CSG Study 2 May 2014 Analyses

Abstract

In an innitial test of the competitive sampling game (CSG, Phillips et al. (2014)), slower players (“receivers”) were forced to take options left behind by the faster choosers. If receivers had the option to reject these options (perhaps in fear that they contained negative outcomes), would players elect to make slower choices do to the decreased cost of being ‘beaten to the punch’? In addition, does playing practice games before ‘real’ trials affect sampling behavior in real, consequential trials? In an empirical study, we tested these questions by having participants in four experimental groups play the CSG. We independendly manipulated two independent variables: whether players played 5 practice games before real consequential trials (yes v no), and whether receivers in the game had the option to take or leave options left by choosers.

Participants

128 participants participated at the MPI. There were 32 total session with four participants per session. Each player played 8 total games, with half playing the first three as practice games, and the other half playing all 8 as real games.

General Results

Sample sizes across conditions

Sampling sizes were higher than original Phillips et al. (2014) study

Across all conditions, the median number of sampling rounds was 2 with a mean of 2.62. These sampling sizes seem consistently higher than that of the original Phillips et al. (2014) study which found a mean of 1.83 and a median of 1. My best explanation for this difference is in how participants were recruited: In the original study, participants were approached in the library at Uni-Basel. In the current study, they travelled to the MPI to take part in this (and other) studies. I think they felt a greater obligation to play the game in this study than the original.

Probability that choosers chose the high-EV option

Next, we looked at the proportion of choosers who chose the high-EV option.

Choosers chose the high-EV option in 60% of games. This is very close to the 58% value we observed in Phillips et al. (2014)

New Results

Does having the option to reject options change sampling behavior?

• Having the option to reject non-chosen options (might) increase sample size, but only by a very small amount.

Next, I look at how the option to reject options left by fast choosers affects overall sampling behavior. Because some options can have negative outcomes, having the option to reject options left behind by the faster choosers decreases the cost of being the slower player. As a result, we would expect that having this option should increase sampling sizes:

When players could reject left options, they tended to sample a bit longer. The mean sample size for players who could not quit was 2.44 and the mean sample size for players who could quit was 2.79. The median for both groups was 2 and 2. A one-sided frequentest t-test is ‘almost significant’ at t(435.42) = 1.65, p = 0.05 However the size of the effect was small and probably shouldn’t be interpreted with much confidence.

How do receivers behave in games where they have the option to quit?

• Receivers were slightly more likely to accept options when they had a positive EV (0.64) than when they had a negative EV (0.51). A one-sided frequentist test of proportions was not ‘quite significant’, z(1) = 2.52, p = 0.06

• Receivers were slightly more likely to accept high-EV options (0.68) than low-EV options (0.53). A one-sided frequentist test of proportions was ‘significant’, z(1) = 3.14, p = 0.04

Was there an effect of practice games on sampling sizes?

• Participants playing practice games had slightly higher sampling sizes for the first three games (mean = 2.93) than those who started with real games (mean = 2.45). A frequentist t-test was ‘non-significant’: t(170.944) = 1.45, p = 0.07.

Conclusions

1. Sampling sizes were generally a bit higher in this study than Phillips et al. (2014). This may be due to differences in how we recruited participants.

2. Choosers chose high-EV options at almost the same rate (60%) that we observed in Phillips et al. (2014).

3. Having the option to reject options left behind by choosers ‘may’ have increased overall sampling sizes slightly (mean of 2.44 versus 2.79). However if the effect exists, it is small.

4. Receivers do not appear to make “accept vs. reject” decisions at random. They are slightly more likely to accept options with positive expected values than those with negative expected values, and are slightly more likely to accept high-EV options than low-EV options.

5. Participants appear to sample slightly more in practice games than in real games; however the effect is small and does not seem to affect future real games.