W1-1 Web Appendix Social Dollars in Online Communities: The Effect of Product, User and Network Characteristics Eunho Park, Rishika Rishika, Ramkumar Janakiraman, Mark B. Houston, & Byungjoon Yoo Web Appendix W1: Overview of Focal MMORPG Snapshot of Focal MMORPG The focal MMORPGs has two play regions: peaceful region and battlefield. We present screen shots of a peaceful region and a battlefield region in Panel A and Panel B of Figure W1.1 respectively. A peaceful region lets gamers (their avatars) socialize (virtually), purchase virtual items, and to rest to regain their power. As can be seen in Panel A, the job of the focal gamer in Panel A (of Figure W1.1) is a magician and she can fight with monsters based on her magic tricks. We note there are no monsters to fight in the peaceful region. There are six other gamers avatars in the near distance from the focal gamer. The focal gamer would be able to see the nickname of these nearby gamers and, by clicking on the avatars of these gamers, the focal gamer can get information (e.g., level, job in the game, etc.) of these gamers and also chat with them. On the right top, the small map lets the focal gamer know of her location in the game. The bottom of the snapshot of the peaceful region also has information on the current level and experience points of the focal gamer and other information, such as the number of health points (in the red circle) and attacking points (in the blue circle). Gamers lose health points when they get attacked by monsters and they lose attacking points when they attack monsters. Although gamers can recover these points slowly over time, they can recover these points immediately by buying functional products (such as energy drinks).
W1-2 A battlefield region has different types of monsters and a focal gamer can choose the missions he would like to complete based on his level. If a monster s level is lower than that of a focal gamer, the gamer can easily beat the monster but would earn fewer experience points when compared to fighting with a monster at a higher level. In other words, if a gamer chooses to fight with a monster at a level that is higher than that of the gamer, he will be awarded more experience points; however, there is a greater chance that the gamer will be defeated and thus would get some penalty. Panel B (of Figure W1.1) presents a screen shot of a gamer fighting with a monster. The focal gamer is seen holding a sword, which suggests that his avatar s job is either a Warrior or a Thief. The focal gamer s game level is 50. The monster s level is also 50 (written in parenthesis in red color font) and the health points of the monster is 66,094 out of 334,912 (written at the top center of the screen). FIGURE W1.1. Game Screen Shots of Peaceful Region and Battlefield A. Example of a Peaceful Region B. Example of a Battlefield Monster s Health Point Map Other Players Monster Lv: 50 Focal Player Lv: 50 Focal Player Health Point Level & Experience Points Attacking Point
W1-3 Functional and Hedonic Products In Panel A and Panel B of Figure W1.2, we present some examples of functional products and hedonic products that gamers can buy. Prices of these products are also shown. FIGURE W1.2. Examples of Functional and Hedonic Products in the Virtual Store A. Functional Products B. Hedonic Products
W2-1 Web Appendix W2: Cross-product Contagion As a part of our analyses that we present in the main manuscript, we test for the effect of possible cross-product contagion. We formulated and estimated a model in which ln Contagion was added as a variable in the model of users purchase of functional products and ln Contagion was added as a variable in the model of users purchase of hedonic products to allow for cross-product contagion. We report the results in Table W2.1. We find no significant effects of cross-product contagion. h it f it TABLE W2.1. Robustness Check: Cross-product Contagion Functional Hedonic Variable Estimate SE Estimate SE ln(contagion).239 *** (.089).454 *** (.091) ln(crosscontagion) -.132 (.094).158 (.097) Experience 2.614 *** (.139) 2.010 *** (.139) NetworkDensity.090 (.094) -.247 *** (.108) ln(experiencepoint).209 * (.124).163 (.129) ln(totallogin).375 *** (.129).437 *** (.129) ln(totalnumfriends) -.810 *** (.147) -.369 ** (.150) Duration -2.387 *** (.261) -3.616 *** (.276) ln(friendsoffriends) 1.390 *** (.206) 2.179 *** (.197) ln(crossfriendsoffriends).899 *** (.209).654 *** (.198) Correlation (rho) - -.564 *** (.007) * p <.1, ** p <.05, *** p <.01 Notes: Standard errors in parentheses. For the sake of brevity, we don t report the result of play decision. All models account for all other control variables including demographic information, job dummies, time dummies, etc.
W3-1 Web Appendix W3: Matching and Average Treatment Effect Dynamic Matching In the main manuscript, we acknowledged the challenges that researchers face in establishing the link between social contagion and individual behavior using observational data. We followed all the prescriptions of the recent literature (e.g., Hartmann et al. 2008) and leveraged the panel nature of our data to address these identification challenges. Among the identification challenges, we noted that the key issue is that of endogenous group formation. To address this key issue in a different way, we conducted additional analysis to supplement the results from the estimation of the econometric model. Specifically, following some recent studies (e.g., Aral, Muchnik, and Sundarajan 2009), we performed dynamic matching coupled with average treatment effect analysis to disentangle the effect of endogenous group formation from the social contagion effect. In our context, matching helps construct a matched pair of gamers, one from the treatment group consisting of gamers who have friends who purchase virtual products and one from the control group consisting of gamers who have friends but none of the friends purchase virtual products. This matching technique helps create statistical equivalence between the matched pair of gamers by balancing them on observed similar characteristics (Rosenbaum and Rubin 1983). Comparison of spending behavior across the treatment group and the control group gamers of a matched pair helps rule out endogenous group formation and establish the effect of social contagion. The objective of any matching technique is to select a sample of control group individuals that has covariate values similar to the treatment group individuals. In terms of matching technique, propensity score matching (PSM henceforth), originally proposed by Rosenbaum and Rubin (1983), constructs a single-index variable (commonly referred to as the propensity score)
W3-2 based on the pre-treatment characteristics of each subject and then matches the individuals in the treatment and the control groups based on the estimated propensity score. Later studies (Rubin and Thomas 2000) suggest that combining PSM with Mahalanobis metric matching technique can effectively reduce biases due to a large number of measured covariates. 1 The argument is that while PSM helps reduce the distance between the treatment and the control group along the propensity score, Mahalanobis distance matching is particularly useful at minimizing the discrepancy between observed covariates of treatment and control groups (Rosenbaum and Rubin 1985). Following recent studies in statistics (Diamond and Sekhon 2013) and in marketing (Avery et al. 2012), we use genetic matching which is a generalization of propensity score and Mahalanobis distance matching techniques. A gamer is placed in the treatment group if the gamer has at least one friend who purchased virtual products in the previous time period (week) and a gamer is classified as a control group gamer if the gamer has friends but none of the friends bought virtual products in the previous time period. A gamer s network of friends changes over time, and as a result, the construction of the two groups varies over time. To address this issue, following the recent work by Aral, Muchnik, and Sundarajan (2009), we perform dynamic matching, whereby individuals are matched in short time intervals. We estimate a binary logistic regression model of treatment group membership as a function of various gamer-specific, game-related characteristics and demographic variables. Our analysis is based on the sample conditional on players decision to play in a given week. We do this dynamically for every gamer over a bi-weekly time period. Note that we perform a series of robustness checks for alternative definitions of treatment group with respect to both the number of friends who purchased and also the time period of analysis. 1 Mahalanobis metric matching selects control subjects based on their Mahalanobis distance from the treated subjects.
W3-3 Further, we use a battery of matching variables: focal gamer s past spending (Spending), focal gamer s level of experience (Experience), focal gamer s network density (NetworkDensity), focal gamer s experience points (ExperiencePoint), number of logins (NumLogin), number of friends (NumFriends), the number of joint play sessions the focal gamer has with other gamers (JointPlay), the number of weeks from the first week of play (Duration). We note that since we perform dynamic matching, all these variables are time varying. More specifically, we use moving average (across all past time periods) measure of all these variables except for Experience and Duration which are focal time period specific. We also use time invariant matching variables which include focal gamer s job type (Job Dummies), and focal gamer s demographic information (Age and Female). We note that since we have two types of products, functional and hedonic products, we perform the matching for each of the two types of products. In Table W3.1, we present the results of the logistic regression model that we use to estimate propensity score. For the sake of brevity, we report results of logistic regression for only one two-week time period (weeks 3 and 4 specifically). TABLE W3.1. Logistic Regression Variable Estimate SE Estimate SE Functional Products Hedonic Products ln(spending -t).085 *** (.050).132 *** (.039) Experience t-1.167 *** (.021).169 *** (.020) NetworkDensity -t -1.306 * (.714) -1.600 ** (.624) ln(experiencepoint -t) -.501 *** (.128) -.516 *** (.112) ln(numlogin -t).098 (.163).042 (.155) ln(numfriends -t).947 *** (.210) 1.060 *** (.202) ln(jointplay -t).436 ** (.206).333 * (.192) Duration t.064 (.076) -.057 (.072) Job 1 (Magician) -.077 (.230) -.214 (.220) Job 2 (Archer).104 (.195).094 (.186) Job 3 (Thief) -.131 (.233) -.073 (.218) Age -.003 (.007) -.001 (.006) Female.262 * (.160).220 (.152) * p <.1, ** p <.05, *** p <.01 Notes: Standard errors in parentheses. We add one to the spending variables before taking the logtransformation. The subscript t denotes moving average (across all past time periods until the previous time period) measure of a particular variable, while t-1 is a (one period) lagged measure.
W3-4 We use 1:n (with n=5) matching. In Table W3.2, we present the percentage reduction in bias for each of the covariates (for the sake of brevity, we report the results for one time period only). Standard bias and standard bias reductions were calculated as per Rosenbaum and Rubin (1985). As can be seen from the table, we are able to achieve reduction in imbalance between the treatment and the control groups after matching.
W3-5 Variable TABLE W3.2. Covariate Imbalance in Matched Samples: Percent Reduction in Bias for Variables Treatment Group Mean A. Functional Products Before Matching After Matching Percent Control Group Mean Standard Bias (%) Control Group Mean Standard Bias (%) Reduction in Bias ln(spending -t).857.370 30.5.531 20.4 33.1 Experience t-1 31.639 20.636 140.1 27.755 49.5 64.7 NetworkDensity -t.071.099-23.6.068 2.1 91.2 ln(experiencepoint -t) 17.281 15.406 117.0 16.698 36.4 68.9 ln(numlogin -t) 2.903 2.373 83.4 2.701 31.8 61.9 ln(numfriends -t) 2.336 1.324 130.3 1.973 46.7 64.1 ln(jointplay -t) 3.208 1.856 132.8 2.702 49.7 62.6 Duration t 2.137 1.742 55.6 1.988 20.9 62.5 B. Hedonic Products Before Matching After Matching Percent Reduction in Bias Variable Treatment Control Standard Control Standard Group Mean Group Mean Bias (%) Group Mean Bias (%) ln(spending -t) 1.451.507 48.1.936 26.2 45.5 Experience t-1 30.301 20.126 129.2 26.475 48.6 62.4 NetworkDensity -t.073.102-23.0.075-1.9 91.8 ln(experiencepoint -t) 17.112 15.284 113.2 16.531 35.9 68.3 ln(numlogin -t) 2.862 2.334 83.0 2.650 33.3 59.8 ln(numfriends -t) 2.252 1.254 129.8 1.865 50.3 61.2 ln(jointplay -t) 3.092 1.764 131.1 2.586 50.0 61.9 Duration t 2.047 1.749 41.5 1.910 19.0 54.1 Notes: Standard bias and Standard Bias Reduction follow formulas in Rosenbaum and Rubin (1985). We report cases only when standard bias before matching is greater than 20%, meaning large initial bias.
W3-6 Average Treatment Effects The next step involves estimating the average treatment effect on the treated (ATT), which measures the difference between average spending of the treatment group and the matched control group gamers. Matching takes into account the homophily effect; thus comparison in spending between the treatment group and the matched control group helps pick up the contagion effect. In Figure W3.1, the black solid line ( ) shows the average spending of the treated group over time; the gray dashed line ( ) represents the average spending of the matched control group. We measure the social contagion effect by the proportion of the difference between average spending of the treatment group and the average spending of the matched control group to the average spending of the treatment group. The difference between these two lines indicates the ATT which corresponds to the effect of social contagion on treated groups spending on virtual products. Our results suggest that contagion effect accounts for 59% and 62% of the gamers spending towards purchase of functional products and hedonic products respectively. We can see that the effect of social contagion is slightly higher on purchasing hedonic products.
Average Spending (Korean Won) Average Spending (Korean Won) W3-7 FIGURE W3.1. Average Spending of Treatment vs. Matched Control Groups A. Functional Products 4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 0 2 4 6 8 10 12 14 16 18 20 Week Average spending of treatment group Average spending of matched control group B. Hedonic Products 3,500 3,000 2,500 2,000 1,500 1,000 500 0 2 4 6 8 10 12 14 16 18 20 Week Average spending of treatment group Average spending of matched control group
W3-8 Robustness Checks Recall that a gamer is placed in the treatment group if the gamer has at least one friend who purchased virtual products in the previous time period (t-1) and a gamer is classified as a control group gamer if the gamer has friends but none of the friends bought virtual products in the previous time period. Following recent studies (e.g., Aral, Muchnik, and Sundararajan 2009), we check the robustness of our definition of the treatment group by redefining the treatment group. First, we varied the minimum number of friends who purchased virtual products that constitutes treatment from one to six and recalculated ATT, which measures the difference between average spending of the treatment group and the matched control group gamers. In other words, we varied the minumum number of friends who purchased virtual products (at time t-1) from one to six. In Panel A of Figure W3.2, we present the average spending of the treatment group and the matched control group gamers on functional and hedonic products. The graph suggests that as the number of friends who purchased virtual products increases, the effect of social contagion increases. Second, we varied the recency of purchase by the friends of a treatment group gamer. More specifically, we defined treatment group gamer (at any given week t) as a gamer who has at least one friend who purchased virtual products but varied the timing of purchase from last period to last eight time periods (this is equivalent to two months since one time period is a week in our analysis). In Panel B of Figure W3.2, we present the average spending of the treatment group and the matched control group gamers on functional and hedonic products with varying purchase windows. As can be seen from Panel B of Figure W3.2, we find a significant effect of social contagion over a period of one to eight weeks since last purchase by friends. We also find that as the recency of purchases made by friends decreases, the social contagion effect decreases.
Average Spending (Korean Won) Average Spending (Korean Won) Average Spending (Korean Won) Average Spending (Korean Won) W3-9 FIGURE W3.2. Different Definitions of Treatment A. By Number of Friends Who Purchased B. By Recency of Friends Purchase 3,500 2,000 3,000 1,800 1,600 2,500 1,400 Functional Products 2,000 1,500 1,000 500 1,200 1,000 800 600 400 200 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 Number of friends who purchased during the last time period Recency (week) Average spending by treatment group Average spending of treatment group Average spending by matched control group Average spending of matched control group 2,500 1,600 2,000 1,400 1,200 1,500 1,000 Hedonic Products 1,000 500 800 600 400 200 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 Number of friends who purchased during the last time period Recency (week) Average spending by treatment group Average spending by matched control group Average spending of treatment group Average spending of matched control group
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