How Can Yes-No Questions Be Informative?

In this paper, we propose to analyze the informativeness of questions, in the context of ‘inquiry games’, where a player, Inquirer, intends to establish a certain conclusion by means of a combination of reasoning and interrogation, using information (answers) from other players, Sources. This paper is one step toward a precise game-theoretic foundation for these games, which where suggested by Hintikka to be a model of rational inquiry.1 Sources may be partially unaware of Inquirer’s goal, and becoming aware of her goal may make them unwilling to achieve cooperation (i.e. answer truthfully whenever they can). This introduces a discrepancy with situations amenable to standard game theory, in which the space of strategies is common knowledge among players. Section 2 introduces the idea of inquiry games, and presents an example borrowed to Holmesian lore, in order to show how questions introduce information in inquiry contexts. We focus on ‘yes-no’ questions, because of their semantic properties which in turn guarantee their availability in questioning strategies. Section 3 presents the difficulties standard game theory face to represent the kind of strategies an inquirer has to rely on to prevent her question to inform her sources when this information could affect their answers. We conclude with some remarks about the relations between the present work and issues in epistemology, an the application of game-theory.