Pacemaker effects on online social rhythms on a social network

Pigg Party is a Japanese avatar communication application, in which players communicate with personally designed avatars in virtual spaces (figure 1). This is available for iOS and Android devices. A previous study [2] indicated the entrainment of online social rhythms among Pigg Party players.

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They can communicate synchronously using text through their avatars in virtual spaces. In addition to sending text messages, players can respond to dozens of avatar animations, known as avatar actions.

Players can send a lightweight and asynchronous message 'like' similar to Facebook's. They send 'likes' by choosing a friend's or stranger's avatar or icon ⁵ .

We conducted a four-week intervention experiment (26 July to 24 August 2022) on online social rhythms. In the intervention term, participants were motivated to use Pigg Party at specified times by incentives from the researchers. We call this the intervention on the online social rhythm of participants. At the specified times, if participants talk to their friends or participants' friends find that participants are online at the specified times, participants' friends may also use at the specified times, i.e. their social rhythms may be similar.

The participants of this experiment were recruited from the Pigg Party (N = 416; see table 1 for information on gender and age composition).

Table 1. Participants' gender and age.

Gender	N	Age (Mean ± SD)
Female	316	$25.6 \pm 12.6$
Male	70	$26.9 \pm 12.7$
Others	30	$22.1 \pm 8.18$

In the experiment, we randomly split the participants into four groups: morning, evening, all-day, and control (the number of participants in each group was 104).

Morning, evening, and all-day group participants are encouraged to send at least 5 'likes' to other players at the corresponding time for each group (morning: 7:00–8:00 AM; evening: 7:00–8:00 PM; and all-days: 0:00–23:59). The Pigg Party administrator sent reminder messages to the participants at the following times: morning group at 7:00 AM, evening group at 7:00 PM, and all-day group at 1:00 PM. Those who achieved 60 % (17 days) of their tasks in four weeks were rewarded with an Amazon gift card (300 JPY) and virtual coins from Pigg Party worth 500 JPY. The control group did not undergo any intervention. Randomly selected 23% of the control group participants received the same rewards as the other group participants for the lottery.

We builted online social networks to study the intervention effects on participants' neighbors for each week, based on a previous study [2]. Therefore, we acquired five networks for the weeks of intervention periods ⁶ . Table 2 shows the network features.

Table 2. Mean values of the network features.

Feature	Mean ± SD
Number of nodes	$280\,766.4 \pm 31\,034.5$
Number of edges	$62\,615.2 \pm 6846.4$
Weighted clustering coefficient [29]	$0.148 \pm 0.005\,17$
Powerlaw coefficient of degree distribution	$4.58 \pm 0.374$
Powerlaw coefficient of edge weight distribution	$3.13 \pm 0.639$

From these networks, we extracted and analyzed players who connected with the participants as neighbors. The numbers of neighbors in the morning, evening, all-day, and control groups were 804, 683, 784, and 797, respectively.

To construct these networks, we used the logs of users visiting other users' private rooms. As in previous research [2, 25, 30, 31], we established a link between a visitor and the owner of a room because visitors are often friends with the owner [32]. The time spent (in seconds) over a week was used to denote the weights of the links (w). The time spent per week was recorded. Although this network does not directly depict a communication network, it should positively correlate with the actual communication network.

We adopted this network as a proxy because data regarding the actual communication routes between individuals are strictly limited owing to constitutionally protected communication privacy in Japan.

We created two variables expressing the relationships between the participants and their neighbors: 1) close-frined: A relationship with $w\gt = 10^{3.1}$ was considered a close friendship because the players' online social rhythms were synchronized when $w\gt = 10^{3.1}$ in a previous study [2]. 2) Number of shared friends: We counted the number of shared friends between the participants and their neighbors because having more shared friends facilitates the spread of online social rhythms [2].

We created vectors representing online social rhythms over a 24 h cycle according to a previous study [2]. Each dimension of the vectors indicated the activity during a specific hour, that is, the dimensions of the vectors were 24. We constructed these vectors using weekly usage data, removing any fluctuations unrelated to the 24 h cycle. This allowed us to construct the social rhythm vectors.

To do this, we first built a time series from users' hourly usage data, then performed discrete Fourier transforms and extracted cycle factors, which were calculated by 24 h divided by integers i ($i = 1, 2, \ldots, 11$), that is, 24, 12, 8, 6, 4.80, 4, 3.43, 3, 2.67, 2.40, and 2.18 h, and calculated the inverse Fourier transforms of these elements. This implies online social rhythm vectors were constructed based on 11 bandpass-filtered frequencies.

The results were normalized to create a weekly social rhythm vector for each participant. For example, we can evaluate the social rhythm similarity using the inner product of these vectors (cosine similarity).

The source code for online social rhythms is available on https://figshare.com/s/d27b9c4858af977ef81f.

Each player's morning and evening activities were constructed using online social rhythm vectors. Morning activity was defined as the similarity between a player's online social rhythm vector and a morning vector, which had one in the seventh dimension (7:00 AM) and zero in other dimensions. The evening activity was also a similarity between a player's vector and the evening vector, which was the 19th dimension (7:00 PM) set to 1 and the others to 0.

Regression analyses were conducted to evaluate the intervention effects on neighbors' morning and evening activities:

$$\begin{align} y &\sim \textrm{Normal}\left(\mu, \sigma\right), \end{align} \tag{ 1 }$$

$$\begin{align} \mu &= \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \gamma_1 c_1 + \gamma_2 c_2 + \gamma_3 c_3 + \gamma_4 c_4 \nonumber \\ & \quad + \gamma_5 c_5+ \gamma_6 c_6 + \gamma_7 c_7 + \gamma_8 c_8, \end{align} \tag{ 2 }$$

where the objective variable y was morning or evening activities, µ was expected values of y, and σ was a standard deviation. µ was the weighted summation of the following explanatory and control variables. The explanatory variables $x_*$ included information on the participants connected to the analysis target players (the number of days in the morning task achievement or those in the evening; x₁) and the relationships between the players and the participants (a dummy variable expressing close friend relations x₂ and the number of shared friends x₃). These explanatory variables were set to zero when the group was not a morning group (or evening group). For the control, we used the neighbor's morning (evening) activity before the experiment (three-week averages; c₁), time-varying covariates for each week (weeks 2–5; week 1 was a reference variable), and the group of participants connecting with each neighbor (control group was a reference variable). We did not analyze these control variables. $\beta_*$ and $\gamma_*$ indicate coefficients of explanatory and control variables.

The Pigg Party application provider collects log data based on their terms of service ⁷ and privacy policy ⁸ . All Pigg Party users accepted the terms of service and privacy policy, which allowed analysis of their behavioral data for service improvements and academic studies. The data were pseudonymized, and identifying information was removed.

Quantitative data outputs are presented at an aggregate level, meaning no identifying information was included.

The experiment in this study was approved by the Ethics Committee of Tokushima University. All procedures were conducted in accordance with the guidelines for studies involving human participants, the ethical standards of the institutional research committee, and the 1964 Helsinki Declaration and its later amendments. The participants provided informed consent to participate in our experiment and were allowed to stop at any time. They could also withdraw their responses after the completion of the experimental process.

We studied players on an avatar communication application, Pigg Party. Considering other online communication platforms, e.g. social networking services (SNS) and massively multiplayer online role-playing games (MMO-RPG) where players' demographic composition will be different and providing different user experiences, etc would broaden the scope of our findings.

As mentioned above, there is room for ingenuity in intervention. Various forms of intervention, such as involving synchronous communication, will need to be considered, although we considered the intervention to asynchronous communication in this study. The ratio of participants was tiny compared to the total number of active users (several hundred thousand active users of Pigparty over a six-month period [34]). Intervening with a more significant number of players or in density clusters may strengthen the ripple effect of the intervention.