Conversation and Games

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. We then show how to tie down the notion of a winning condition to specific discourse moves using techniques from Mean Payoff games and discounting. We argue, however, that this still requires another addition from epistemic game theory to define appropriate solution and rationality underlying a conversation.

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