The effect of goals and environments on human performance in optimal stopping problems.

Abstract

In optimal stopping problems, people are asked to choose the best option out of a sequence of alternatives, under the constraint that they cannot return to an earlier option once it is rejected. We examine human performance on variations of the optimal stopping problem, with different environments and with different goals. Specifically, we consider environments that have relatively high or low numbers, under the goals of choosing the maximum or the minimum. A natural consequence of this design is that we study the decisions that people make in both congruent situations, in which the environment and goal align, and incongruent situations, in which the environment and goal differ. First, we present empirical evidence that people adapt to both high and low environments as well as to both maximum and minimum goal frames, and that they make decisions consistent with using threshold-based models. Second, we apply a previously developed threshold model of individual performance to our data, inferring the thresholds people use. Lastly, we use Bayes factors to test whether people are sensitive to environments, goals, and congruency in optimal stopping problems. Overall, our results suggest that there are psychological similarities in congruent situations, pointing toward invariances and rationalities in the way people solve optimal stopping problems as the environments and goals change, without contaminating framing effects.

Learning When to Stop Searching

“…Information about the distribution was also conveyed to participants in a study by Rapoport and Tversky (1970), in which seven individual participants viewed an impressive 15,600 draws from probability distributions over several weeks before playing secretary problem games with values drawn from the same distributions. In a study where participants played secretary problem games on five values drawn from either a left-skewed or a right-skewed distribution, Guan and Lee (2017) provided information about the distribution by requiring participants to first play eight "practice problems" before beginning the main part of the experiment. These investigations are similar to our study in that they both involve repeated play and that they present players with actual values instead of ranks.…”

“…First, to our knowledge, our study is the first study to begin with an unknown distribution that players can learn over the course of the experiment. Previous studies have provided rank information only (e.g., Seale and Rapoport 1997), given a full description of the distribution (leaving no scope for learning) (e.g., Lee 2006), or presented samples from the distribution to the participants before the main experiment (e.g., Tversky 1970, Guan andLee 2017). Seemingly small differences in instructions to participants could have a large effect.…”

“…For example, Campbell andLee (2006, p. 1068) attempted to get participants to learn in the full information condition by offering enriched feedback and even financial rewards in a repeated secretary problem, but they concluded that "there is no evidence people learn to perform better in any condition." Similarly, Lee (2006) and Guan and Lee (2017) found no evidence of learning in the full information version of the problem, and Seale and Rapoport (1997) found no evidence of learning in the no information (ranksonly) version.…”

Untitled

“…Some studies have investigated tasks closer to real sequential choice problems by presenting the actual value of the option to the decision makers (Guan & Lee, 2017;Guan, Lee, & Vandekerckhove, 2015;Kogut, 1990;Lee, 2006;Shu, 2008;von Helversen & Mata, 2012). In this version, the optimal solution is based on calculating the expected reward of the remaining outcomes.…”

“…From this expected reward, a threshold is calculated for each option in the sequence as described by Gilbert and Mosteller (Gilbert & Mosteller, 1966). Results showed that human behavior was systematically biased away from the optimal threshold (Guan & Lee, 2017;Guan et al, 2015;Lee, 2006). Furthermore, these studies still kept the restriction that only the best alternative is rewarded-a payoff function that does not correspond well with everyday experiences.…”