 If the roles of Sender and Receiver are permanently assigned to individuals — as Lewis envisaged — then there are only two signaling systems: \(\langle\)Sender 2, Receiver 2\(\rangle\) and \(\langle\)Sender 3, Receiver 3\(\rangle\). All other possible combinations of strategies result in the players failing to coordinate. The coordination failure occurs because the Sender and Receiver only pair the appropriate action with the state of the world in one instance, as with \(\langle\)Sender 1, Receiver 1\(\rangle\), or not at all, as with \(\langle\)Sender 2, Receiver 3\(\rangle\).