Intolerable nuisances: some laboratory evidence on survivor curve shapes

Abstract

The fraction of a user population willing to tolerate nuisances of size x is summarized in the survivor curve S(x); its shape is crucial in economic decisions such as pricing and advertising. We report a laboratory experiment that, for the first time, estimates the shape of survivor curves in several different settings. Laboratory subjects engage in a series of six desirable activities, e.g., playing a video game, viewing a chosen video clip, or earning money by answering questions. For each activity and each subject we introduce a chosen level $x \in [x_{\min }, x_{\max }]$ of a particular nuisance, and the subject chooses whether to tolerate the nuisance or to switch to a bland activity for the remaining time. New non-parametric techniques provide bounds on the empirical survivor curves for each activity. Parametric fits of the classic Weibull distribution provide estimates of the survivor curves’ shapes. The fitted shape parameter depends on the activity and nuisance, but overall the estimated survivor curves tend to be log-convex. An implication, given the model of Aperjis and Huberman (SSRN, doi: 10.2139/ssrn.1672820, 2011), is that introducing nuisances all at once will generally be more profitable than introducing them gradually.

Appendices

Appendix 1: Details

1.1 Details on inconveniences

Table 4 summarizes the inconvenience levels and the number of observations at each level. Along it, Table 5 reports the p-values of a Fisher exact test comparing switch rates across tasks for each value of x. As mentioned, the results suggest that all tasks share a similar underlying distribution of subject tolerance for nuisances.

Table 4 Nuisance values (and numbers of observations)

Table 5 P-Values of the Fisher exact test comparing switching decisions for all treatment levels

1.2 Robustness checks

Table 6 presents robustness checks to supplement Table 4. The additional variables are dummies for the different orders in which the activities were presented (i.Order), and the several dummies $Pibigpop_{i,j}$, $Popbigpi_{i,j}$, $Readbigsat_{i,j}$, $Satbigread_{i,j}$ that test for similar activities with different levels of nuisance. For example, the dummy $Pibigpop_{i,j}$ ($Popbigpi_{i,j}$) indicates trials in which the nuisance level for Movie/Pi (Movie/Pop) is higher than the nuisance level for Movie/Pop (Movie/Pi); similarly $Readbigsat_{i,j}$ ($Satbigread_{i,j}$) is a dummy for the case where Reading (SAT) has a higher nuisance level than does SAT (Reading). Because we also present the predicted probability results, the table includes values for the cases in which these latter dummy variables had a value of zero. These are reported as $NotReadbigsat_{i,j}$, $NotSatbigread_{i,j}$, $NotPibigpop_{i,j}$, and $NotPopbigpi_{i,j}$.

Table 6 Switching probit model

The Probit results show that 2. Order and 4. Order are somewhat different to the baseline 1. Order, while the other order dummies are not. These differences arise from the small number of observations for some combination of order/treatment. For example; 4. Order has 40 observations for Treatment = 2 with 28 non-switchers and 12 switchers, while 1. Order has only 5 observations for this treatment level and no switchers. Similarly $Pibigpop_{i,j}$ (for which there are only 8 observations) seems to have an effect.⁷

We conclude that our results are sufficiently robust, and that the few dummies with significant estimates probably arise from small sample bias.

1.3 Fit of the estimation for all activities

In Fig. 8 we present a summary the pooled data across all treatments along with the survivor curve resulting from a Weibull distribution with the estimated parameters from Table 3. The fit of the curve to our empirical data points is remarkably good.

Fig. 8

Overview the pooled data across all activities. The red (blue) line shows the upper (lower) bound of the S(x). The black line is the average between the upper and lower bound. The percentage of subjects that did not switch ($Y=0$) for each inconvenience level (x) are represented by the green bars. The thicker dark red line is the survival curve resulting from a Weibull distribution with the estimated parameters. (Color figure online)

Appendix 2: Description of activities

In this appendix we list all the activities that were not described in detail in the methods section.

1.1 Movie/Pop

Subjects were presented with a menu of two video clips (an interview of Zack Galifianakis by Letterman, and a clip on how to do crossover moves in basketball). After 100 s of visualization, a 15 s long pop-up would appear on the screen. This pop-up would partially cover the video clip, and have flashing colors; moreover, while the pop-up was on the screen, the movie clip would continue playing in the background but with no sound. The unit of the nuisance $x \in [5, 30]$ is the number of seconds between consecutive pop-ups, e.g., if a subject was assigned a nuisance level of $x=5$, then she would have a 15 s pop-up every 5 s. If the subject decided that the nuisance was too big, then she could switch to the bland activity which, as in all movie activities, was a video of gentle waves breaking at La Jolla beach. Once a subject switched to the bland activity she would remain there until the end of the round. Rounds lasted 8 min.

Note on wave watching: The bland activity for all movie activities is “watching waves”. We decided to use this video because as it has no plot, that is, its “replay value” is very high, allowing us to reuse it with almost no loss in its (relative) attractiveness.

1.2 Slug

Slug is a version of the classic video game Snake.

Snake was a popular arcade game in the 1970s but gained world-wide acceptance in 1998 as it became the standard pre-loaded game in Nokia phones. The game has been used as “Easter egg” by both Youtube and Gmail. In this game the objective is to get “food”, which corresponds to colored pixels that appear at random points of the enclosed “playing space”. Each time the player gets to food she earns points, but the slug increases in size, making it harder to maneuver. To get to the food subjects control the slug with the keyboard arrows. If the slug bumps into the walls of the enclosed playing space, or if it hits itself, the player loses. Losing has no cost in points, the subject just need to restart the game by pressing the refresh button (F5 on the keyboard), and the game starts over with the same amount of accumulated points. As mentioned, points are awarded by getting to food; 10 points for regular food and 40 points for bonus food. The difference between these two types of food is that bonus food only stays on screen during 10 s, while normal food is there until eaten. Food is color coded, with bonus food being yellow, and regular food blue. Each point was worth $0.01. The jitter nuisance would start 50 s into the round, and involves a random turn (left or right) each pixel with probability $x \in [.10, .25].$ The bland activity towards which subjects could switch was the same exact game without the jittering nuisance, but paying only one fourth of the amounts in the original activity (i.e., 10 points per bonus food, and 5 points for each piece of regular food “eaten”). Each round lasted 7 min.

1.3 Read

Subjects are given a menu with a series of articles from the New York Times (an article on the Proposition B for LA county, an article on veterans of the Iraq war coming back to the US, and an article on fee increase at the UC system). The nuisance $x \in [.15, .30]$ is the (independent) probability for each letter of being dropped. The first 15% of the text would be nuisance free. On the other hand, the text was presented broken into paragraphs. To ensure that subjects actually read the text, they could only move to the next paragraph by clicking a “next” button that would appear 10 s after the start of every new paragraph. The bland activity was counting bits, which presented subjects with a binary string of 15 digits, and asked them to count how many 1’s were in the string. If the answer was correct, then a new string was generated. If the answer was wrong the subject would be given a new opportunity until he answered correctly. This would last until the end of the round, which was 6 min long.

1.4 SAT

Subjects could pick between two different texts taken from an SAT practice web-page. The text would be presented to subjects along with only one of the 8 multiple choice questions they had in this round. All answers were final, and once a choice was made the next question would appear, with no way of going back. This was a paid activity and each correct answer would pay $0.40, while each incorrect answer would penalize $0.10. The nuisance for this activity was letter dropping, and worked exactly as in the Read activity. In this case each letter was dropped with probability $x \in [0.06, 0.21]$. The bland activity was the same task with all the letters, but paying one fourth (i.e., $0.10 for each correct answer and −$0.02 per incorrect answer). If a subject decided to switch, she would not start over all the questions, but would start the bland activity at the same question where she switched to activity B.