Forward Induction and Communication

Abstract

The resources of game theory promise to help solve some of the difficulties which have faced attempts to work out, in detail, Grice's theory of conversational implicature[1][5]. As a formal theory of rational interaction, game theory may provide the means to generalize and formalize Grice's rather loose framework of maxims and principles of rational conversation. At least that is the hope. My goal in this paper is to describe and analyze two specific cases of conversational implicature using the game theoretic notion of forward induction.[4][3] In the first case, a speaker conversationally implicates something by remaining silent. The second case is the wellknown recommendation letter example, often held up as the paradigm example of conversational implicature. Consider the stark situation in which a conversational participant remains silent rather than making an utterance. An act of remaining silent, arguably, can generate conversational implicatures.[2]. How can these implicatures be detected by the hearer? By considering the possible utterances that the speaker might have been expected to make, but failed to make. The game theoretic notion of forward induction will help in understanding the stark situation. Using forward induction reasoning, one player, on the assumption that common belief in rationality will persist into the future, can sometimes determine the other player's next move. The reasoning depends on recognizing available actions which are not chosen. One player, in a sense, ``signals" her next move by not choosing some available actions.