Are Smarter Groups More Cooperative? Evidence from Prisoner’s Dilemma Experiments, 1959-2003

Are Smarter Groups More Cooperative? Evidence from Prisoner’s Dilemma Experiments, 1959-2003

Garett Jones

Abstract

Are more intelligent groups better at cooperating? A meta-study of repeated prisoner’s dilemma experiments run at numerous universities suggests that students cooperate 5% to 8% more often for every 100 point increase in the school’s average SAT score. This result survives a variety of robustness tests. Axelrod (1984) recommends that the way to create cooperation is to encourage players to be patient and perceptive; experimental evidence suggests that more intelligent groups implicitly follow this advice.

I. Introduction

Are more intelligent groups of people better at cooperating? Repeated prisoner’s dilemma (RPD) experiments run at numerous universities since 1959 may hold the answer. Overall, the tendency is clear: Students at schools with higher average SAT and ACT scores cooperate much more often, yielding about 5% more cooperation for every 100 combined SAT points (see Figures 1-3). Students at the best schools cooperate about 15% more often than typical college students. [...]

The fact that causation can run through multiple channels and in both directions makes it all the more important to use detailed micro-level evidence to identify which channels are quantitatively crucial. The results presented here begin to do just that. Cooperation is key to most definitions of social capital (Putnam 2000) and trust (Fukuyama 1995), both of which have been explored as possible drivers of income differences across countries (inter alia, Knack and Keefer 1997, Francois and Zabojnik 2005, Temple and Johnson 1998, and especially Landes 2000, though see Miguel et al. 2005, for contrary evidence). … Clearly, economists are used to thinking of agents within countries as playing a prisoner’s dilemma and to thinking that difficulty cooperating is likely to hurt national economic performance. The evidence presented here provides one explanation for why some countries are better at resolving this dilemma: Their populations are, on average, more intelligent.

III. Results

Tables 2 and 3 contain the main results. Appendix 1 reports nonparametric results (including kernel estimates, nearest neighbor estimates, and rank correlations) that tell much the same story. Table 2, the correlation matrix, demonstrates that higher rates of cooperation tend to occur at schools with more intelligent students, regardless of which test one uses to measure intelligence. The lowest correlation between rates of cooperation and a school’s average test score is 0.36, while the highest is 0.67. Thus, a substantial fraction of the variance in the rates of cooperation in an RPD can be predicted just by knowing the average SAT score at a given school. As Figures 1 through 4 indicate, these results are not driven by one or two outliers.

Additionally, if one glances at the correlations between the various test scores themselves, one sees that the values are always greater than 0.7, implying that average test scores at the same school have, for the most part, remained stable over the decades. This means that getting the precise test score for the precise year in which each study was conducted is unlikely to change the major results.

Indeed, the fact that these test scores are somewhat noisy measures of the true average intelligence of the students in a given study introduces a classic errors-in-variables problem, implying that the coefficients are biased downward. Therefore, one can reasonably expect the true relationship between intelligence and cooperation to be even stronger than reported here.

The regression results in Table 3 show quantitatively how important higher intelligence is likely to be. Regardless of the SAT measure used, a 100 point increase in the average SAT score at a school is associated with between 4.6% and 8% more cooperation. All results are significant at the 5% level. Even if the true coefficient value is the lowest of these estimates, then cognitive ability appears to be an important predictor of cooperation.

How large are these effects? Using our weakest results, those from the 2006 SAT regression, one sees that moving from “typical” American universities in the database such as Kent State and San Diego State (with SAT scores around 1000) to elite schools like Pomona College and MIT (with scores around 1450) implies a rise in cooperation from around 30% to around 51%, a 21% increase. Thus, substantially more cooperation is likely to occur in RPD games played at the best schools. It indeed appears that smarter groups are better at cooperating in the RPD environment.

With appropriate caution, one can use the Frey and Detterman equation to convert SAT scores into IQ points to give a back-of-the-envelope estimate of the relationship between IQ and cooperation. If a school’s math and verbal scores each increased by 50 points, then a 5 point increase in average IQ would predict a 5% increase in cooperation, a simple one-for-one relationship between IQ points and the rate of cooperation. Since Lynn and Vanhanen document a 38 IQ point gap between countries in the 5th and 95th IQ percentiles, one can reasonably expect sizable increases in cooperative behavior as one moves from low-average-IQ to high-average-IQ countries.

IV. Robustness tests

[...] In addition, the timing of the experiments themselves do not seem to matter: Omitting the earliest or latest 10% of the experiments (e.g., pre-1962 or post-1977) had no substantial impact on the results, and inclusion of a linear or quadratic time trend likewise had no substantial impact on the results.

Further, for each study information was collected on the number of rounds in each study’s RPD, whether actual money was involved, and whether the interaction was face-to-face versus across some kind of screen. When all were included simultaneously in broader regression specifications, none of these four features had any impact on the results; SAT 2006 was significant at the 2% level, the rest at 1%. Results are reported in Table 4. Only the number of rounds was statistically significant in any specification 7, but the inclusion of these three variables impacted the statistical or quantitative significance of the test score variables.

As in Sally (1995), longer games had less cooperation.

An additional robustness test checked to see whether the effect is simply due to students at private schools being more cooperative, perhaps due to their smaller class sizes and smaller campus populations, or perhaps due to cultural differences associated with the higher average socioeconomic status of private school students.

In these regressions, in addition to the money, interaction, and trial number variables, a dummy variable was included for private schools: a 0.5 was coded for two studies that included a mix of public and private school students (the main regressions likewise used a simple average of the test scores for these two mixed-school studies; omission of these studies had no substantial impact on the results). Results are reported for Table 5. Controlling for test score, the private school dummy was never significant at conventional levels; its p-values ranged from 22% to 95% depending on the test score measure included, and the dummy’s value implied that private school students cooperated from -0.5 to +8% more often. 8

8 Perhaps paying with cash matters more at public schools, where poorer students might value cash more; accordingly, I also ran specifications that included a private school/money interaction dummy that was never statistically significant.

The cognitive ability coefficient estimates were little changed. For the SAT 1966, SAT 1970, and ACT 2006 results, the results were statistically significant at the 5% level; and for SAT 2006 results, at the 10% level. Out of all the specifications reported here, this SAT is the only one that falls below the 5% level. Since SAT 2006 performs well across many specifications while the private school dummy always performs poorly, one may plausibly take this single estimate as only weak evidence against the robustness of cognitive ability. 9

9 One may be concerned that with such small sample sizes, adding so many controls is statistically unwarranted, but even when only one, two or three controls are added at a time, the cognitive ability measures still perform well. SAT 2006 always is always the weakest, but that coefficient’s magnitude changes little across specifications.

Finally, log and semilog specifications had no substantial impact on the results, though the linear specification used in the previous section was slightly more statistically significant in general. The semi-elasticity of cooperation with respect to SAT score (omitting other controls, which, as noted, never quantitatively impact the coefficient estimate) was estimated to equal .094 per 100 year 2006 SAT points, and equal to 0.17 and 0.16 for the 1966 and 1970 SAT scores, respectively. The ACT 2006 semi-elasticity of cooperation was 4.6 percent more cooperation per ACT point. The 2006 SAT results were significant at the 10% level, while the 1966 and 1970 SAT estimates were well under the 5% value; the ACT estimate was significant at the 1% level. One might summarize these semi-elasticity results by saying that a 400-point increase in a school’s SAT score (or a 20-point increase in a group’s average IQ) is associated with roughly 50% more cooperation. Overall, these robustness tests appear to confirm the result from the preceding section: Groups with high cognitive abilities appear to cooperate more often when playing a repeated prisoner’s dilemma.

V. Discussion and Conclusion

[...] Patience is surely one way of enlarging the shadow of the future, and recent research (Warner and Pleeter 2001, Fredrick 2005, Benjamin, et al. 2006) has shown that persons with higher cognitive ability tend to be more patient and less impulsive. Warner and Pleeter (2001) show this in the context of military personnel choosing a lump-sum severance payment versus an annuity; personnel with higher test scores had a lower implied discount rate. Fredrick (2005) and Benjamin et al. (2006) both showed that smarter individuals (as measured by cognitive tests) were more patient in experimental settings, and Fredrick in particular refers to a number of other studies from the psychology and economics literatures illustrating the link between cognitive ability and patience.

In the psychology literature, the raw correlation between cognitive ability and a preference for immediate rewards is widely recognized (inter alia, Jensen 1998 passim); this IQ-impulsivity link is analyzed in a particularly thorough manner in De Wit et al. (2006). Using a large sample of middle-aged Americans, they found that IQ was a robust predictor of impulsive experimental behavior even after controlling for socioeconomic status, race, gender, and survey measures of impulsiveness. All told, research by economists and psychologists alike indicate that smarter groups are likely to be patient groups.

[...] Axelrod emphasizes the need to perceive the identity of one’s opponents as well as to perceive what truly counts as a move of “cooperate” or “defect,” but in both experimental settings and real-world prisoner’s dilemmas, the most important kind of “perceptiveness” offered by intelligent players may simply be that they have a better chance of accurately and quickly perceiving the rules of the game, as well as remembering the payoffs and the game’s recent history. One well-established fact about higher-IQ individuals is that they tend to have larger working memories (inter alia, Conway et al. 2002), thus giving them a better chance of remembering precisely what kind of game they’re playing and what has happened in the course of the game. All told, there is abundant evidence that smarter groups are generally more patient and more perceptive, traits that Axelrod recommends as keys to cooperative behavior.

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