Reflectivity relates differently to pro sociality in naïve and strategic subjects

Is pro sociality a natural impulse or the result of a self-controlled behavior? We investigate this issue in a lab in the field experiment with participants from the general adult population in Italy. We find two key results: first, that there is a positive relationship between pro sociality and strategic reasoning. Second, that reflectivity relates to lower pro sociality but only among strategic subjects, indicating that the intuitive view of pro sociality is valid only among strategic individuals. Non-strategic individuals are instead intuitively selfish. We surmise that these results emerge due to a common cognitive root between strategizing and pro sociality, namely empathy.

Contents S1 Comparative analysis between DG game and the PGG (run on the full dataset) 3 S1. 1  S4 Literature review to support the potential connection between mentalizing, empathy and pro sociality 22 S1 Comparative analysis between DG game and the PGG (run on the full dataset) The experiment described in this paper consisted of a series of tasks, on a sample of the general population completed in the order presented in Table 1, main text. The first task is a Public Goods Game. We briefly describe the main feature of the Public Goods Game that we use as a robustness check on the results of our paper.
The Public Goods Game We use a discrete form Public Goods Game, in order to make the choice easier for participants: all group members receive an endowment of e = 40 experimental points and have to decide simultaneously how much of their endowment to invest in a common project, choosing a contribution level among the following possible values, (c i ∈ 0, 10, 20, 30, 40), knowing that the residual from this contribution would remain in their private account. Every point invested in the group is doubled and shared equally among group members. Individual earnings are determined according to the following equation, with π defined as the payoff: where α is the marginal per capita return (MPCR) of the public good. Free-riding is the dominant strategy, for rational self-interested individuals, because MPCR is above 1/N and below 1. Social welfare is instead maximized when everyone contributes the whole endowment. These two opposing results define this game as a social dilemma.

S1.1 Statistical analysis
Here we report the study of the statistical relationship between pro sociality and cognitive abilities elicited with the guessing game and the CRT game, using both the results of the DG game and the PGG game.

S1.1.1 Stepwise regression
As a preliminary procedure, we run a backward stepwise regression analysis on both models, to explore the best available model according to the data, using the R Mass package.
The results for DG equation are reported in Figure S1. The stepwise regression suggests to use the results of the CRT and of the guessing game (GUESS), the interaction variable between the two and whether the indivduals answered correctly to the comprehension questions made before the game (gg right1).
For the PGG equation, the results of stepwise regression are reported in Figure S2 and support the inclusion of the interaction term and of the age of participants, but not of the main effects of strategic thinking and reflectivity. We will test the relevance of the interaction for the PGG later in the analysis.

S1.1.2 Interaction plots
In this paragraph we report the comparative interaction plot, aimed at measuring whether the interaction term, suggested by the step wise procedure, should be included in the estimation of our model for the DG and the one for the PGG.
An interaction plot is a simple line graph examining interactions between variables in factorial designs. Quoting (Lovie, 2014) on how to read interaction plots "For a two factor design, the cell means on the response variable for each level of one factor are plotted over all the levels of the second. The resulting profiles are parallel when there is no interaction and nonparallel when the interaction is present". In our case, we are interested to the effect on two response variables, the choices in PGG and DG, of two factors, i.e. strategic reasoning and cognitive reflection at the center of the analysis reported in the main text.
Our interaction plots report then on the x-axis, the dichotomous variable strat, on the y-

S1.1.3 Regression analysis
The final step of our analysis include the comparison of a regression analysis using as dependent variable both the choices in PGG and in DG respectively, including the data for the whole sample (i.e. without eliminating people declaring random guesses). This analysis provides a test of the appropriateness of the using the DG as a tool to test our hypothesis and excluding instead the PGG. We also provide a robustness check to the result on the DG reported in the main text, where data of random guesses in the guessing game have been dropped. The procedure adopted is the same as the one used in the main text, but here we are running regressions with the complete dataset (N = 176), thus providing a robustness check for our results, and confirming that they are stable to the use of both datasets.
In Table S2, we study the model for the DG: Model 1 reports the model with variables guess (the raw choices in the guessing game) crt (the number of correct answers in the CRT), and the interaction term between the two. We select this model according to the result of the stepwise regression analysis in Section S1. We find that the variable related to the guessing game is always significant, both as raw variable, and as dummy strat. In the first case, the coefficient is negative (Model 1   Table S2), which means that larger guesses are related to lower fairness (pro sociality in the DG can be called fairness, to distinguish it from pro sociality measured as cooperation in the PGG): less(more) strategic subjects are less(more) prosocial if we only consider this term. In Model 1, also the CRT variable is significant and negative, which could indicate that reflectivity leads to lower pro sociality. These conclusions need to be complemented by the consideration of the value and of the sign of the interaction term. The interaction term is of opposite sign with respect to both coefficients, indicating that the interaction could change the effect of the direct coefficients on the dependent variable. To make a conclusion it is thus necessary to measure the net effect. The value of the coefficient is also very small because of the different scale of the two variables: to calculate with higher clarity this effect, we perform this analysis using the dummy versions of the variables.
In Model 2, the coefficient of dummy strat, is significant and positive: the dummy strat is codified to have value 1 for subjects with higher levels of strategic reasoning , which correspond to values of guess lower than 50. This explains the inversion of the sign of the coefficient of Model 2 with respect to Model 1, but the information reported is consistent. Thus the positive value shows that strategic subjects are more pro social (or fair).
crt variable here is also significant, but the coefficient changes sign, due to the change in codification of the variable guess. Finally, the interaction term is significant and with negative sign, which imposes us to calculate the net effects of coefficients in order to evaluate the influence of regressors on dependent variable. Model 3 shows the results using all dummy variables, which simplify the calculation of net effects.
In Table S1, we extend the models reported in Table S2, to include the variable training question which is the variable capturing whether subjects have answered correctly to the control question for the guessing game. This extension of the model is suggested by the stepwise regression analysis, which always considers this variable in the final step of the procedure. For remaining variables, results do not change qualitatively with respect to the models in Table S2. Considering that models including training question always present better statistics related to the quality of the regression, we use these for the analysis of calculated coefficients.
We also stress that the results are consistent across the three Models presented, so we use Model 3.
In Table S3 we run regressions using PGG as dependent variable. The results of the stepwise regression did not suggest to use an interaction term, however we tested the model for comparison with the DG and found no significance. In Model 2, we eliminate the interaction and just tested the correlation between direct effects of crt and guess on the dipendent variable: here we find that a higher guess in the Guessing Game is positively correlated with the choice in the PGG. We also test the models with dummies, and the results confirm that for the case of the PGG, the only significant variable is strat, negatively related to pro sociality. Table S4 reports the estimates using the model proposed by the stepwise, i.e using the guess and the variable age. Here the effect on the choice in the PGG is basically related only to the level of strategic reasoning and age. Notes: Complete dataset. Guess: value of the guess in the GG. crt: number of correct answers to the CRT; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers,2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1 Notes: Complete dataset. Guess: value of the guess in the GG. crt: number of correct answers to the CRT; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers,2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1 Notes: Complete dataset. Guess: value of the guess in the GG. crt: number of correct answers to the CRT; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers,2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1 Notes: Complete dataset. Guess: value of the guess in the GG. crt: number of correct answers to the CRT; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers,2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1

S1.1.4 Calculated coefficients
We previously confirmed the importance of the interaction term in our regressions for DG, while the results have shown that direct and interaction terms have different signs, which implies that to evaluate the final effect we must calculate the composite coefficient.
For this analysis, we use for DG, the results of Model 3 in Table S1 and calculate the net effects using the following equation:  On the contrary, being naïve and intuitive, shows a coefficient of 1.51, lower than the one of subjects with naive and reflective behavior (2.01). As in the main text, reflectivity relates to lower pro sociality among strategic subjects, while it relates to higher pro sociality in naïve subjects. We can thus confirm that: strategic subjects are intuitively pro social while the opposite is true for non-strategic subjects.
The results for the PGG are reported in Table S6 . Here results report only the direct effect of strategic reasoning and age on contributions, without need to resort to calculated coefficients. According to this equation, older participants contribute more on average, while strategic subjects contribute significantly less. The absence of an interaction effect makes the calculations trivial.

S1.1.5 A comment to the comparative analysis
We believe that the comparative analysis qualifies in an important way our main result which is that fairness in the DG, is related to strategic reasoning, mediated by the reflectivity in the CRT.
Results for PGG and DG are different, because of the diversity of the two tasks. In the PGG, the decision to contribute depends directly from the contribution of others. Expectations of high contributions from group members, can lead to a decision to contribute a lot-in a behavioral model -or to defect-following a Nash equilibrium strategy. In all cases, subjects need to form their own expectations about the group, to decide what they want to contribute because their payoff depends directly on the others and their expectations about them depend on their level of trust, social norm of cooperation, learnt behavior and so on and so forth.
The inner nature of the PGG game implies a strategic decision. This is also what best reply strategies or Nash equilibrium calculation procedure use to find an equilibria. For this reason, while the strategic and non-strategic games have been generally observed to produce correlated results, the PGG is not the right task to prove whether pro sociality is related to strategic reasoning, given that it is intrinsically impossible to separate strategic considerations from other motivations.
A different story applies to the distribution game that we use (DG). Participants know that they must choose an income distribution, but are informed that they their payoffs do not depend on the choices of other group members. The computer decides which state of the world that will happen after everyone made his decision. What the others do, never affects directly the individual. Each participant is has detailed information about this. In this task there is no scope for strategic considerations. The way this game is structured is crucial in determining the different results, and motivates the choice of using the distribution game as a task to measure pro sociality in our design.

S2 Estimated marginal means
We use estimated marginal means to provide a robustness check for the results presented in the main text using theoretical and calculated coefficients analysis. Moreover, this methodology allows to solve problems related to potential imbalances present in the data, estimating what the marginal means would be, had the experiment been balanced. We first calculate a reference grid using the DG as dependent variable and our dummy variables, strat and crt.dummy and the interaction as regressors. We then use the function emmeans in the RPackage to calculate the estimated marginal means reported in Table S7. In the top panel we run the calculations with the complete dataset while in the bottom with the reduced dataset. The column emmean reports the calculated estimated marginal means. To compare the results of this analysis to our coefficients, we rewrite the results of Table S7 in a 3 by two matrix , which has a similar structure to the one of our analysis. This is done in Table S8. Our main results are confirmed for both complete and reduced datasets: for strategic subjects the estimated marginal means increase for increasing levels of reflectivity while for non-strategic subjects they decrease with higher reflectivity. In Figure S7a, we plot the value of the predicted marginal means for the dependent variable -choice in the DG -as a function of the value of the crt.dummy, comparing strategic and non strategic subjects.
The values for strategic subjects are plotted with a dashed line, while a solid line is for non strategic subjects. Strategic subjects show a predicted level of fairness that decreases with the level of reflectivity (from value 0 to value 2 of the crt.dummy as well as from 1 to 2.) On the contrary, non strategic subjects, solid line, present a predicted level of fairness that increases with the level of reflectivity (positive slope of the line). In Figure S7b the same patterns appear, with a clearer effect for strategic subjects, which present lower level of predicted fairness as a function of increasing reflectivity.

S2.2 Variance Inflation Factors
As a robustness check on the use of the both the reflectivity and the strategic behaviour variables, we calculate the value of the correlation between strategizing and reflectivity, for the two datasets, which are equal to -0.26 for the reduced dataset (N=93) and -0.1 for the complete dataset (N=176).
Secondly, we report the VIF of the model estimated without the interaction term and with the interaction term and compare them. We find that the VIF increases with the inclusion of the interaction term, which is to be expected 1 , but it is not so high as to create concerns. 2 We also report for completeness, the calculation of the VIF for the model with interaction and including the complete dataset. The complete dataset presents a higher VIF for the interaction term, which suggests that our procedure to reduce data is parsimonious and in the direction of higher reliability of the data (because it reduces the potential concerns related to the correlation between terms in the interaction). Also with the complete dataset the VIF is never high enough to be cause for concern on the use of both reflectivity and strategic behaviour in our regressions.

S3 Discussion of exclusion criteria for random choices in the GG
Our experimental setup includes a series of tasks, as reported in main text, among which the non incentivized request of comments related to the Guessing Game. The procedure implemented to request these comments was the following (the detailed time line of the experiment is in Table 1, main text): first, instructions about the GG were read aloud to all participants. Participants respond to control questions and then are asked to provide their chosen number. No feedback is given to the participants concerning the GG. After the choice was made and submitted to the software, participants were asked to write on a piece of paper with ID number reported, a comment about their choice, specifying that they can explain, if they want, the reasoning process or strategy that led them make the choice in the game. Such papers were then closed in an envelope and delivered to the experimenter.
their product. This is not something to be concerned about, however, because the p-value for xz is not affected by the multicollinearity. This is easily demonstrated: you can greatly reduce the correlations by 'centering' the variables (i.e., subtracting their means) before creating the powers or the products. But the p-value for x 2 or for xz will be exactly the same, regardless of whether or not you center. And all the results for the other variables (including the R2 but not including the lower-order terms) will be the same in either case. So the multicollinearity has no adverse consequences. cit. Paul Allison, Multiple regression (1999) 2 To calculate these values we used the command vif() in the R package car().
We collected these papers and codified the responses according to a basic criterium: whether participants were running consistently the Guessing Game, or whether they were using strategies unrelated to the game. In the latter case, the choices were defined as 'random' guesses.
In the following lines we list translated examples of reported comments for the GG for cases that were maintained in the database and for cases that were dropped, defined GGrandom in Table 4, main text. The codification was made by three researchers independently: the results of the categorization coincided among the three.
Examples of comments codified as GG-random: • The choices of the number was given randomly because I did not understand the question • I chose 56 because I was born in 1956 • No rule, this number is my favorite number • I chose 13 because I was born the 13th • I chose 12 because my daughters were born on the 12th • I chose 12 because it is the number written on the tablets I am using this morning • I chose 38 because it is my shoe size • I chose 31 because I dreamt this number tonight. Also, it is not too high or too low, so it seemed reasonable to me.
• It is the age of my grandma • If everyone chose 50 (mean number), the winning number would be close to 33. I choose 40 to make it closer to the others' choice.
• I chose thinking about what the others would choose.
• I chose a not very big number in order to reduce its influence in the calculation of the general mean and in the attempt to make the values get closer to the central value of the interval.
It is important to stress that we only dropped those observations, as in the previous set of examples, where the participant appeared not to have played the game and used criteria unrelated to the game. People making a wrong statements were kept because -thanks to their answers -we were reassured that they were actually playing the game we intend to study.
Finally, to further support our choice of the data exclusion, we report in Figure S8 the distribution of choices in the GG in total sample, and clean sample (after removing random guesses.). As it is possible to see from the pictures below, the distributions are very similar, as observations of random choices distributed across possible values (with a relative concentration toward smaller values). Considering the motives of random guessers discussed above, this bias for lower values is likely to be due to the fact that everyday events suggest more smaller numbers than high. Further, the picture shows that we did not just eliminate non-strategic answers, but answers in all the spectrum of possible answers to the guess. S4 Literature review to support the potential connection between mentalizing, empathy and pro sociality With our experimental setup, we find that there is a role of strategizing in the relationship between reflectivity and prosociality and we speculate that this depends from a common cognitive root of empahy and strategizing. While proving this hypothesis remains outside the scope of this paper, we propose the following steps to explore the support from the literature to this hypothesis. In order to sustain the aforementioned hypothesis, we need to discuss the literature in support of the following statements and relationships: Strategic reasoning is the ability to predict others' mental states in order to make own decisions. Strategic reasoning is defined as the ability to think about others thoughts and mental states to predict their intentions and actions (Coricelli and Nagel, 2009). The guessing game is commonly used in the literature to investigate whether and how a player's mental process incorporates the behavior of the other players in conscious reasoning (Nagel, 1995). It is important to qualify the term strategic reasoning in relationship with mentalizing or Theory of Mind (Leslie, 1987), because the concept of strategizing is more specific to the experimental economics literature while mentalizing and Theory of Mind (ToM) are terms used in the psychological literature. However, the two concepts are the same when considering strategic games, and in particular the guessing game, as suggested by Coricelli and Nagel (2009) : "playing against other subjects in the Beauty Contest game activated the mentalizing network ".
Empathy and strategic thinking are related. Hooker et al. (2008) maintains that there is a natural connection between mentalizing and empathy. This interpretation is in line with what we hypothesize being the link between empathy and mentalizing in our design: while analyzing the potential outcomes of the DG game, the individual endowed with higher mentalizing abilities, would have a better ability to simulate the experience of the other which is given an unfair allocation of money, without any merit or guilt that can be ascribed to the person that receives the unfair allocation. In our design, the individual which is deciding the allocation of resources could identify himself with the subject that potentially receives an unfair share of the pie, and by projecting upon himself the potential outcome accruing to others, could elicit a (pro social) empathic response. According to Hooker et al. (2008), this ability can be inferred and does not need to be generated out of an observable experience. In their study, the authors isolate neural mechanisms involved in predicting a future emotional response of another person and investigate how activity in these neural mechanisms is related to empathy. They suggest that when people predict an emotional response in someone else, they generate an internal affective representation of the predicted emotional response. This natural ability could indicate that "dispositionally empathic people are more practiced at generating emotion representations in the course of their relationships, thus were more likely to use emotion representations in our task " (Hooker et al., 2008).
From these results we deduce that there is a potential neural connection between a prediction about a future emotional response of another person and empathy. We further deduce that this ability is associated with dispositionally empathic people, i.e. this ability is a natural disposition of individuals. This is what our CRT, played at the end of the experiment, aims at capturing: we use the intuitive versus reflective codification of the CRT to capture the general disposition of the person in the experiment. This is a starkly different approach with respect to that of most of the literature which consider tools to elicit an intuitive versus a reflective response (as oppose to its predisposition) in the same person (See for example Kvarven et al. (2020) for a meta-analysis).
A more recent contribution we found in support of the idea of common processes charac- focusing on the underlying processes that characterize tasks related to both, and connect them, using common neurocognitive components engaged by different empathy and ToM tasks. To this purpose they proceed with a meta-analysis that -through a clustering treeaims at capturing relationships among sub-components across general tasks related to Tom and Empathy. Their results suggest the presence of common neurocognitive components across mentalizing and empathy tasks, which means that empathy and TOM share specific processes and therefore brain activities. In building their 3 clusters, authors do not consider the specific task we use in our design, but we surmise that it can be considered as part of the intermediated group, which combines cognitive and affective processes 3 .
Link between empathy and pro social behavior The final step that we need to explore is the one linking empathy to pro social behavior. Recent contributions, like Lockwood et al. (2013) have found a number of reasons to connect empathy with pro social behavior and we refer to these studies for a complete review Lockwood, 2016;Lockwood et al., 2014). However, it is important to notice that Lockwood et al. (2016) identify a precise mechanistic link explaining the connection between empathy and prosocial learning i,e. through the higher ability of more empathic people to learn to benefit others.
The authors tested whether individuals higher in empathy learned at a similar rate to obtain rewards for others compared with themselves and whether variability in empathy modulated neural responses to prosocial prediction errors. They find that more empathic people learn more quickly when benefitting others, identifying the precise link between the two processes.
This concludes our analysis of the literature performed with the aim of identifying support for empathy as the common root explaining our result that links strategic reasoning, reflectivity and pro sociality. While we find some support from the literature, this is by no means conclusive and a set of more specific experimental designs are needed to confirm or reject this hypothesis.

S5 Additional Statistical Analysis
This section presents additional statistical analysis concerning the relationship between pro sociality, strategic reasoning and cognitive reflection. All results reported in this section refer to the dataset where random guesses have been dropped from the dataset. Table S11 confirms the robustness of results of Table 6 of the main text, by reproducing the OLS test with standard errors clustered at the session level.
Table S12 confirms the robustness of results of Table 7 of the main text, by reproducing the computation of theoretical and estimated coefficients for the CRT.01 specification of the relectivity (Models 1 and 3) .
In Table S13 and Table S14 we run the same regressions on the datasets that respectively include and exclude the observations related to subjects that admitted to have hazarded a guess in the Guessing Game. All Models which include an interaction term between strategic reasoning and the crt outcome (Models 4-6-7-8-9-10), present coherent results: The term strat is positive and significant, as well as the dummies related to the outcome of the CRT, crt.01 and crt.dummy which are positive and significant. Furthermore, the interaction terms strat:crt.01 and strat:crt.dummy are always negative and significant independently from the inclusion of the control variables student, age, gender and training question. Age is negatively related to being pro social -the older the selfish -and consistently being a student is positively related to pro sociality (as students are younger in general and in our sample). The training question is not significant showing that the results is not related to the understanding of the rules of the game. The significance of these results is confirmed in Table S15 where standard errors clustered at Session level are reported.
As a robustness check we run a ordered logistic regression and report the results in Table S16: the sign and the significance of all terms is consistent with what found in Table S14.
In Table S17, S18, S19, S20, S21, S22 the odds ratios and confidence intervals for the ordered logit models are reported. Finally, in Table S23 and Table S24 we also tested our OLS estimation with a codification of the Distribution Game in two categories, defining as selfish subjects opting for choices A and B in the DG and pro social those making the choice C. Also in this case the results are consistent with our previous results, both with standard OLS and with clustering at session level. In Table S25 we run the same estimates with a logit model with clustering at session level in Table S26.
Finally, considering the large age span of the participants our experiment (from18-65-year-old) and the relationship between age and cognitive ability which has been detected in a large number of experimental contributions, the age effect on the strategizing and reflectivity needs to be assessed. In particular it is necessary to test whether the moderate effect of strategizing on reflectivity and prosociality depends from age. For this reason, in Table S27 we regress age on each of the key dimensions of our analysis (guess, crt, pro sociality). We find that only the relationship between age and the choice in the dictator is significant and negative: older people are more likely to choose the selfish option. Interestingly (though not statistically relevant) the relationship between age and the choice in guessing game is positive, while the relationship with the CRT is negative. This means that older people tend to be less strategic and less able to engage in cognitive reflection, but not in a statistically significant way. Overall this means that the effect of age on pro sociality, observed in Table   6 of the main text is a direct effect, not significantly mediated by strategic or cognitive abilities. Notes: The dependent variable is the outcome in the Distribution game that measures pro sociality. The term strat is a dummy variable taking value one for subjects with a guess lower than 50 in the GG. The term CRT.01 is a dummy taking value 1 for subjects responding correctly to at least one question in the CRT and zero otherwise. crt.dummy is a dummy variable taking value 1 for subjects with no correct answers to the CRT, value 2 for those responding correctly to 2 or 3 questions, and 3 otherwise. The term gender is equal to 1 for male and training question takes value 1 for subjects responding correctly to the training question of the GG. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1 pro soc = α + b 1 strat + b 2 crt.01 + b 3 strat : crt.01  Figure S9: Estimated Coefficients Model 3 (of Table S12)  number of correct answers to the CRT; gender=1 for male; training question: dummy variable equal to one for subjects responding correctly to the control question for the GG; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.01: dummy equal to one for subjects responding correctly to at least one question in the CRT and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers, 2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1. num-df and den-df indicate degrees of freedom for the numerator and denominator, effect size and significance for multiple regression power calculation.  Notes: Ordered logit. Dependent variable: distribution game. crt: number of correct answers to the CRT; gender=1 for male; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.01: dummy equal to one for subjects responding correctly to at least one question in the CRT and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers, 2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1   Notes: Ordered logit. Dependent variable: distribution game. crt: number of correct answers to the CRT; gender=1 for male; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.01: dummy equal to one for subjects responding correctly to at least one question in the CRT and zero otherwise. Notes: Ordered logit. Dependent variable: distribution game. crt: number of correct answers to the CRT; gen-der=1 for male; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers, 2 for two and three correct answers, 3 otherwise.  Notes: Ordered logit. Dependent variable: distribution game. crt: number of correct answers to the CRT; gen-der=1 for male; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers, 2 for two and three correct answers, 3 otherwise. Notes: Dependent variable: prosociality from DG outcome codified in two levels: A and B (Selfish) versus C (Pro social) crt: number of correct answers to the CRT; gender=1 for male; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.01: dummy equal to one for subjects responding correctly to at least one question in the CRT and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers, 2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1 Notes: Standard errors clustered at session level. Dependent variable: prosociality from DG outcome codified in two levels: A and B (Selfish) versus C (Pro social). crt: number of correct answers to the CRT; gender=1 for male; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.01: dummy equal to one for subjects responding correctly to at least one question in the CRT and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers, 2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1 Notes: Standard errors clustered at session level. Dependent variable: prosociality from DG outcome codified in two levels: A and B (Selfish) versus C (Pro social). crt: number of correct answers to the CRT; gender=1 for male; strat: dummy equal to one for guesses in the GG smaller than 50, and zero otherwise; crt.01: dummy equal to one for subjects responding correctly to at least one question in the CRT and zero otherwise; crt.dummy: dummy taking value 1 for no correct answers, 2 for two and three correct answers, 3 otherwise. Significance Levels: * * * p < 0.01, * * p < 0.05, * p < 0.1. Logit Model

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We inform you that at the end of the study you will be rewarded of 5 euro for your participation and of a further bonus depending of the choices you and other participants in this room will make. You will receive the reward at the end of the study, in private.
We ask you to turn off your phone. From this moment, no conversation among people in this room is allowed and communication with people outside the room is forbidden.
If you have doubts or questions to ask, at any time during the course of the study, please do not hesitate to raise you hand and one of us will come from you to clarify any doubts. The survey consists of 5 parts. In each of these 5 parts, you'll be part of a group. Besides you, the group will consist of three other people. The composition of the group is anonymous. You will never be able to know who is part of your group as well as the others will never know who is in theirs. The group composition will change in each part of the study.
For each part the computer will do a random draw and establish the new group you will join.
During the study, you will be asked to take decisions. Each decision can be changed any time you want, before clicking "next" at the end of the page.
When you have clicked on "next", the last decision you've selected becomes the final one.
From this point on, your reward will be expressed in token/points. Every token/point is equal to 0,04 euro.
Click on "next" when you're ready to start. Now the computer will form NEW groups of 4 random participants.

Page 27 -Fourth Part -Instructions Instructions
You have to choose one number between 0 and 100, with 0 and 100 included.
Differently from the previous parts, in this part there is a winner in each group.

Who is the winner
The winner is the participant who chooses the closest number to the mean of the numbers chosen by the components of the group, multiplied by 2/3.
The winner obtains 50 tokens, while the other participants do not receive anything. In case of a tie the 50 tokens are divided equally among all winners.

Example
Let us imagine that you choose 15, and that the other components of your group choose 25, 58 e 12. The total is: 15 + 25 + 58 + 12 = 110. In order to obtain the mean, we need to divide this sum by 4: so 110 divided by 4, we obtain 27, 5. Then, in order to obtain the winning number, we need to multiply by 2/3 (so we multiply the mean by 2 and divide it by 3); in our example the number to guess is then 27, 5X2 = 55 and then 55 : 3 = 18, 3 (the decimal numbers do not matter, so we say 18).
The winner is the person who guessed 15, as this is the closest number to 18.
In this case then you win because you choose 15 and you obtain 50 tokens.
Is everything clear? Are there questions?
In the next page, you will answer two questions who do not have any effect on your final payoff, but that guarantee that you correctly understood the instructions. Click "next" when you are ready. Is everything clear?

Page 28 -Fourth Part -Training questions
Click "Next" when you are ready to proceed.

Page 30 -Fourth part -Decision
Please chose a number from 0 to 100: FORM

Page 31 -Fourth part -A comment on your choice
Now please, we ask you to write on the sheet of paper on the table a comment on your choice in this part of the study.
Did you apply a rule? If yes, could you describe shortly which one?
Click "Next" when you are ready to proceed.

Page 32 -Fifth part -Instructions
Now the computer will form NEW groups of 4 participants, chosen randomly.

Page 33 -Fifth part -Instructions Instructions
In this part of the study you find three choices that indicate possible numbers of tokens to assign to the four members of your group.
Note that the total number of tokens assigned to your group does not change for the three choices. Only the number of the tokens assigned to each component changes.
The possible choices are the following: [See figure S11] What do you have to do? You have to select the choice you prefer.
How is your reward computed?
After everybody has made its choice, the computer will randomly extract one of the members of your group, that decides the rewards of all members of the group.
• If for example you are extracted, your choices will determine the rewards for all members of your group.
The person extracted, in this case you, will get the reward indicated in RED with the label YOU, while the other components of the group will get a number of tokens equal to those indicated in the image, depending on the fact that they are extracted as BLUE, GREEN or VIOLET person.
For example, If you choose A and you are extracted to decide the rewards of all components of your group, you take 30 tokens, while the others obtain 51,9 and 6 tokens, depending on the fact that they are extracted by the computer as BLUE, GREEN or VIOLET person.
• For example, if you are NOT extracted, it will be the decision of another participant to determine your reward and the one of all other members of your group.
Your reward will correspond to the reward labelled BLUE, GREEN or VIOLET person, depending on the computer's extraction.
For example, if the person extracted by the computer to decide the rewards of all members of the group indicated Choice C, that person obtains 24 tokens, if you have been extracted by the computer as VIOLET person you get 12 tokens, the other two members of the group obtain instead 18 and 42 tokens.
The instructions will remain available on the screen for the duration of this part of the study.
Do not hesitate to raise your hand and ask questions. One of us will come to you to answer them.
Before making your choice, we ask you to answer two questions that WILL NOT HAVE ANY EFFECT on your final reward, but that guarantee that you correctly understood the instructions.
Click "Next" when you are ready to proceed.
Page 34 -Fifth part -Training Questions If another member of your group is extracted to decide the rewards of all members of the group and that person has chosen Choice C. In this case your reward is: 1. 42 or 18 or 12 tokens, according to the random extraction of the computer.
2. 45 or 15 or 9 tokens, according to the random extraction of the computer. Did you apply a rule? If yes, could you describe shortly which one?
Click "Next" when you are ready to proceed.

Page 38 -Your results
Thanks for participating to this study, in the following you can find your results.
{REPORT RESULTS FIRST PART -OMITTED}

{REPORT RESULTS SECOND PART -OMITTED}
{REPORT RESULTS THIRD PART -OMITTED}

FOURTH PART
You have chosen X [Xs represent the numerical information presented to the participant].
The others have chosen X, X and X. The two third of the mean was X and the closest number was X. There are X participants that have chosen this number and you are one of them.
Consequently, you receive X tokens.
For this part of the game you will be paid: X,XX e

FIFTH PART
You have chosen X.
Someone else has been selected as Person 2.
You have been selected as Person 1.
Thus, your reward for this part is XX tokens.
For this part of the game you will be paid: X,XX e

PARTICIPATION REWARD
As reward for your participation, you will further receive a fix amount of: e5.00 THE TOTAL REWARD THAT WILL BE PAID TO YOU IS: eXX,XX

BEFORE LEAVING:
Thank you for your availability. We ask you a last effort and patience while we prepare the payments of the rewards. While you are waiting, we ask you to answer to a short questionnaire. The information provided, as well as the results of the whole study, will be managed with the upmost respect for your privacy and used solely for scientific purposes.

QUESTIONNAIRE
Questionnaire 1 -Clarity of the study Thank you very much again for the participation to this study. As this experience draws to an end we would like to ask you a few questions: Were the instructions of the todays' study clear?

Very Clear
This study has been realized with the support of tablets such as the one you keep in your hands. We would like your opinion on the easiness of using this tablet from your point of view. We ask you to indicate the answer on a scale where 1 corresponds to "Absolutely difficult to use" and 10 corresponds to "Absolutely easy to use". (Radio Button Answer from 1 to 10).

Absolutely easy to use
We would like to have your opinion on the software interface used for this study.
We ask you to indicate the answer on a scale where 1 corresponds to "Absolutely difficult to use" and 10 corresponds to "Absolutely easy to use". (Radio Button Answer from 1 to 10). Do you think that most people would try to take advantage of you if they got a chance, or would they try to be fair? Please choose one answer in the scale from one to 10, where 1 means that "people would try to take advantage of you", and 10 means that "people would try to be fair": 1.People would try to take advantage of you 10. People would try to be fair Have you ever studied in a school or university abroad? (One of the following an-

swers)
Have you ever worked abroad with an independent activity or had been a employee of a foreign company abroad? (One of the following answers)

Final Summary
Thanks for having participated to this study.
The study is now finished, your results for each part of the study as well as the total amount of money that you will receive are summarized below: Please answer the following questions: 1. If you flipped a fair coin three times, what is the probability that it would land "Heads" at least once?. . . percent S10 Parameters of the Distribution Game abs(P ayof f i − DictatorP ayof f ). Minimax is the value of the minimum payoff among the four components of the group in each presented possible choice. Middle is the simple mean of the payoffs of the group in each choice excluding the dictator.