Network Interventions for Changing Physical Activity Behaviour in Preadolescents

Abstract

Network interventions can help achieve behavioural change by inducing peer-pressure in the network. However, inducing peer-pressure without considering the structure of the existing social network may render the intervention ineffective or weaker. In a 7-week school-based field experiment using preadolescents' physical activity (PA) as a proxy for estimating behavioural change, we test the hypothesis that boys' and girls' distinct networks are susceptible to different social incentives. We run three different social-rewards schemes, in which classmates' rewards depend on the PA of two friends either reciprocally (directly or indirectly) or collectively. Compared to a random-rewards control, social-rewards schemes had an overall significantly positive effect on PA (51.8% increase), with females being more receptive to the direct reciprocity scheme (76.4%) and males to team (collective) rewards (131.5%). Differences in the sex-specific sub-networks can explain these findings. Network interventions adapted to the network-specific characteristics may constitute a powerful tool for behavioural change.

Peer to peer interactions can be an important source of social influence in the diffusion of ideas and behaviours in both physical and digital social networks¹. The quality characteristics of interpersonal ties and interactions (e.g. strength, direction, frequency, locality, etc.) among the members of the network determine the magnitude of peer-pressure exerted by one peer on another and eventually the size of social influence in the network². Network induction or alteration interventions³ can achieve behavioural change by changing or fixing some of these quality characteristics. However, different subgroups of individuals with different quality characteristics and/or conflicting interests may exist within the same network (sub-networks). This makes isolating the effect of different network interventions difficult⁴. In this study, we take the advantage of the controlled environment of sex-segregated school-class networks⁵ to induce different network interventions (based either on collective or reciprocal interaction schemes) and measure their impact in boys' and girls' distinct sub-networks^6,7. As obesity and physical fitness have been established in the literature as "contagious" concepts^{8, 9, 10, 11} we use physical activity as a proxy for conceptualizing behaviour and estimating behavioural change. As changing usual behaviour and habits is a complex task² requiring focused interventions, further generalisation of the results should however be done with caution.

Introducing social norms or inducing peer-pressure can both result in social influence. In the first case, individuals are not required to take any conscious action while contagion happens through observation and copying others' behaviour, perceived (or presented or induced in the context of network interventions) as social norms (descriptive or injunctive)^12–14. In the second case, the focus of this study, peer-pressure requires individuals and peers to make conscious decisions to exert pressure¹⁵ as a response to a specific external stimulus which inter-relates peers' welfares. One can consider that also in this case, a new social norm is created and maintained at least for the period during which an external stimulus exists^16,17. The power of social influence in various socio-economic areas is highlighted in several empirical studies (see review¹⁸). Recent field-, laboratory- and internet-based network experiments or interventions have demonstrated a role for peer-pressure in social mobilization for problem solving¹⁹, product adoption¹, health behaviours²⁰ or altruism²¹). Peer-pressure plays a particular important role in the promotion of cooperative behaviour²². In evolutionary biology, it is well established that cooperation evolves through different mechanisms²³ which all work by exploiting the local-dyadic interactions (i.e. direct reciprocity, kin selection), the global-network interactions (i.e. indirect reciprocity) or both (i.e. network reciprocity, group selection). Social influence in general, and peer-pressure in particular, can be intentionally induced through carefully designed network interventions targeting socially desirable outcomes. The term "induction interventions" was introduced by Valente to classify interventions that stimulate or force peer-to-peer interactions to create cascades in information or behavioural diffusion³. Moreover, interventions on the network structure either by adding or deleting nodes and links, or by rewiring existing links are classified as "alteration interventions". The experiment presented here incorporates elements from both types of interventions. Building on the theoretical model by Mani and colleagues²⁴ (and also its experimental application²⁵), we induce peer-pressure by reallocating individuals' positive externalities towards their friends. The performance of an individual affects only and repeatedly his/her close-friends' payoffs. At the same time, we intervene in the structure of the network by suspending any rewiring process which would naturally emerge^{26, 27} as a reaction to the negative (i.e. lack of positive) externalities suffered by an individual due to his/her close-friends' adverse performance - a process which in evolutionary game theory is dubbed "spatial selection"¹⁵ or "link reciprocity"²⁸. Exerting peer-pressure towards harmful (not beneficial) friends is the only alternative reaction to be taken by someone who is interested in improving his/her personal payoff. Physical activity is used in this study as a "behavioural proxy" for estimating the size of behavioural change after our interventions. However, it was also chosen for its importance on children’s physical and mental health²⁹; developing and evaluating effective interventions to increase physical activity in children is a public health priority³⁰ and one of the core points of our study. We approach the promotion of physical activity as a "complex contagion" problem² which requires multiple exposures to a stimulus (our experimental incentives) reinforced by multiple strong-tied sources (participants' friends). Using peer-pressure induction and network-rewiring suspension as basic principles, we designed three different social-rewards schemes, based on team (collective)^{26, 31}, direct reciprocal²¹ or indirect reciprocal^32,33 interaction schemes and test them, together with the individual reward schem^{34, 35} against a random reward scheme which represents our control condition.

We conducted the study in two experimental phases (see methods), with 10 fifth-grade (i.e. 9-11 year-olds) elementary-school classes participating in the winter phase (92 females and 84 males from 7 schools) and 9 different classes in the spring phase (85 females and 88 males from 8 schools). Each class participated in only one of the experimental conditions while classes from the same school and phase were assigned to the same condition to avoid contamination. Following ethical and data protection approval (see Methods: Ethical approval), and parental consent, network-data was collected with the help of the class teachers who served as mediators between students and researchers throughout the whole experiment to preserve students' anonymity. For the same reason, researchers also avoided collection of any other data not directly linked to the intervention (e.g. socio-economic data). The strength of all dyadic ties (1≤τ_ij≤5) between any two classmates i and j was elicited through a self-reported network questionnaire. This information was then used for the formation of interacting teams or pairs (consisting of same-sex relatively good friends (τ_ij≥3 and τ_ji≥3), henceforth partners) in the social-rewards schemes. Inducing same-sex groups was both fair, due to the known sex differences in physical activity³⁶, and also natural, due to the existence of sex homophily in the actual networks (E-I-index(τ_ij=5)= -0.54, p_value<0.001, see 37 and "Supplementary Notes: Network Analysis" and supplementary fig. S7-S8).

In both winter and spring phases, following a one-week preliminary period (p₀), each school was randomly assigned to one of five study conditions and received the corresponding instructions about incentives, rewards and grouping information (where applicable). The interventions were conducted in parallel for five consecutive weeks divided into four periods: three one-week long periods (p₁,p₂ and p₄) and one longer period (p₃) of two weeks. Data was also recorded for an additional one-week long post-experimental period (p₅) in which students did not receive any kind of incentive or reward.

Physical activity was continuously recorded using Actigraph accelerometers (either GT1M, GT3X or GT3X+; ActiGraph, Pensacola, FL.) throughout the seven-week experiment (except for the days in which data had to be extracted and prepared for participants' feedback, see supplementary fig. S1). Using Evenson and colleagues'³⁸ cut-points, minutes spent in moderate-to-vigorous physical activity (>2296 counts per minute (c.p.m.)) was communicated to participants as "minutes of intensive physical activity". This information was given to each participant individually (in a sealed envelope) at the onset of each period (for all p_t≥1) together with information on their absolute performance, their relative classification (described as Gold, Silver or Bronze medal) and the corresponding points (100, 80 or 60) obtained in the previous period (p_t-1). In the same letter, boys and girls were also informed about the sex-specific upper and lower thresholds for achieving one of the classification medals in p_t. These thresholds corresponded to the upper and lower tertiles of boys' and girls' physical activity distributions in p_t-1 (see Methods: Physical Activity Measurement and Feedback). In the social-rewards schemes, participants were also informed about the relative performance and points of their partners.

The different experimental conditions assigned to the school classes defined the allocation rules of the points earned. In the individual reward scheme, participants received the points corresponding to their own relative performance. In the social rewards conditions, points were not dependent on their own but on partners' performance (fig. 1). In the direct and indirect reciprocity schemes each individual’s points were divided between two partners (point takers), while they themselves received half of the points from each one of the same (in direct reciprocity) or other (in indirect reciprocity scheme) two partners. Finally in the team scheme, three partners were assigned to the same team and engaged in a sharing scheme similar to a Public Goods Game³⁹; the points of all team members are summed up and then shared equally among them. At the end of the experiment (during p₅), all points from all periods were added for each participant individually who could exchange them for one or more items from a gift-list. In the control condition, students entered a draw for having worn the accelerometer correctly. At the end of each experimental period (p₁-p₄), these participants randomly earned 100, 80 or 60 points (with 1/3 chance), irrespective of their physical activity performance. The expected payoff per period (for all p_t≥1) for a random student in all conditions, including the control, was equal to 80 points. The total expected payoff from all periods (p_t≥0) was 420 points (min=340 points, max=500 points).

Fig. 1. Rewarding, interactions and allocation of points in the social-rewards schemes.

A hypothetical scenario of 9 classmates is presented. A) Rewarding for physical activity performance. Red, blue and green upper rectangles represent children's relative physical activity performance in the classroom in one period and correspond to 100, 80 and 60 points respectively. B-D) Points allocation in Social-Rewards Schemes; each red, blue and green slice (arrow) corresponds to 50, 40 and 30 points allocation (transfer) respectively. B) Direct reciprocity scheme; each child divides his/her points between two partners and receives half of the points that each one of these partners generated. C) Indirect reciprocity scheme; each child divides his/her points between two partners and receives half of the points that two other partners generated. D) Team scheme; the points of 3 partners belonging to the same team are added to a common pot and then shared equally among the partners.

Results

Following standard processing practices in child-based accelerometry^40,41, data before 07:00 and after 23:00 were excluded and non-wear time was removed. An additional filter excluding days with less than 10 hours of valid wear time left 9776 valid days with a mean of 28.1 CI_95%[13.4, 42.8] days per participant for our analysis (supplementary table S1). A minimum of three independent classes were assigned to each experimental condition with a mean of 35.4 females CI_95%[19.3, 51.5] and 34.4 males CI_95%[20.9, 47.9] participating in each experimental condition (see supplementary table S2). Classes did not differ with respect to their network characteristics (i.e. density, centrality, transitivity and reciprocity. See Supplementary Notes: Network Analysis). The mean valid wear time per day was 814 CI_95%[633, 996] and this did not differ significantly between conditions (Kruskal-Wallis⁴², χ² (4)= 9.042, p_value=0.0601). Overall, participants wore accelerometers significantly longer (≥60 min) on weekdays than on weekend days (Mann-Whitney non-parametric ranking⁴³ test (henceforth M-W): z_weekend=5.042, p_value<0.001). All tests used in this analysis (including the above two) are two-tailed.

Cut-points identified by Evenson and colleagues³⁸ were used to classify time spent in sedentary (≤100 c.p.m.), light (101 - 2295 c.p.m.), moderate (2296-4011 c.p.m.), or vigorous intensity physical activity (≥4012 c.p.m.) (fig. 2). To check the robustness of our main findings, different cut-points were used to classify the same data (see supplementary fig. S2). We used minutes of moderate intensity and above (moderate-to-vigorous physical activity; MVPA) as a comparability measure³⁶. Because of the sex-specific design and sex differences observed in MVPA (M-W for all and p₀ periods: z_all=7.238, z_p0=4.948; p_values<0.001), the data was analyzed and presented separately for boys and girls (fig. 3). Significant daily MVPA fluctuations of the actual mean MVPA (black line) (Kruskal-Wallis test⁴² for difference among different week days; χ²(6)=72.157, p_value<0.001) have been smoothed out by displaying the estimates of a locally (bandwidth: 0.3) weighted regression of MVPA on experimental days (red line). Fig. 3 shows the significant differences in children's MVPA on different days of the week, different weather conditions, and between holidays and school days (see M-W tests in supplementary material). These persistent environmental effects render statistical adjustment necessary.

Fig. 2. Classification of Daily Activity-Time for all experimental conditions (n_phase1 =176, n_phase2=173).

The classification uses Evenson and colleagues cut-points (30).

Fig. 3. Average Daily Minutes of Moderate to Vigorous Physical Activity (MVPA).

Data is aggregated and averaged at day-level for 92 and 85 females and for 84 and 88 males in Phases 1 and 2 respectively. Black line corresponds to the means of the actual MVPA while the red line are the estimates from a locally (with 0.3 bandwidth) weighted regression of MVPA on experimental days. Black dots and triangles indicate Mondays and Saturdays respectively. Blue, yellow and green shadowed days-periods highlight, rainy (precipitation more than 5mm), warm (temperature higher than 10°C) and holidays days/periods respectively.

In fig. 4 we averaged out all these effects by pooling data from both phases (A) and all experimental periods (B) for each of the different experimental conditions (by sex). To account for the different number of observations in the two experimental phases, we weighted each observation with the inverse of its probability of being sampled in experimental phase 1 or 2 (i.e. assuming the same number of observations by treatment and sex in each phase, see supplementary fig. S3 for non-balanced sample). The estimates of the locally (bandwidth: 0.3) weighted regression of MVPA on experimental days are presented in part A, with dotted left and right line-extensions indicating preliminary (p₀) and post-experimental (p₅) periods, respectively. Information from these two non-incentivized periods is not included in the calculation of the pooled average MVPA from all periods, illustrated by bar graphs (part B). Red error bars correspond to 95% confidence intervals of the respective subsamples (see also supplementary fig. S4 for box-plots). M-W tests on MVPA between different treatments (see supplementary table S3) confirm that for boys, team rewards consistently and significantly elicit higher levels of MVPA than the control scheme in both experimental phases. For girls, this was the case for the direct and indirect reciprocity schemes.

Fig. 4. Average Daily Minutes Moderate to Vigorous Physical Activity (MVPA) by experimental condition and sex (167 females and 162 males).

(A) Locally weighted estimations of MVPA on experimental days (pooled data from both experimental phases). Dotted lines correspond to non-incentivized periods. (B) Pooled data from all experimental periods (p₁-p₅) with 95% confidence interval error bars. (A-B) Each observation has been weighted by the inverse of its probability of being sampled in experimental phase 1 or 2.

We used a multilevel hierarchical model to control for all observed (weather, weekends, holidays) and unobserved environmental effects in a more systematic way and allow the variance of the unit effects to be estimated conditional on the data and parameters at all different nested levels. In particular we estimated a 3-level mixed effects model in which repeated daily measurements (level 1) were nested within the same child (level 2) who was nested in one of the classrooms (level 3) participating in the study. Four different dummies, one for each different condition (IV-individual, DI-Direct Reciprocity, IND-Indirect reciprocity, TE-Team rewards) were included in the fixed part of the model together with the dummy variable fem indicating females and the continuous variable val_time indicating the daily minutes of valid accelerometry wear time. The control condition (random rewards) was omitted and functioned as a baseline level. Cross-classification of the repeated within-subject measurements was also handled in the fixed part of the model by including 73 day-dummies, Dum_t (i.e. ((37) valid experimental days * (2) experimental phases) -(1) the baseline day). Most importantly, using time-dummies in the fixed part of the model also served for controlling for all observed (weather, holidays, weekend etc.) or unobserved environmental effects.

With regard to the random part of the model, in the classroom level-3 we included a random coefficient for sex (u_0j+u_1j*fem_jt) accounting for the different sex composition of the different classrooms and the sex-specific weekly relative scores and thresholds. In the child level-2 we simply included a random intercept υ_0ji. Finally, we accounted for heteroskedasticity by classroom in the level-1 repeated measurements by adding 19 independent residual errors (ε_jit), one for each classroom $(\text{i.e}.\forall j:{\epsilon }_{jit}\sim N(0,{\sigma }_{\epsilon j}^{2}I)$, so that $E_{jit}={\sum }_{j=1}^{19}{\epsilon }_{jit})$ (see Methods and Supplementary methods). The resulting model, additionally including the interactions between the different conditions and sex, is described by the following equation:

$$\begin{array}{l}MVP{A}_{jit}={\beta }_0+{\beta }_{1}I{V}_j+{\beta }_{2}IN{D}_j+{\beta }_{3}D{I}_j+{\beta }_{4}T{E}_j+{\beta }_{5}fe{m}_i+{\beta }_{105}I{V}_{j}fe{m}_i+{\beta }_{205}D{I}_{j}fe{m}_i\\ +{\beta }_{305}IN{D}_{j}fe{m}_i+{\beta }_{405}T{E}_{j}fe{m}_i+{\beta }_{6}val\_tim{e}_{it}+{\displaystyle \sum _{t=2}^{74}{\beta }_{t+5}Du{m}_t}+u_{0j}+u_{1j}\\ *fe{m}_{jt}+{\upsilon }_{0ji}+E_{jit}\end{array}$$ (1)

Table 1 shows the coefficients, standard errors and 95% confidence intervals of the main variables (IV, DI, IND, TE, fem) of the fixed part in eq.1 (see supplementary text for the complete regression analysis). In M1, team incentives and direct reciprocity have a positive and significant effect on MVPA (β₄ = 4.93, p_value=0.001, CI_95%:[1.99, 7.88] and β₃ = 4.30, p_value=0.010, CI_95%:[1.05, 7.56] respectively), corresponding to a respective 67.1% (β₄/β₀) and 58.5% (β₃/β₀)) improvement as compared to the control condition (captured by β₀). Indirect reciprocity also had a positive effect, but this was marginally non-significant (β₂=2.69, p_value=0.061, CI_95%:[-0.13, 5.50]). Pooling data from all social reward schemes together (IND, DI and TE) into one common regressor in M2 we found that in general social incentives had a positive and significant (β_2-4=3.81, p_value=0.001, CI_95%:[1.50, 6.12) effect on MVPA, with a 51.8% higher value compared to the control condition. In contrast, MVPA in the IV scheme was found not to be significantly different (β₁=2.30, p_value= 0.093, CI_95%:[-0.38, 4.97) from the MVPA in the control condition.

Table 1. Multilevel Regression Models on MVPA.

			(M1)	(M2)	(M3)	(M4)
FIXED EFFECTS Coefficients	Conditions	β1 (IV)	2.32 (1.36) [-0.34, 4.98]	2.30 (1.37) [-0.38, 4.97]	1.85 (1.66) [-1.41, 5.11]	1.80 (1.68) [-1.49, 5.09]
		β2 (IND)	2.69 (1.43) [-0.13, 5.50]	3.81** (1.18) [1.50, 6.12]	2.12 (1.87) [-1.54, 5.77]	4.37** (1.42) [1.60, 7.15]
		β3 (DI)	4.30** (1.66) [1.05, 7.56]		3.47 (2.10) [-0.66, 7.59]
		β4 (TE)	4.93** (1.50) [1.99, 7.88]		8.77*** (2.11) [4.63, 12.92]
		β5 (fem)	-14.27*** (2.47) [-19.12, -9.43]	-14.34*** (2.47) [-19.19, -9.50]	-13.79*** (2.38) [-18.46, -9.12]	-14.11*** (2.54) [-19.10, -9.13]
	Interactions	β105 (IV*fem)			1.03 (2.01) [-2.92, 4.98]	1.03 (2.02) [-2.92, 5.00]
		β205 (IND*fem)			1.08 (2.23) [-3.29, 5.45]	-1.029 (1.448) [-3.87, 1.181]
		β305(DI*fem)			1.97 (2.83) [-3.57, 7.52]
		β405 (TE*fem)			-6.24* (2.46) [-11.06, -1.43]
		β0 (Constant)	7.01 (3.58) [0.004, 14.02]	7.35* (3.62) [0.26, 14.44]	6.67 (3.54) [-0.27, 13.61]	7.24* (3.63) [-0.14, 14.35]
Model Stats	Observations		9776	9776	9776	9776
	Wald χ2		2063.2	2057.4	2078.1	2059.0
	pvalue<		0.0001	0.0001	0.0001	0.0001

Notes: Minutes of Moderate to Vigorous Physical Activity (MVPA) is the dependent variable in all models. Standard errors and 95% confidence interval in parentheses and brackets respectively. * p < 0.05, ** p < 0.01, *** p < 0.001. Four different dummies, one for each different condition (IV-individual, DI-Direct Reciprocity, IND-Indirect reciprocity, TE-Team rewards) and their interaction with sex (in M3 and M4) are included in the fixed part of the model. Control (valid time, date) variables, random effects parameters and residuals as described in eq.1, are omitted from the table for facilitating illustration. In M2 and M4, variables IND, DI, TE are collapsed to one variable (social rewards).

Including interaction terms between different conditions and sex (M3), we found that the effect of the team rewards on boys' MVPA was very high and significant (β₄=8.77, p_value<0.001, CI_95%:[4.63, 12.92), corresponding to a 131.5% (β₄/β₀) increase compared to the control condition (β₀). While for girls the effect of team rewards was non-significant (β₄ + β₄₀₅=2.53, χ²(1)=2.02, p_value=0.1555), the direct-reciprocity scheme affected girls' MVPA significantly (β₃ + β₃₀₅=5.441, χ²(1)=5.82, p_value=0.0159) and positively (76.5% improvement compared to control ((β₃ + β₃₀₅)/(β₀ + β₅))). Direct reciprocity did not affect boys' MVPA and indirect reciprocity was also non-significant for both boys and girls (only marginally (β₂ + β₂₀₅=3.195, χ²(1)=3.27, p_value=0.0706) for the latter). When combining all social rewards conditions in M4, we found that social reward schemes had a positive and significant effect both in boys’ (β_2–4=4.375, p_value=0.002, CI_95%:[1.60, 7.15]) and girls’ (β_2–4 + β_205–405= 3.346, χ²(1)=6.15, p_value=0.0132) MVPA. The individual incentives however did not significantly impact MVPA for either sex. The significant increases in MVPA in males in team scheme (β₄=11.20, p_value<0.001, CI_95%:[6.23, 16.18) and in females in direct reciprocity scheme (β₃=4.21, p_value=0.040, CI_95%:[0.20, 8.23]) are confirmed when running eq.1 regression model for the two separate sex subsamples (column M53 to M56 in supplementary table S5). Finally, testing for post-experimental effects (see supplementary methods and table S7), we found that while MVPA in all social incentives return to their initial levels (i.e. no significant differences between MVPA_pre from p₀ and MVPA_post from p₅), interestingly, the MVPA_post in individual scheme was significantly lower than the corresponding MVPA_pre. As we discuss later this result is probably partly driven by students' enthusiastic and over-reactive behaviour at the beginning (p₀) of the study due to the Hawthorne⁴⁴ or demand⁴⁵ effects.

Discussion

Two main points may be inferred from our findings. First, unlike individual schemes, social reward schemes were found to have a significant overall effect in changing preadolescents' physical activity behaviour, translating into 24.4 additional minutes of MVPA per week (as compared to the control). Second, the different social reward schemes have asymmetric effects in boys and girls. Boys were more susceptible to the team incentives, achieving an additional 59.2 minutes of MVPA in a week compared to controls, while girls were more receptive to the direct reciprocity scheme, achieving an additional 36.9 minutes of MVPA per week. It is important to stress here that these two findings are net from any design-effects already introduced (but not measured) in the control condition (e.g. weekly point system and final rewards, performance feedback, relevant positioning in the classroom, game spirit, accelerometer use, etc.). Moreover, through regression analysis we statistically controlled for any environmental effects which could potentially influence participants (e.g. weather, holidays, etc.) or school-classes (e.g. influence by school directors, teachers, etc., also known in the literature as Hawthorne effects⁴⁴).

Although we cannot claim that our design entirely excludes self-interest (incentives which are directly linked to individual payoffs) from the social rewards schemes (e.g. participants may comply to "peer-pressure" for increasing their individual payoffs by reducing "social" sanctions), the results from individual reward scheme indicate that self-interest itself is not a significant driver of behavioural change in this situation. In contrast, induced peer-pressure (likely together with other confounding factors, such as image scoring⁴⁶, and observability power⁹) has an additional effect on the participants’ time spent in MVPA as seen with the social rewards schemes. To understand the sex differences between the different social rewards schemes we should focus on the interplay between the different interactions induced (by design) and the different characteristics of the pre-existing sex-segregated networks.

Boys appear to maximize their MVPA performance when exposed to the team-competitive environment of the team rewards scheme, a result which is in agreement with a well-established finding in the literature^6,7 that male preadolescents are in general more interested than females in playing team games and forming larger networks^{5, 47}. Interestingly, our within-classroom network analysis (see Supplementary Notes: Network Analysis) also shows that, compared to girls, boys are more frequently characterized as good or best friends (τ_ij≥4) and have a more central role (higher closeness) both in the overall and in the within sex-specific classroom network.

In contrast, girls maximized their MVPA performance under the direct reciprocity scheme. This result can also be related to the preference of preadolescent females for small intimate groups^{6, 4}, usually including two or three reciprocal friendships⁴⁸. In our dataset we also find that although girls have fewer "best-friendships", these friendships are more frequently reciprocated than in boys. We would argue that as direct bilateral interactions are more common within girls' intimate friendships, girls were therefore more responsive to direct reciprocity interaction schemes than boys.

As a robustness check we repeated our regression analysis (see supplementary table S6) using (a) an alternative activity-time classification, characterizing MVPA according to the cut points proposed by Freedson and colleagues^{49, 50}, (b) a less conservative filter including the accelerometer-delivery days (Wednesdays) with at least 5 hours of valid wear time (1359 additional observations) and (c) an additional control for the initial physical activity levels of the participants. In all cases, our sex-specific findings were retained.

Our study used randomly chosen independent small social networks to compare different incentive schemes and interaction structures for increasing physical activity in preadolescents; however, the work does have limitations. Although schools were located in different villages, they were all from a small geographical zone which makes it difficult to prevent contamination and also challenges the external validity of the study. On the other hand, recruiting subjects from the same area also reduces socio-economic differences between schools (at an aggregate level), and minimizes other environmental effects. At a disaggregate level though (students), we were unable to control for potential socioeconomic differences, which could be affecting the effectiveness of the network intervention. For instance, during the "pairing" process we took into account of the sex-based homophily but we were unable to take other characteristics into account (e.g. socio-economic status, racial or ethnical identification). This could have potentially affect the structure of the network (due to homophily) and therefore affect the intervention outcomes.

Moreover, the existence of other within-classroom environmental factors related to the methods, and most importantly with the conductors or monitors⁴⁴ of the experiment, should also be treated with caution as they might have an impact on children's behaviour, especially at the start of the study. However, we argue that these reactivity effects⁵¹ decline over the course of our 7-week study and substituted by the intended effect of our interventions. To address this point specifically, we repeated the analyses using only the data collected during the third period of the experiment as subjects are already exposed to the monitors for three weeks, there is no end-of-the-game effect and it lasts for two consecutive weeks (with no feedback or researcher contact). Here, our main sex-specific results were also retained (see supplementary table S6 column M64). Finally, due to significant sex differences in MVPA, it was impossible for us to test the possible implications of our network interventions on mixed-sex groups, which may be a topic of interest for future research.

Our design also allows us to draw conclusions on post-experimental effects as we measured physical activity for an additional week after the intervention period (when subjects did not receive additional points or prizes). As in many other intervention studies focusing on post experimental effects^{51, 52} and on the effectiveness of intrinsic (vs. extrinsic) incentives^16,17, we also found that physical activity levels in our social incentives schemes returned to pre-experimental levels (no significant differences between MVPA_pre and MVPA_post, see column M72 of supplementary table S7). This result primarily suggests that our intervention did not create lasting change in norms but was completely contingent on the social rewards scheme. However, our post-experimental analysis reveals an additional information; activity levels of those in the individual incentive scheme were significantly lower in the post-experimental as compared to pre-experimental period (-7.57 minutes per day (p_value=0.002, CI_95%[-12.37, -2.78]). In contrast, participants in the social incentives schemes simply returned to their initial physical activity levels. This implies that at least in relative terms, social incentives were more sustainable than individual incentives.

As the primary focus of this trial was not to study the persistence (or not) of post-experimental effects, we are unable to provide evidence-based explanations for these findings but instead hypothesize on the reasons. The researchers observed and teachers confirmed that in the pre-experimental period students were very enthusiastic in participating and particularly interested in and curious about their "magic box" (accelerometer). This observation gives reason to believe that pre-experimental performance might be higher than "normal" performance due to Hawthorne⁴⁴ and demand effects⁴⁵. This would imply that, compared to "normal" levels, the post-experimental performance might be actually higher in social incentives (and comparably, not that low in the individual incentives). As our design does not allow controlling for "normal" physical activity level, this is only a conjecture based on our observations in the field which would need to be tested with a different experimental design.

Our network interventions were conducted in two steps. In the first step we elicited within-classroom social networks and fixed the interaction structures (between same-sex friends of the same pairs or teams) which remained "locked" until the end of the study. In the second step we simply induced peer-pressure among friends within the locked-structures by attributing and exchanging points as a result of engaging in MVPA. It is likely that the interaction structures in the social rewards schemes would normally change after the first interactions if they were not enforced by-design. For instance, high performers would most probably seek to team up with other high performers in order to achieve higher rewards, or popular students could have benefited from their extensive network by grouping with high-performing best friends, exchanging in a way their social capital for a higher return in terms of game-points^{26–28, 15}. By using locked interaction structures we sought to create a situation in which peer-pressure was the only reaction mechanism for any child seeking to increase his/her rewards; s/he simply had to encourage his/her partners to be more active. It is important to add that we did not observe any bullying effects against the weak performers. In contrast, teachers informally reported an increase in the quality of social behaviour among children.

The results indicate that sex-specific network interventions might be a powerful tool to positively change lifestyle behaviours of preadolescents, with boys being more susceptible to team interaction structures and girls to dyadic reciprocal structures. Changing usual behaviour and habits is complex, and this achievement may signal that this approach may have different applications in tasks of equal complexity. One needs to be aware however that our network interventions may not be that effective in eliciting change in behaviours of a different nature. For instance, in our study we took advantage of the inherited competitive nature of physical activities (especially in the school environment) which may not be relevant for other sorts of behavioural change (e.g. substance use). In a more abstract context, carefully designed network interventions based on the specific characteristics of the social networks and the nature of the bilateral relations and interactions may constitute a powerful tool for achieving behavioural change.

Methods

Recruitment

Students were recruited from 19 fifth-grade elementary-school classes in the same geographical region in Italy to minimize environmental effects. Over 98% of children provided signed parental informed consent (supplementary fig. S5) and participated in the study (Four parents did not sign the informed consent and they children did not participate in the study. One student dropped out due to health issues (unrelated to the study).

No prior sample size calculation was performed. The size of the sample was determined by the projects capacity and practical restrictions such us the number of available accelerometers (about 180 devises) and the number of recruited classes (19). To increase the sample size, the intervention was repeated twice (winter and spring experimental phases). Supplementary table S2 shows these sub-sample sizes by gender, classes and phases. The final sample size (and the respective size of sub-groups by gender, classes, experimental conditions and phase) was sufficient to perform non-parametric (Mann- Whitney, Wilcoxon and Kruskal-Wallis) and parametric (multilevel hierarchical model) analyses and testing, even when the data was collapsed at subjects level (one observation per individual).

Network Data Elicitation and Teams-Pairs formation

The strength of all dyadic ties (τ_ij) between classmates i and j was elicited through a teacher-administered self-reported questionnaire in which participants rated individually each one of their classmates (see supplementary fig. S6) from 1 "… is not my friend" to 5 "…is one of my best friends" (1≤τ_ij≤5). In the supplementary fig. S7 we use modern Multidimensional Scaling⁵⁴ to visualize spatial distance only between best friends (τ_ij=5). Separate colours highlight boys and girls, while we also illustrate all friendships of τ_ij≥3. These graphs demonstrate that most networks are sex-segregated.

The network data was used for the formation of interacting teams or pairs only in the social reward schemes. Only same-sex classmates with relatively strong ties (τ_ij≥τ_ji≥3) were randomly matched together (only two exceptions where τ_ij≥3≥τ_ji). Considering that school networks were characterized by sex homophily (see supplementary fig. S7-S8) and that students would probably self-select to pair or team up with same-sex colleagues, we followed this natural predisposition and induced same-sex matching that also allowed us to control for known sex differences on children's physical activity levels³⁶. Matching relatively strong-tied classmates was purposely designed to maximize peer-pressure between relatively close friends²⁴ and also to minimize the possibility of any adverse effects between distant friends. Pseudo-randomisation was preferred to self-selection matching to ensure compatibility in the matching process for all classmates even in the most complicated interaction schemes (i.e. indirect reciprocity).

Experimental Phases, Periods and Conditions

The study was conducted in two experimental phases in 2014, with 10 classes (from 7 schools, classes from the same schools were participating in the same condition) participating in the winter phase (N_w=176) and 9 different classes (from 8 schools) in the spring phase (N_s=173). Principal teachers served as contact points between students and researchers throughout the whole experiment to preserve students' anonymity (teachers were not informed about the performance of the students throughout the whole experiment, see supplementary fig. S9 for teachers' instructions). In both phases, after a 1-week preliminary period (p₀), schools were randomly assigned to different intervention conditions which were conducted in parallel for 5 more consecutive weeks divided into 4 periods: three 1-week (p₁,p₂ and p₄) and one 2-week (p₃) period. As researchers required knowledge about the experimental condition in order to prepare and deliver the corresponding feedback, data collection and analysis were not performed blind to the conditions of the experiments. However, the main outcome measure is objectively measured and therefore researcher bias will have unlikely to have influenced the outcome assessment. The study concluded with a final 1-week post-experimental period (p₅) in which students did not receive any kind of incentive (points). Classification medals were given virtually and corresponding to 100, 80 and 60 points in all but the control condition (in which the random allocation of points was used). The different experimental conditions implemented in the classes defined the points allocation rules among classmates. In the individual reward scheme (IV) participants received the points corresponding to their own classification medal. In the social rewards conditions, though, points were not allocated to the "self" but to other classmates (fig. 1), who were bilaterally satisfying (with two exceptions) the condition τ_ij≥τ_ji≥3 (for facilitating analysis henceforth we call them as "partners"). In the direct (DI) and indirect reciprocity (IND) schemes each individual was engaged in two active and two passive interactions; s/he a) was sending half of her/his points to one partner (point-taker) and b) the remaining half to another point-taker while s/he c) was receiving the half of the points of one partner (point-giver) and d) the half of the points of another point-giver. In the IND each participant was interacting with four different partners while in the DI they only interacted with two partners who were at the same time both point-givers and point-takers. Open network structure was imposed on all same-sex networks assigned to DI, by preventing an individual's point-givers/takers to interact with each other. However, in the IND, the open network structure condition was satisfied only for those same-sex IND networks with N≥10 (4 out 6). For the remaining two IND networks, we allowed for interaction between point-givers and point-takers but never within point-givers or within point-takers. Finally in the team scheme (TE), three partners were assigned to the same team and engaged in a Public Goods Game³⁹ which the points of all team members were gathered together and then shared equally among them.

Instructions of the Game (accelerometers and conditions)

Special attention has been given to the explanation of the instructions both to the teachers and to the students. Teachers received general instructions about their role in the conduct of the experiment during the recruitment period. The supplementary fig. S9 shows the written instructions given to the responsible teachers. Prior to the experiment, researchers also organized an interview with each one of the teachers in order to be sure that they accurately understood the general instructions. Moreover, researchers met teachers in the school on a weekly base during the collection/delivery of the accelerometers and answered any questions raised by them or the students.

For the instructions to the students we used a "game" language (e.g. we use the term "Magic Box" instead of accelerometer) which was easier to be understood by students. Instructions were given in two different stages in order for them not to be overwhelmed with new information: A) Participants were instructed at the beginning of p₀ to wear the accelerometers on a belt on their right hip, during all waking hours (except when performing water or contact sports) throughout all periods (and p₅), including weekends. Additional to the written illustrated instructions (see supplementary fig. S10), researchers gave a small demonstration in the classroom for the correct use of the accelerometers. B) Incentive-instructions and classmates grouping/matching (where applicable) were revealed to students at the beginning of p₁. In the social incentive schemes students received their partners' names and were described in detail how their behaviour can potentially affect their partners' points. In addition, we attached on each child's accelerometer a personalized key ring which was indicating the names of his/her partners (when applicable). In supplementary fig. S11 we show the exact information received by the students.

At the beginning of period p₂ when researchers (through teachers) gave the students their first feedback (corresponding to their performance in p₁), there were only few cases in the social incentive schemes where students reported that they had not understood the interaction scheme with their partners. However, the further information given at that stage (see supplementary fig. S13) was enough to erase any confusion, as in the next week (beginning of period p₃) teachers did not receive any further questions regarding the interaction schemes and assured the researchers that all students already knew their partners and were aware of how the points were distributed or exchanged. The students participating in the random rewards scheme found it most difficult to understand that their points were independent of their performance. However, after receiving further information at the beginning of p₁, this was resolved. Supplementary table S6 (column M64) demonstrates that our main results were retained even after excluding these potentially "noisy" periods.

Physical Activity Measurement and Feedback

Physical activity was measured by Actigraph accelerometers (either GT1M, GT3X or GT3X+; ActiGraph, Pensacola, FL.) and was communicated individually to classmates as minutes of intensive physical activity (examples were given in the classroom and from p₁ participants could also observe it in the provided histogram-feedback). Accelerometers were handed out at the beginning of each period (Wednesday, 12:00), and collected at the end of the period (Tuesday, 08.00) for data extraction, recharging and feedback preparation (see supplementary fig. S1).

At the beginning of each period (for all p_t≥1) participants received individual information (see supplementary fig. S12-S13) including:

• a)a histogram of their average hourly MVPA minutes in p_t-1 and their average individual period-score (s_i,pt-1),
• b)the upper $(T_t^H)$ and the lower $\left(T_t^L\right)$ within-classroom thresholds defined for the current period p_t for boys and girls separately and coinciding to the upper (Pr[S_t-1>s_t-1]≤2/3 and Pr[S_t-1≤ s_t-1]≥2/3) and lower (Pr[S_t-1>s_t-1]≤1/3 and Pr[S_t-1≤ s_t-1]≥1/3) tertiles of boys and girls score-distributions (S_t-1) in p_t-1.
• c)Their relative classification in p_t-1 falling into one of the following three categories: Golden if ${\text{s}}_{\text{i,t-}1\ge }{T}_{t-1}^H$, Silver if $T_{t-1>}^H{\text{s}}_{\text{i,t-}1\ge }{T}_{t-1}^L$ and Bronze medal if ${\text{s}}_{\text{i,t-}1<}{T}_{t-1}^L.$
• d)The points obtained based on their (or on their partners') performance in p_t-1. In the social reward schemes, participants were also informed about the medals and points of their partners. This 3-category medal system was designed in order to dampen competition (after p₁ all students could potentially reach $T_t^H$ and win the gold medal)) which, if too extreme, could cause negative side effects (e.g. hostile behaviour towards high performers). This reward system proved successful as teachers reported no conflicts among students but an increase in the team spirit especially for the ones participating in the team condition.

Instruction intelligibility among 9-11 year old students was a key challenge of this study due to the complexity of the interaction schemes. However, we managed to address this issue by a repeated interaction with teachers and students before and during the experiment and by offering clear instructions and feedback on a regular basis. In supplementary fig. S1 we show the timeline of the experiment, highlighting in red letters all the occasions when researchers interact with teachers and students during the experiment. After p₁ teachers reported that students did not have any more questions and they fully understood the rules of the game.

Experimental Payments

Additional to the points earned in p₁-p₄, participants received a 100-points bonus at the end of p₀ for correctly wearing accelerometers. Irrespective of condition, points from all periods (p_t≥0)were summed at the end of the experiment (during p₅) for each participant individually who could exchange them with one or more items from a gift-list including 94 items of different points-value (see supplemetary fig. S14). This was also true for the control condition, in which students were earning 100, 80 or 60 points with 1/3 wining probability after a lottery draw at the end of each experimental period (p₁-p₄). The expected payoff per period (for all p_t≥1) for a random student in all conditions, including the control, was equal to 80 points, with the total expected payoff from all periods reaching (p_t≥0) 420 points (min=340 points, max=500 points). By providing all participants with the same-size material incentives we ensured that any resulting differences between students participating in different experimental conditions would be due to the different intervention scheme and not to the size or the material incentive itself. Hence, material incentives were included as a methodological tool for quantifying physical activity performance while their effectiveness⁵⁵ does not constitute an objective of this study.

Physical Activity Data Collection and Filtering

Accelerometers were set to record at 10-second epochs, and data from the accelerometers were downloaded using ActiLife software (version 5.7.4, full edition). Data before 07:00 and after 23:00 were excluded and non-wear time was removed, using a criterion of consecutive runs of zero counts per minute (cpm) for a minimum duration of 60 minutes, allowing for a ‘spike tolerance’ of 2^{36, 38}. Remaining data were included if accelerometer wear time was at least 10 hours per day. The application of this last filter basically removed all delivery and recollection days and left our sample with a total of 9776 valid days (see supplementary fig. S15-S16 and table S1). At least three independent school-classes were assigned to each experimental condition with an average of 35.4 females and 34.4 males participating in each condition (see suplemtary table S2). The mean number of valid days per individual was 28.1 (SD) with team scheme (TE) only being significantly different (p_value<0.01 in all between-conditions bilateral Mann-Whitney non-parametric ranking⁴³ tests including the TE) to the other schemes mainly due to the late involvement of two TE classes. The mean number of valid minutes per day was 814 (SD), which did not differ significantly between conditions (Kruskal-Wallis χ²= 9.042 with 4 d.f. and p_value=0.0601). However, accelerometers were worn for significantly longer (≥60 min) on weekdays as compared to weekend days (M-W: z_weekend=5.042, p_value<0.001).

Regression Analysis

We performed regression analysis to control for any environmental effects in a systematic way. The dependent variable was the total daily minutes in MVPA. In order to capture treatment effects we used the following four dummy variables as the main regressors for our model:

• Individual (IV): takes value 1 for all those measurements recorded during the implementation of the individual rewards scheme, otherwise 0.

• Direct (DI): takes value 1 for all those measurements recorded during the implementation of the direct reciprocity scheme, otherwise 0.

• Indirect (IND): takes value 1 for all those measurements recorded during the implementation of the indirect reciprocity scheme, otherwise 0.

• Team (TE): takes value 1 for all those measurements recorded during the implementation of the team rewards scheme, otherwise 0.

Note that these dummies take the value 0 for all those measurements recorded during p₀ and p₅ when all children either received the 100 points bonus or not received any points at all. The dummy variable control taking the value 1 for all those measurements recorded during the implementation of the control scheme is used as control group for our regressions and therefore omitted from the regression table.

We used a multilevel model (using maximum-likelihood estimator) to allow the variance of the unit effects to be estimated conditional on the data and parameters at all different nested levels (school-class(j) > student(i) > measurements(t)). In particular we used a 3-level mixed effects model in which repeated daily measurements (level 1 t-level) are nested within the same child (level 2 or i-level), who is nested in one of the classes (level 3 or j-level) participating in the study. Treatments' dummies were included in the fixed part of the model together with the dummy variable fem indicating females and the continuous variable val_time reporting the number of validated daily minutes. Note that we filtered out all data with val_time≤600 minutes. Cross-classification of the repeated within-subject measurements was also handled in the fixed part of the model by including 73 day-dummies, Dum_t (i.e. ((37) valid experimental days * (2) experimental phases) -(1) the baseline-reference day). Using time-dummies (Dum_τ, τ ∈ [1,74]) in the fixed part of the model also enabled controlling for all observed (weather, holidays, weekend etc.) or unobserved environmental effects.

With regards to the random part of the model, at the class-level we included a random coefficient for sex (fem) to account for the differences in sex composition of the different classrooms, expecting classes with a high percentage of males to have a higher average classroom performance. The random sex coefficient also accounted for the fact that although boys and girls in the same classroom were allocated to the same condition, their relative performance and weekly thresholds were sex-specific. We also allowed for the random effects at level-3 to be correlated (general symmetric covariance matrix). At level-2, random effects accounted for heteroskedasticity by classroom at the measurements-level (see supplementary table S4, column M43). Note that heteroskedastic residuals at this level also captured phase-heteroskedasticity since each class participated in either the first or in the second experimental phase. See supplementary material for regression model and post-hoc testing and diagnostic. Data distribution in this analysis was assumed to be normal but this was not formally tested. In supplementary figure S18 we show the actual residuals distribution. As compared to the normal distribution, the distribution of our residuals is slightly skewed on the left (0.83) and leptokurtic (5.56).

Ethical Approval

Ethical approval was given by the Experimental Economics Research Ethics Committee, Joint Research Centre, European Commission. The regional representative office of the Italian Ministry of Education (Ufficio Scolastico Territoriale per la Lombardia) authorised the study in the schools of its territory and coordinated the collection of parental informed consent. The experimental design was also approved by the European Data Protection Supervisor who approved the study in respect to the data protection rights of the participants. All relevant approvals and documents are available upon request.