This dissertation consists of three essays in which I study prospect theory preferences in non-cooperative game-theoretic frameworks. In decision-making experiments, it is commonly observed that actual choice behavior might violate the axioms of expected utility theory (EUT). Kahneman and Tversky (1979) argue that such experimental findings invalidate EUT as a descriptive model and propose prospect theory as an alternative representation of preferences. Later, Tversky and Kahneman (1992) propose cumulative prospect theory (CPT). Both of these theories stipulate that individual preferences can be represented by a pair of functions: probability weighting function and value function. These functions capture three key aspects of the theory: subjective probability weighting, reference dependence, and loss aversion. In the first essay of this dissertation, I study mixed strategy equilibrium for finite normal form games in which agents' preferences are represented by the pair of functions suggested in CPT. I introduce the notion of CPT equilibrium, prove the existence of CPT equilibrium for finite normal form games, and analyze the set of CPT equilibria for some normal form games. In the second essay, I study correlated equilibrium for finite normal form games in which agents' preferences are represented by the same pair of functions. I relate the notion of correlated CPT equilibrium to the notion of CPT equilibrium and investigate the differences between the sets of correlated equilibria under EUT and CPT preferences. Finally, in the third essay, I study a first-price sealed-bid auction. I concentrate on subjective probability weighting and analyze overbidding behavior which is commonly observed in first-price auction experiments. I show that inverse S-shaped probability weighting functions cannot completely explain overbidding and that such functions can provide a partial explanation for bidders with high valuations. Keywords: Correlated Equilibrium, First-price Sealed-bid Auctions, Mixed Strategy Equilibrium, Nash Equilibrium, Prospect Theory.