Language games

Abstract

In this paper we summarize concepts from earlier work and demonstrate how infinite sequential games can be used to model strategic conversations. Such a model allows one to reason about the structure and complexity of various kinds of winning goals that conversationalists might have. We show how to use tools from topology, set-theory and logic to express such goals. Our contribution in this paper is to offer a detailed examination of an example in which a player ‘defeats himself’ by going inconsistent, and to introduce a simple yet revealing way of talking about unawareness. We then demonstrate how we can use ideas from epistemic game theory to define various solution concepts and justify rationality assumptions underlying a conversation.