Relying on the experimental findings that actual choice behavior often violates the axioms of expected utility theory (EUT), we study non-EUT preferences in a noncooperative game-theoretic framework. In particular, agents’ preferences are represented by the pair of functions suggested in cumulative prospect theory (CPT). Accordingly, three key aspects of CPT are incorporated: subjective probability weighting, loss aversion, and reference dependence. We introduce a correlated equilibrium and two mixed strategy equilibria for agents with CPT preferences. We prove the existence of equilibria for finite normal form games and investigate the sets of equilibria in some examples.