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Deterrence is the backbone of military strategy. Dissuading an opponent from taking a specific action by threat of violence is the definition of deterrence. From the outset of the Cold War there has been a strong link between the study of deterrence and game theoretic analysis. There are compelling epistemic reasons for studying deterrence as a game. By doing so, the strategic interaction between actors is placed at the centre of the analysis, mapping the possible outcomes and revealing the strategies available to the actors. Discussions about various models’ appropriateness and model comparison therefore play a central role in deterrence research; from underlying assumptions and deterrence representation to theory and evidence. This dissertation treats aspects of all of these topics. Article I, “Prospects of Deterrence – Deterrence Theory – Representation and Evidence”, analyses the relationship between model and theory and what happens to a deterrence theory when the rationality assumption is switched to a prospect theoretical utility function. Article II, “A Misfit Model – Bounded Rationality and Deterrence Representation”, defends and remodels Schelling’s idea of irrational threats for effective deterrence. Article III, “Comparable Deterrence – Target, Criteria and Purpose”, treats the issue of how one can compare game theoretic models with one another and proposes a meta-model for how this can be done. Article IV, “Deterring the Dauntless – Appraising the Effects of Naval Deterrence against the Somali Piracy”, estimates whether and to what extent Somali piracy was deterred by the naval intervention.