Optimal stopping with behaviorally biased agents: The role of loss aversion and changing reference points

We explore the implications of two central human biases studied in behavioral economics, reference points and loss aversion, in optimal stopping problems. In such problems, people evaluate a sequence of options in one pass, either accepting the option and stopping the search or giving up on the option forever. Here we assume that the best option seen so far sets a reference point that shifts as the search progresses, and a biased decision-maker's utility incurs an additional penalty when they accept a later option that is below this reference point. Our results include tight bounds on the performance of a biased agent in this model relative to the best option obtainable in retrospect (a type of prophet inequality for biased agents), as well as tight bounds on the ratio between the performance of a biased agent and the performance of a rational one.