Influence in Social Networks

2023-01-19

2024-02-13

We will have two primary outcomes
- A measure of influence.
- A measure of the extent to which people act on their influence.

see abstract.

In our experiment participants play a sequential coordination game in a group of $N$ people organized in a network. Each participant chooses (in random order) whether to ``Go In'' or ``Stay Out''. Payoffs are increasing piece-wise linearly with the number of people in the network who choose ``Go In'' with a steeper increase where payoffs are positive. Initially everyone's state is ``Out'' and participants choose sequentially whether to move ``In''. They can observe the state (``In'' or ``Out'') of their direct network neighbours. They cannot observe the state of anyone who is not a direct neighbour.

We plan to conduct different treatments that differ along two dimensions

-The presence of a robot player (yes/no).
- The network structure.


\paragraph{Presence of a robot player} In some treatments one of the nodes in the network (randomly chosen) will be played by a ``robot''. The robot will always be the first mover and will choose ``Go In'' with probability $\frac{1}{2}$.

Participants are informed about all these elements including about the fact that there might be a robot player, but they are not told which decision rule the robot follows or whether an observed move is by a human or robot.

\paragraph{Network Structure} We plan to conduct sessions with 5-player networks, 10-player networks and possibly 20-player networks. (We will not conduct 20 player networks if we already observe near complete coordination failure with 10 players).

We will start with three network structures for the 5-player and 10-player networks. One network will be the complete network (corresponding to the case of global information) and two networks will have local information, i.e. participants can only observe their direct network neighbours and they will not be linked to everyone in the network. A picture of these networks is attached.
Depending on the results we may investigate further networks, but if we do we will mention in the paper that these additional networks were added afterwards.

Participants sign up for sessions and treatments are randomly assigned to sessions.

Participants will play 15 rounds of this game. Before the start of each round they are randomly assigned a network and network position. Each session will have one or multiple ``silos'' (depending on the number of people in a network) within which participants are rematched. Different silos can be considered independent observations.

individuals

Yes

10 silos of 10 participants each for the 5-player networks and 5 silos of 20 players each for the 10-player networks.

100 participants per treatment

100 participants per treatment

Main Tests For each of our main outcomes we will have one main empirical test. Power is based on the first outcome (``measure of influence''), but sample sizes are then adjusted to take into account our ability to test for certain dimensions of heterogeneity (see below) as well as the second main outcome (`` measure of the extent to which people act on their influence''). \textbf{Measure of Influence}: We will measure influence using only the robot treatments, where we will compare situations where the robot chose ``Go In'' in period 1 with situations where they chose ``Stay Out''. Our empirical measure of influence of a particular position in a particular network is the difference between the share of participants who choose to ``Go In'' following the robot's choice to ``Go In'' in period 1 and the share of participants who choose to ``Go In'' following the robot's choice to ``Stay Out'' in period 1. Our main specification will be a logistic regression where we regress the binary variable indicating ``Go In'' on a dummy variable indicating whether the robot chose to ``Go In''. The regression will be run separately for each network position. (Positions that are the same up to relabeling are treated as the same position). We will report odds ratios. Standard errors will be clustered at the silo level. We will report several specifications including demographic control variables, round fixed effects and controls for position in the sequence, but our main pre-registered specification will be the one without any controls. We will also conduct linear probability models with the same regressors and report those results in the Appendix. Power analysis is done based on t-tests comparing the proportion of participants choosing to ``Go In'' following the robot's choice to ``Go In'' or ``Stay Out'' in period 1. The t-tests are conducted on an initial set of sessions conducted with Network 2B (see attached graphs). We conducted these sessions to get a sense of the magnitude of possible effect sizes in order to enable us to do more meaningful power analysis. In these sessions we found the following effect sizes for network positions A/E, B, C and D: 12$\%$, 22$\%$, 37$\%$ and 4$\%$. Power analysis revealed that to detect these effect sizes with 80 percent power at the 5$\%$ level we would need 14, 5, 4 and 37 silos of 10 participants each, respectively. \textbf{Sample Size} Based on these numbers we decided to use 10 silos of 10 participants each for the 5-player networks and 5 silos of 20 players each for the 10-player networks. (Note that in the robot treatments one participant per network is played by a robot). This should allow us to reliably detect influence at least for the more influential network positions. \textbf{Awareness of Influence}: We will use the treatments without robots and regress the binary variable indicating whether individual i in network position j chose to ``Go In'' in period 1 on the measure of empirical influence of network position j obtained from the sessions with robot. We will also include a fixed effect for the rate of entry in the network as a whole. Otherwise the empirical specifications will be the same as those above. \paragraph{Other Tests} We will explore heterogeneity based on answers in a post -experimental questionnaire and based on the sequence of decisions. We will also use decision-time as a secondary measure of awareness of influence. Last we will contrast empirical influence with theoretical measures of influence of a node (e.g. centrality measures).