Interpretation of optimal signals

According to the optimal assertions approach of Benz and van Rooij (2007), conversational implicatures can be calculated based on the assumption that a given signal was optimal, i.e. that it was the sender's best choice if she assumes, purely hypothetically, a particular naive receiver interpretation behavior. This paper embeds the optimal assertions approach in a general signaling game setting and derives the notion of an optimal signal via a series of iterated best responses (cf. J¨ager, 2007). Subsequently, we will compare three different ways of interpreting such optimal signals. It turns out that under a natural assumption of expressibility (i) the optimal assertions approach, (ii) iterated best response and (iii) strong bidirectional optimality theory (Blutner, 1998, 2000) all prove equivalent. We then proceed to show that, if we take the iterated best response sequence one step further, we can account for M-implicatures (Horn's division of pragmatic labor) standardly in terms of signaling games.