Simulated dangerous climate change

In the first game of the 18-players treatment and of the 6-representatives treatment, only 33% of the groups reach the target sum. By contrast, groups in the six-players treatment are almost twice as likely to collect sufficient contributions in the first game, with 60% of the groups reaching the target sum (Fig. 2a–c), similar to a previous study14. The percentage of groups reaching the target sum increases towards game 3 in the six-players and the six-representatives treatment, but the increase is not statistically significant. In game 3, the groups in the 18-players treatment are the least successful (Fig. 2a–c), but again differences are not statistically significant.

Figure 2: Group success in reaching the target sum (left) and group investments (right). (a,d) Six-players treatment; (b,e) 18-players treatment; (c,f) 6-representatives treatment. In f, the sum invested is divided by 3 to allow comparison among treatments. Means±s.e.m. of 15 groups per game and treatment are shown. See text for statistics. Full size image

The total sums contributed per group do not differ among treatments in games 2 and 3 (Fig. 2e,f). In game 1, the six representatives contribute less than the six players (P=0.019, z=−2.341, n 1 =n 2 =15 groups, Mann–Whitney U-test, two-tailed; we use two-tailed tests throughout, with the group of six or 18 players as our statistical unit if not stated otherwise). Because in game 1, representatives are randomly picked from the group (see methods), the only difference between the two treatments is that representatives are contributing on behalf of their observing group. In such situations, representatives may have a more competitive mindset7, which would explain why groups in the six-representatives treatment reach the target less often. Total contributions show a small increasing trend from the first to the third game in all treatments (Fig. 2e,f), but the differences are statistically significant only between games 1 and 2 in the six-representatives treatment (P=0.026, z=−2.230, n=15, Wilcoxon signed-rank matched pairs test). Summed up over all three games per group, contributions relative to the target sum are lowest in the six-representatives treatment, significantly lower than in the six-players treatment (P=0.0061, z=−2.742, n 1 =n 2 =15, Mann–Whitney U-test).

Fair and selfish players

For the group to reach the target sum, each player must on average contribute half of her total endowment—the ‘fair share’ of €20 (€60 per representative in the six-representatives treatment). Thus, whenever the target sum is not reached, one or several players must have contributed less than their fair share. We call these ‘selfish players’ to distinguish them from the ‘fair players’ who give at least their fair share. The percentage of selfish players is highest in the 6-representatives treatment (Fig. 3a), higher than in the 6-players treatment (P=0.01, z=−2.559, n 1 =n 2 =15, Mann–Whitney U-test) and almost significantly higher than in the 18-players treatment (P=0.06, z=−1.862, n 1 =n 2 =15, Mann–Whitney U-test). The average contribution of a selfish player (relative to the fair-share contribution) is lower in the 18-players treatment than in both the 6-players (P=0.02, z=−2.302, n 1 =n 2 =15, Mann–Whitney U-test; Fig. 3b) and the 6-representatives treatment (P=0.006, z=−2.739, n 1 =n 2 =15, Mann–Whitney U-test) (Fig. 3b). Over all three games, the net payoff (including trials where the group fails to collect the target sum and loses all remaining money) is higher for selfish than for fair players (Fig. 3c). Selfish players achieve a higher net payoff in the 6-players treatment, compared with both the 18-players treatment (P=0.024, z=−2.261, n 1 =n 2 =15, Mann–Whitney U-test) and the 6-representatives treatment (P=0.020, z=−2.325, n 1 =n 2 =15, Mann–Whitney U-test, shown per represented player; Fig. 3c).

Figure 3: Fair and selfish strategies. (a) The percentage of selfish players per group, (b) the average contribution of a selfish player (relative to the fair-share contribution), (c) the net payoff per fair and selfish player. Means±s.e.m. of 15 groups per treatment are shown. See text for statistics. Full size image

Using a classification of players in a social dilemma proposed by Fischbacher and Gächter19, the selfish representatives might be ‘pessimistic conditional cooperators’ who dislike that others contribute less than their fair share and thus stop contributing. However, all selfish representatives contribute more in the end than in the beginning (P=0.0002, linear regression of contribution per selfish representative per group on rounds 1–10, analysed for game 3) and resemble ‘imperfect conditional cooperators’19. By increasing their contribution during the 10 rounds as do fair representatives (P=0.002), the selfish players help reaching the target, though they contribute much less than fair representatives.

Voters choose selfish representatives

After both games 1 and 2, representatives can be either re-elected or voted out. After game 1, those representatives who are re-elected have contributed significantly less in game 1 than those who are voted out (Fig. 4a) (P=0.01, z=−2.587, n=15, Wilcoxon signed-rank matched pairs test). While this is not the case after game 2, we still find a tendency that selfish representatives are preferentially re-elected, based on their past contributions. In addition, before each election the players formulate election pledges specifying their contribution strategy if elected. The percentage of selfish pledges (see Methods) is higher among the 6 elected representatives than among all 18 players of that treatment (Fig. 4b), although significantly so only after game 2 (P=0.0071, z=−2.692, n=11, Wilcoxon signed-rank matched pairs test). Thus, representatives who act selfishly in game 1 are preferentially re-elected, and players who pledge to be selfish are preferentially elected after game 2.

Figure 4: Voting success and behaviour of selfish and fair representatives in the six-representatives treatment. (a) Previous investment of representatives who are either voted out or re-elected, (b) percentage of selfish players, according to their election pledges, available and elected, (c) future fulfilment of election pledges by selfish and fair players. Means±s.e.m. groups are shown, for 15 groups in a and 11groups in b and 10 groups in c. See text for statistics. Full size image

Players classified as selfish according to their election pledges vote in 71.3% for classified selfish players and in 10.1% for classified fair representatives. Players classified as fair vote in 78.9% for classified fair players and in 14.6% for classified selfish players (the complement missing from 100% is due to players that could not be classified as either selfish or fair). Hence, selfish players want selfish representatives, and fair players want fair representatives.

Representatives who have pledged to be selfish contribute less in the following game than those who have pledged to be fair (Fig. 4c; after game 1: P=0.007, z=−2.692, n=10; after game 2: P=0.0051, z=−2.803, n=10, Wilcoxon signed-rank matched pairs test). Thus, players fulfil their pledges when acting as representatives.

Identification of selfish players as extortioners

Theorists have predicted for a long time that cooperative and fair strategies such as Tit-for-Tat would eventually succeed in social dilemmas20,21,22,23. Why then would subjects vote for representatives who mainly pursue the success of their own subgroup while disregarding the risks for the whole community? We hypothesize that the election procedure would favour representatives who motivate the other subgroups’ representatives to reach the target, but at the same time ensure that the own subgroup contributes less than other subgroups. Individuals would like their representatives to be steadfast and to convince the other subgroups’ representatives to compensate for any missing contributions. Such behaviour is reminiscent of the recently discovered class of extortionate ZD strategies for the repeated prisoner’s dilemma24,25,26,27,28,29,30, where extortionate players incentivize their opponents to cooperate although they themselves are not fully cooperative. In pairwise encounters, these extortionate players cannot be beaten by any other strategy, and they are predicted to perform well among adaptive co-players24,25,27,29. In the Methods section, we extend the theory of ZD strategies to the collective-risk social dilemma, and we prove that also in our experiment players may adopt extortionate strategies. Such players exhibit the following three characteristics: (i) Extortioners gain higher payoffs than their co-players by contributing less towards the climate account; that is, if x i is the total contributions of an extortioner, and if x −i is the average contribution of the other group members, then

(ii) Extortioners persuade their co-players to make up for the missing contributions; that is, the collective best response for the remaining N−1 group members is to choose x −i such that the group reaches the target sum T,

(iii) Extortioners are consistent, meaning that the properties (i) and (ii) are not only satisfied in one particular instance of the game, but in every game the player participates in. We now test whether the selfish players in our experiment meet these three criteria.

Because we find both fair and selfish players in all three treatments, we perform a proof-of-principle with players of all treatments combined. To keep the group as statistical unit, we enter contribution averaged over all fair players of each group; contributions of representatives are divided by 3 to be comparable ‘per player’ to the other treatments. The contribution per fair player increases over the three games (Fig 5a; P=0.0057, F 2,130 =5.3788, generalized linear model (GLM) with family=Gaussian). By contrast, the contribution per selfish player does not increase significantly (P=0.66, F 2,131 =0.4163, GLM). We find a significant interaction between fair and selfish players’ contributions over the three games (P=0.032, F 2,261 =3.4798, GLM). Over the three games, as the contributions of fair players increase, so does the payoff of both fair players (P=0.010, F 2,132 =4.7574, GLM, with family=gamma) and selfish players (P=0.015, F 2,132 =4.339, GLM, with family=gamma; Fig. 5b). In each game, selfish players gain more than fair players; the difference increases from game 1 to game 3 (Fig. 5c) (P=0.046, z=−1.995, n=45, Wilcoxon matched pairs signed ranks test).

Figure 5: Comparison of contributions and payoffs for fair players and selfish players across all three games. (a) Contribution of fair and selfish players; (b) net payoff of selfish and fair players; (c) difference in payoff between fair and selfish players. We enter contributions averaged over both all fair and all selfish players of each group. Contributions of representatives are divided by 3 to be comparable to other treatments. See text for statistics. Full size image

To test whether other group members are willing to compensate for missing contributions, we compare the contribution deficit of all selfish players in a group (the sum of all their negative deviations from the fair share) with the contribution surplus of all fair players (the sum of positive deviations of all the fair players; Fig. 6). For example, in game 1 in the six-players treatment, the dot most to the left (Fig. 6a) shows a group where the five selfish players contribute only €80 instead of the fair-share contribution of €100. The single fair player of that group contributes €22, €2 more than her fair share but not enough to compensate for the deficit of €20 caused by the selfish players. Hence the group misses the target sum of €120, and everybody loses the money not invested with 90% probability. As another example, the leftmost dot of those exactly on the red line depicts a group where the three selfish players invest €44 instead of €60, causing a deficit of €16, which is exactly compensated by the three remaining fair players. Thus the group meets the target of €120, but the selfish players receive a higher payoff than the fair players.

Figure 6: Fair players’ compensation of their selfish players’ deficit. (a–c) Six-players treatment; (d–f) 18 players treatment; (g–i) 6-representatives treatment. Each dot represents a group; larger dots show overlaid results from two or three groups. Black and blue lines depict simple regressions. The red lines depict all combinations of hypothetical contributions in which fair players exactly compensate for the deficit caused by all selfish players of that group. Thus, dots on or above the red line correspond to groups that reach the target sum. See text for statistics. Full size image

If selfish players were indeed able to persuade the remaining group members to compensate for missing contributions, we would expect the regression lines in Fig. 6 to have a significantly negative slope and to be close to the red lines marking exact (hypothetical) compensation. We see this compensation in the six-players treatment in game 2 (Fig. 6b, simple regression, F-test=36.257, degree of freedom (DF)=1, P=0.0001) and in game 3 (Fig. 6c, simple regression, F-test=26.204, DF=1, P=0.0002) and in the six-representatives treatment in game 3 (Fig. 6f, simple regression, F-test=17.286, DF=1, P=0.0011). By contrast, we find no significant compensation in the 18-players treatment.

In the 6-players treatment, fair players compensate or overcompensate the selfish players’ deficit in 9 groups in games 1 and 2 (Fig. 6a,b) and in 13 groups in game 3 (Fig. 6c). In the 18-players treatment, fair players compensate or overcompensate the selfish players’ deficit in 5 groups in game 1 (Fig. 6g) and in 7 groups in games 2 and 3 (Fig. 6h,i). In the 6-representatives treatment, the deficit of the selfish players is only compensated in 4 groups in game 1 (Fig. 6d) but in 9 groups in game 2 (Fig. 6e) and in 10 groups in game 3 (Fig. 6f). Over all treatments and games, selfish players or selfish representatives successfully drive their fair counterparts to compensation in 73 out of 135 individual games (54%). Moreover, groups become increasingly successful in reaching the target, improving from game 1 (40%) to game 2 (56%) and game 3 (67%). Because only fair players raise their contributions over the three games but not selfish players (see Fig. 5a), these results suggest that a considerable fraction of fair players learn to become even more cooperative in response to extortioners. The learning effect is demonstrated by the observation that the contribution per fair representative has no relation to the number of selfish representatives per group in game 1 but correlates significantly in game 3 (Supplementary Fig. 2).

Players behave consistently across the 3 games in the 6-players and the 18-players treatments, as witnessed by significant positive correlation of the contributions (see Supplementary Information for detailed analysis). For the six-representatives treatment, we have analysed the behaviour of representatives after being re-elected. In 34 out of the 42 cases in which a selfish representative is re-elected, the representative remains selfish in the next game (P=0.005, Fisher’s exact test, two-tailed compared with 50%). Overall, we have thus established that selfish players gain much higher payoffs (Fig. 5); they are often successful in persuading their fair co-players to compensate for missing contributions (Fig. 6); and they are consistent across different games. Thus, selfish players show all three characteristics of extortionate behaviour.