 Finally, let us consider a much more challenging action: the misleading private announcement of p to agent a. The idea of this action is that agent a is told p in a completely private manner but all other agents are misled into believing that a received the private announcement of \(\lnot p\) instead. So to construct an action model for this, we need a few elements: events for the private announcement of \(\lnot p\) to a that the non-a agents mistakenly believe occurs and an event for the actual announcement of p that only a knows occurs. As for the events for the private announcement of \(\lnot p\), it follows by a simple modification of  Figure 3  that the private announcement of \(\lnot p\) to agent a is the action \((\Pri_a(\lnot p),e)\) pictured as follows: 