 So even if agents have “almost” common knowledge, in the sense that the number of levels of knowledge in “Joanna knows that Lizzi knows that … that Joanna knows that \(\omega_2\) occurred” is very large, their behavior is quite different from their behavior given common knowledge that \(\omega_2\) has occurred. Indeed, as Rubinstein points out, given merely “almost” common knowledge, the agents choose as if no communication had occurred at all! Rubinstein also notes that this result violates our intuitions about what we would expect the agents to do in this case. (See Rubinstein 1992, p. 324.) If \(T_i = 17\), wouldn’t we expect agent \(i\) to choose \(B\)? Indeed, in many actual situations we might think it plausible that the agents would each expect the other to choose \(B\) even if \(T_1 = T_2 = 2\), which is all that is needed for Lizzi to know that Joanna has received her original message and for Joanna to know that Lizzi knows this! Binmore and Samelson (2001) in fact show that if Joanna and Lizzi incur a cost when paying attention to the messages they exchange, or if sending a message is costly, then longer streams of messages are not paid attention to or do not occur, respectively.