This paper proposes a strategic analysis of politeness strategies stated in terms of game theory. After reviewing some facts about lexical strategies for linguistic politeness, we turn to our game-theoretic account, which involves treating polite and impolite acts as action choices in an indefinitely repeated game. We show that such games have winning strategies and that these strategies can be of differing degrees of complexity in a mathematical sense. Finally, we outline some avenues for future work.
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