Predicting Behavior in Games: Loss Aversion vs. Rank Dependent Utility vs. Range Utility Theory

Rank dependent probability weighting—an integral part of cumulative prospect theory—has come to dominate the behavioral modeling of risk preferences in non-strategic settings over the last 40 years. We draw attention to some serious limitations of rank dependence when it comes to game-theoretic settings. First, in strategic settings where the probability of payoffs may be determined by the joint choice of all players, ranking outcomes (in a matrix) from lowest to highest becomes psychologically unnatural. Second, existence and interpretation of equilibrium when players possess rank-dependent preferences is problematic. Third, rank dependent models are notoriously complex to compute. In contrast, we argue that an alternative model, range utility theory, preserves much of the descriptive realism of rank-dependent utility, while sharing the theoretical and computational advantages of expected utility. We compare the two models using simple games of strategy as examples, and discuss the importance of accounting for loss aversion.