Optimal Stopping with Behaviorally Biased Agents: The Role of Loss Aversion and Changing Reference Points

One of the central human biases studied in behavioral economics is reference dependence - people's tendency to evaluate an outcome not in absolute terms but instead relative to a reference point that reflects some notion of the status quo [4]. Reference dependence interacts closely with a related behavioral bias, loss aversion, in which people weigh losses more strongly than gains of comparable absolute values. Taken together, these two effects produce a fundamental behavioral regularity in human choices: once a reference point has been established, people tend to avoid outcomes in which they experience a loss relative to the reference point. A well-known instance of the effect is the empirical evidence that individual investors will tend to avoid selling a stock unless it has exceeded the price at which they purchased it.

In more complex examples, the reference may shift while an agent is making a decision. Consider for example an agent who is trying to make a large purchase or hire a job candidate, and does this by evaluating candidate options in one pass in a take-it-or-leave-it fashion - with each candidate they must either accept it and end the search, or give up on it as an option forever. Experimental studies by Schunk and Winter [7] show that people in this type of task behave consistently with the notion that they are maintaining a time-varying reference point equal to the best option they have seen so far. This means that if they settle for a candidate A that is worse than a candidate B that they have seen in the past, their utility from selecting A will be reduced by some notion of loss relative to the high reference point set by B. In these studies people operate so as to reduce the chance that they will choose a future option that is dominated by one that they have passed up.