 A signaling game, then, is a game of asymmetric information between a sender \(s\) and a receiver \(r\). The sender observes the state \(t\) that \(s\) and \(r\) are in, while the receiver has to perform an action. Sender \(s\) can try to influence the action taken by \(r\) by sending a message. \(T\) is the set of states, \(F\) the set of forms, or messages. The messages already have a semantic meaning, given by the semantic interpretation function \(\llbracket \cdot \rrbracket\) which assigns to each form a subset of \(T\). The sender will send a message/form in each state, a sender strategy \(S\) is thus a function from \(T\) to \(F\). The receiver will perform an action after hearing a message with a particular semantic meaning, but for present purposes we can think of actions simply as interpretations. A receiver strategy \(R\) is then a function that maps a message to an interpretation, i.e., a subset of \(T\). A utility function for speaker and hearer represents what interlocutors care about, and so the utility function models what speaker and hearer consider to be relevant information (implementing Grice’s Maxim of Relevance). For simplicity, it is normally assumed that the utility functions of \(s\) and \(r (U_s\) and \(U_r)\) are the same (implementing Grice’s cooperative principle), and that they depend on (i) the actual state \(t\), (ii) the receiver’s interpretation, \(i\), of the message \(f\) sent by \(s\) in \(t\) according to their respective strategies \(R\) and \(S\), i.e., \(i = R(S(t))\), and (iii) (in section 2.3) the form \(f = S(t)\) used by the sender. Nature is taken to pick the state according to some (commonly known) probability distribution \(P\) over \(T\). With respect to this probability function, the expected, or average, utility of each sender-receiver strategy combination \(\langle S,R\rangle\) for player \(e \in \{s,r\}\) can be determined as follows: