of  time.[34]  However, because of the probability \(\varepsilon\) of transmission failure at every stage of communication, the sequence of confirmations stops after finitely many stages with probability one. With probability one, therefore, the agents fail to achieve full common knowledge. But they do at least achieve something “close” to common knowledge. Does this imply that they have good prospects of settling upon \((B, B)\)?