We examine the traditional deterrence game between Challenger and Defender. We treat two variations of the game – the complete information game and the one-sided information game where the first mover, Challenger, is the uncertain player. We employ sequential decision theory to analyze the game of incomplete information. The analysis is basic in that we employ a simplifying assumption, specifically that Challenger’s valuation of the status quo is fixed at zero. We examine the behavior of Challenger using both a von-Neumann-Morgenstern decision rule and a Kahneman-Tversky decision rule. The formal results show that given the right combination of outcome valuations and probability values and weightings, Challenger can make choices under the von Neumann-Morgenstern decision rule that are reversed from those made under the Kahneman-Tversky decision rule. We then relate these reversals to the concept of misperception found in the International Relations and Peace Science literatures. Finally, we comment on extensions of the ensuing analysis.