# Economic Classroom Experiments/Search
## Overview

Students engage in a stylized model of costly search.

### Objectives for learning (Intended Learning Outcomes)

* Review of cost-benefit calculation (marginal revenue = marginal cost).
* Understanding and avoiding the "sunk-cost" fallacy.
* Understanding the role modeling assumptions make when drawing conclusions.

### Suitable modules

Advanced Micro. This is a good first experiment for a course in game theory or strategy, to illustrate individual decision-making prior to moving on to games proper.

### Level (year of programme)

Upper-level undergraduate, or MSc or MBA.

### Prerequisite knowledge

Intermediate microeconomics (theory of firm behavior, as far as marginal revenue=marginal cost) is helpful, but not necessary.

## Procedures

A three-treatment sequence is suggested. This experiment is most easily run on computers, for example, with the Search experiment on Veconlab.
* Treatment 1: Draws from interval [0.00, 0.90], distribution known, search cost 0.05, recall permitted;
* Treatment 2: Draws from interval [0.00, 0.90], distribution known, search cost 0.20, recall not permitted;
* Treatment 3: Draws from interval [0.00, 9.00], distribution unknown, search cost 0.50, recall permitted.
A design with ten search sequences in each treatment (thirty overall) generally takes about 40-45 minutes, including reading the instructions aloud to the students.
For these treatments, the optimal cutoff strategy for risk-neutral searchers is to search until a draw of at least 0.60 in Treatment 1, 0.30 in Treatment 2, and 6.00 in Treatment 3. (Note that Treatment 3 is Treatment 1 with all parameters multiplied by 10.)
One can show this by first examining Treatment 1. Let $v$ be the cutoff. At $v$, one would be indifferent to drawing a new value. Assume there is recall. Then the benefit is the odds of getting a higher draw $(.9-v)/.9$ times the expected gain from this new value $((.9+v)/2)-v$. The benefit should equal the cost, thus $((.9-v)^{2}/1.8)=c$. When $c=.05$, we have $(.9-v)^{2}=.09$. Thus $v=.6$. Also notice that (without a time limit) not allowing recall does not affect the cutoff since one would not want to recall values below the cutoff.

## Integration into course

The sequencing of treatments is designed to illustrate that the importance of recall depends on the extent to which one knows the distribution of values. Students generally react negatively when recall is "taken away" from them at the beginning of Treatment 2, especially coupled with the increase in search costs. In Treatment 3, when recall is returned, the distribution of values changes enough to give search an additional informational value, as the results of draws now give information about the possible values. Students who draw relatively low values at the beginning of Treatment 3 tend to be happy with their draws, while those drawing very high values often do some additional searching, since they realize their old information about the distribution of values is no longer accurate.
Generally, the risk-neutral cutoff prediction does a good job of organizing the data. However, not all students will immediately see that the solution is found by equating the expected benefit of the next draw against the cost of the draw. Some other heuristics students report include
* Computing the average draw (0.45 in Treatments 1 and 2) and searching until a draw that exceeds the average is obtained. The instructor should point out that this leaves out the search cost, an important economic variable, entirely.
* Loss avoidance. Students sometimes report that they want to avoid getting a negative total earnings on a search sequence, and therefore stop searching as soon as their search costs exceed, or come close to exceeding, their current value. This is a variation on the "sunk cost" fallacy. The instructor should remind the students of the distinction between fixed, unavoidable costs and marginal, avoidable costs, and how those costs do and do not come into play in economic decision-making.
In relating this abstract experiment to real-world applications, focus on the extent to which the distribution of values is known, whether recall is possible, and what the nature of search costs are, reminding students that "all costs are opportunity costs." For a bit of levity, introduce dating as one application, and ask students whether recall is possible in that setting!
This experiment is part of an integrated course teaching principles of strategy through experiments. Here is a list of questions students can answer either as part of a writing assignment, or to lead off class discussion of the results of the experiment.
* Outline your strategy for each of the three treatments. How did you decide to make the choices you made?
* How did your strategy depend on the search cost?
* Do you think lowering the cost of an individual draw will necessarily lower the total amount spent searching on average? Why or why not?
* Did having recall (i.e., the ability to go back and take a value from a previous draw) help? In some treatments? In all treatments? In none of the treatments?
* Write a brief description of a search example drawn from “real life.” Give particular attention to (a) whether the distribution of values is “known” or “unknown;” (b) what corresponds to the search costs (purely financial, or perhaps psychic, etc.); (c) whether recall of previous draws is or is not possible.

## Instructor hints

Since this is an individual choice experiment, this is suitable for assigning to students outside of class time, and can be done with large classes.
If you are considering doing a set of experiments in a course, this makes a nice first experiment because of its relative simplicity. Students new to classroom experiments may take some time to get used to lab procedures, so having an experiment where each can work at their own pace is ideal to start off with.
If you do this experiment during class time, you are likely to have a wide variety of paces at which students work; it is probable you may have a student or group finish an entire treatment before another student finishes the first round. If students are waiting on "slowpokes," remind student that everyone sees different draws, and therefore will work at different paces. Most of the students who start slowly do so because they attempt to figure out their strategy in detail in the first round; once they make their determination of strategy, they tend to catch up quickly.