This paper provides a game-theoretic analysis of contrastive focus, extending insights from recent work on the role of noisy communication in prosodic accent placement to account for focus within sentences, sub-sentential phrases and words. The shared insight behind these models is that languages with prosodic focus marking assign prosodic prominence only within elements which constitute material critical for successful interpretation. We first take care to distinguish the information-structural notion of focus from an ontologically distinct notion of givenness marking, and then (...) outline the core properties of focus. We then introduce a signaling game between a speaker and hearer in which the goal is to transmit semantic content with the smallest signal possible. We apply the Iterated Best Response method of Franke to find equilibrium strategies in this game, where a unique equilibrium strategy in this case picks out the “critical information” of an utterance, which by hypothesis constitutes its focus. We show that iterating this game at different syntactic levels of a sentence makes correct predictions about the role of contrast in determining stress within words and phrases, and can be extended to account for association and second occurrence focus effects. (shrink)