Who Dunnit: The Party Mystery Game for Analyzing Network Structure and Information Flow

To prepare students to learn about network concepts, introductory readings on measures of network centrality and subgroups (e.g., Monge and Contractor, 2003, Chapter 2; Hanneman and Riddle, 2005, Chapters 10 and 11) can be assigned. Instructors may also assign an overview reading of social network analysis (e.g., Borgatti et al., 2009), especially for students without background in the field.

The game will work with a minimum of 10 and a maximum of unlimited players. Figures 1 and 3 provide examples of network configurations and corresponding nodelists for 14 players and 28 players, respectively. The size of the group of students playing the game dictates the number of nodes that will be in the network and the network configuration. If the group is smaller than the network to be used, nodes (i.e., each player in the game) should be removed from the nodelist – starting from the highest numbered nodes (e.g., node ID 14 in a 14-player network, then node ID 13, etc.) – until the number of nodes matches the number of players. In both 14-player and 28-player networks, the highest numbered nodes are located on the periphery of the network to assist with such adaptation. For class sizes ranging from 15 to 27, nodes should be removed from the 28-player network. The 28-player network is built upon the 14-player network so that, if node IDs 15 to 28 are removed, the network will become identical to the 14-player network. If the number of players exceeds beyond 28, the instructor should split the class into two groups of a smaller number of players in each. In this case, having multiple networks of similar size is recommended in order to allow discussing the players’ shared experiences of how information exchange unfolded in each network, and comparing them against each other. For instance, for a class of 30 students, two 15-player networks can be set up. For a class of 35 students, one 17-player and one 18-player network can be set up. A class of 70 students can be divided into one 24-player and two 23-player networks. Edges (i.e., ties that indicate which players can communicate with which others) should be modified accordingly. For example, for a 12-player game, remove 13 and 14 from other players’ rows in the nodelist.

Figure 1:

Figure 2:

Figure 3:

The network structure is designed to show communities and bridges in both versions of the network. In class sizes that do not consist of exactly 14 or 28 players, the recommendation for using the larger network and cutting nodes, rather than using the smaller network and adding nodes, is because the provided networks have been designed such that nodes may be removed while preserving the overall integrity of the exercise. In the proposed 14-player and 28-player networks, nodes that are high in each of the four centrality measures are differentiated. For instance, in the 14-player network (see Table 2, Figure 2), nodes 4, 8, and 9 are the highest in degree, closeness, and betweenness centrality, respectively. Node 7 is the second highest in eigenvector centrality other than node 4, which is noticeably the highest due to its high degree. These differentiations between node centralities are preserved when the network is adapted to a different number of players. In addition, there will always be peripheral nodes that have constraints in their number of communication partners. For example, if nodes 11 through 14 and associated edges are removed for a 10-player game, these differentiations are still maintained: node 4 has the highest degree centrality; node 8 has the highest betweenness centrality; nodes 4 and 8 are the top two highest in closeness centrality; and node 7 is the second highest in eigenvector centrality other than node 4, which remains the highest.

See Table 3 and Figure 4 for nodes that occupy positions of four different types of centrality in the 28-player network. The manners in which the centrality measures are distinguished from each other will vary slightly by network sizes (e.g., in some networks, a similar set of nodes occupy high closeness and betweenness centrality positions; in other networks, a similar set of nodes occupy high degree and eigenvector centrality positions). Yet, in all possible network sizes ranging from 10 to 28, the structure is configured to show differences when nodes that rank top 2 in each centrality measure are compared. Overall, the larger the network, the more nuanced the discussions could be around the intricate differences between the measures. For instance, in the 28-player network, node 10 ranks among top 4 in all three measures of degree, betweenness, and closeness centralities, despite lacking connections to other well-connected nodes (i.e., low eigenvector centrality). This node is in stark contrast to node 4, which has the same number of direct contacts (i.e., degree centrality) but to other higher degree nodes (i.e., high eigenvector centrality) that are connected with each other (i.e., low betweenness centrality).

Figure 4:

Clues (i.e., the 28 pieces of information regarding the five suspects) are included in Appendix 2. Prior to class, the clues should be printed and cut out individually (see Online Appendix: Clue List), and players can use the blank side of the strips of paper their clue(s) are on to block other clues when exchanging information with their classmates. Please note that the clue number corresponds to the node ID (i.e. clue No. 1 is given to the student assigned to node ID 1). There are five pieces of information about Lisa and Jake and six about Brandon, Adam, and Erica. There is one piece of key information about each of the four suspects that is crucial for exonerating them, and four pieces of information that make the correct suspect suspicious. All players should be given the same number of clues to start, receiving two clues in network size 14 or smaller. Note that key pieces of information are distributed in various locations of the network, all within nodes 1 to 10, so the game will work with a minimum of 10 players. The rest of the clues can be distributed to corresponding node numbers. For instance, in a class of 14 students (Figure 1), node ID 1 can be given clues number 1 and 15, node ID 2 can be given clues number 2 and 16, and so on. To account for unexpected student absences, the highest numbers are assigned to positions in the network which are not necessary to be filled. The instructor can easily take out all the highest numbers until the number of nodes matches the number of students in class on the day of the activity.

Below is a list of materials that are needed for the activity, as presented in the figures, tables and Appendices that are included at the end of the paper. In addition, as an extra set of Online Appendices, we provided Appendices 2, 4, 5, and 9 where page arrangements are configured so that they can be directly printed and cut to be used for the activity:

Node ID tags, in an envelope, cup, or bag to be randomly picked by each player (Appendix 4).

After students are introduced to the game setup (Appendix 1), they will pick the tag of a random number (‘node ID’; Appendix 4) that represents their position in the network. Ask them to attach the tag to their clothing so that it is visible to other players. Students will each be given a copy of the Who Dunnit Clue Track Sheet (Appendix 5). Next, a nodelist of who can communicate with whom will be shown (Figure 1). Students can be given approximately 2 min to write down the list of node IDs they can communicate with on their Track Sheet, and also use the nodelist data to visually map the network structure on a piece of paper. This process will help them acquire some knowledge of the network structure and make strategies about who they would like to speak with to maximize their access to clues. Yet, as people often do not have a global vision of their network in the real-world, it is suggested that students are not given enough time to completely map the network. Limiting students’ knowledge of the global network helps to recreate real-world scenarios where they typically have incomplete and differential understandings of existing communication networks. Yet, an adaptation can be made where the instructor elects to provide only a personal nodelist (i.e., who the individual can talk to) to each player, if the goal is to test the extent to which different players actively make efforts to identify the patterns of connections. If this is the case, the instructor can enlarge, print out, and cut apart the nodelist in Figures 1 and 3 and distribute each row to the corresponding player.

Students are then introduced to the rules (Appendix 3) and instructed to use the Track Sheet to record the clues when they receive any (Appendix 5). Next, students will be given a clue, or two clues, to begin with (i.e., a slip of paper with a piece of information on it). Once students become familiar with the rules, the game starts.

Players will exchange information. Players should engage in one-to-one information exchange, which helps to control for possible confounding factors. For example, generosity (Flynn, 2003) and likeability are individual differences that are likely to have effect on how resources are exchanged. By including a stipulation that only one clue is to be exchanged by each person per round, the effects of individual differences unrelated to centrality (e.g., how quickly one writes the clues down, or how outgoing or shy one might be in approaching others) can be minimized, but not completely eliminated. The effects of clues not being accurately or fully communicated are also reduced by this set up. Additionally, this restriction slows the pace at which clues are accumulated by each player, such that a result of almost every player in the network having almost every clue is less likely to be observed. Students are permitted to ask one additional time for a clue if the clue that they receive is not new to them. They are also not required to have ‘new’ information to give the person they exchange with in order to get ‘new’ information from them. However, if a player continues to not have new information to provide, eventually that person will likely no longer be sought as a partner.

The instructor should remind students to continue trying to solve the mystery to encourage information exchange and reduce distraction. In larger network sizes, as the time it takes for players to access a reasonable number of crucial clues will be lengthened, it is suggested that the game involves more rounds. After 15 to 20 min (i.e., approximately 10 rounds for network sizes 20 or smaller; 15 rounds for network sizes 21–28), players return to their seats. Students will then be asked to guess who the suspect is by evaluating all the clues they acquired, and writing the name of the guilty person on their sheet (Appendix 5). The guesses will then be recorded for the class to see. Ask each student to come to the front to write the suspect they guessed and the total number of information pieces they acquired on a board or input them on a slide (Appendix 6).

The instructor will reveal the suspect who stole the company secrets, as well as a complete list of clues. The clues can be displayed on two pages of slideshow. The network map is also shown after students have had a chance to review the complete list of clues. The instructor can also ask students about what they think the overall network looks like before showing the network map. Students are asked to reflect on why they were or were not able to guess the suspect by comparing the full set of clues against the clues they acquired. Draw focus toward the clues with two asterisks in Appendix 2, which are the crucial pieces of information (clue numbers 1, 7, 9, 10), in addition to clues with one asterisk (clue numbers 6, 11, 15, and 21), which illustrate that the suspect had both motive and opportunity. Some players may notice that they received a clue, but the information provided was inaccurate or missing some parts. Instructors can then lead the class in discussions of the outcomes, analyses of the network structure, and evaluations of the practicality of the game.