We present a new theory of decision under uncertainty: third-generation prospect theory (PT3). This retains the predictive power of previous versions of prospect theory, but extends that theory by allowing reference points to be uncertain while decision weights are specified in a rank-dependent way. We show that PT3 preferences respect a state-conditional form of stochastic dominance. The theory predicts the observed tendency for willingness-to-accept valuations of lotteries to be greater than willingness-to-pay valuations. When PT3 is made operational by using simple functional forms with parameter values derived from existing experimental evidence, it predicts observed patterns of the preference reversal phenomenon.
The prospect theory is one of the most popular decision-making theories. It is based on the S-shaped utility function, unlike the von Neumann and Morgenstern (NM) theory, which is based on the concave utility function. The S-shape brings in mathematical challenges: simple extensions and generalizations of NM theory into the prospect theory cannot be frequently achieved. For example, the nature of monotonicity of the indifference curve depends on the underlying mean. Price hedging decisions also become more complex within the prospect theory. We discuss these topics in detail and offer a general result concerning the sign of a covariance from which we then infer desired properties of the indifference curve and also justify hedging decisions within the prospect theory. We illustrate our general considerations with a thoroughly worked out example.
Analysis of the use of prospect theory since the mid-1980s identifies significant impact on research on important puzzles in international security and international political economy. Research since the mid-1990s has identified the scope conditions of framing effects, loss aversion, and patterns of probability estimation on international behavior. New research using multiple methods has strengthened the validity of findings on the impact of framing effects and loss aversion under different conditions. Future research opportunities for psychological explanations of international behavior are identified.