 Notice that, in point (2) of his definition of sender-receiver games, Lewis requires two things: that there be a unique best response to the state of the world (this is what requiring \(F\) to be one-to-one amounts to) and that everyone in the audience agrees that this is the case. Since we are considering the case where there is only a single responder, the second requirement is otiose. For the case of two states of the world and two responses, there are only two ways of assigning responses to states of the world which satisfy Lewis’s requirement. These are as follows (where \(X \Rightarrow Y\) denotes “in state of the world \(X\), the best response is to do \(Y\)”):