Optimal Stopping with Multi-dimensional Comparative Loss Aversion

Linda Cai, Joshua Gardner, S. Matthew Weinberg

Abstract: Motivated by behavioral biases in human decision makers, recent work by [11] explores the effects of loss aversion and reference dependence on the prophet inequality problem, where an online decision maker sees candidates one by one in sequence and must decide immediately whether to select the current candidate or forego it and lose it forever. In their model, the online decision-maker forms a reference point equal to the best candidate previously rejected, and the decision-maker suffers from loss aversion based on the quality of their reference point, and a parameter \(\lambda \) that quantifies their loss aversion. We consider the same prophet inequality setup, but with candidates that have multiple features. The decision maker still forms a reference point, and still suffers loss aversion in comparison to their reference point as a function of \(\lambda \), but now their reference point is a (hypothetical) combination of the best candidate seen so far in each feature.