Supplementary Materials for "Collective Action, Rival Incentives, and the Emergence of Antisocial Norms"

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Online Appendix A. Simulation Protocol
Click the link below to download a document summarizing the operation of the computational model and the design of the experiments.
• Simulation Protocol

Online Appendix B. Supplementary Figures (2b,2c,3b,3c,4b,4c)
The following document shows surface plots for enforcement behavior corresponding to the surface plots for collective action shown in the paper. Figures 2b, 3b, and 4b show the prosocial norms (enforcement behavior promoting collective goods) corresponding to Figures 2, 3, and 4 in the article. Figures 2c, 3c, and 4c show the antisocial norms (enforcement behavior opposing collective goods) corresponding to Figures 2, 3, and 4 in the article.
• Supplementary Figures

Online Appendix C. Sensitivity Analyses
Figures 2, 3, and 4 in the article are maps of equilibrium outcomes ("response surfaces") over ranges of experimentally manipulated parameter values. Each experiment holds constant a set of other parameters. Sensitivity analyses -- presented here as a series of animated movies -- show robustness of my conclusions on the model's qualitative behavior to variation in some of these other parameters. Note that each movie is not an animation of the model's behavior over time, but is a shifting map of the model's equilibrium response surface as a third parameter is manipulated.
Movies are standard ".avi" format, and can be viewed with most media players, such as Windows Media Player or Apple QuickTime.

In Experiment 1, Figure 2 showed the response surface for productivity with zero rivalness (λ=0) and Figure 3 showed this response surface with maximum rivalness (λ=1). The animation of Figure 3 shows the changes in this response surface over the entire range of rivalness, between these two extremes.
• Figure 3 (Productivity x Cohesiveness x Incentive Value) animated with rivalness increasing from λ=0 to λ=1
• Figure 3b (Promotion x Cohesiveness x Incentive Value) animated with rivalness increasing from λ=0 to λ=1
• Figure 3c (Opposition x Cohesiveness x Incentive Value) animated with rivalness increasing from λ=0 to λ=1
  The animation of Figure 3c shows the appearance and expansion of stable oppositional norms as rivalness increases from zero. The expansion of prosocial norms as rivalness increases in Figure 3b seems counterintuitive, but is due to second-order shirking at low rivalness: When most actors are contributing to the collective good, individuals may abstain from promoting work, but effective antisocial norms dampen productivity and thus create an opportunity for prosocial norms to emerge at high rivalness.
  
  In the experiments presented in the article, enforcement is moderately costly (e=2). The following animations show the changes in model response surfaces as enforcement cost increases from perfectly costless (e=0) to extremely expensive (e=5).
• Figure 3 (Productivity x Cohesiveness x Incentive Value) animated with enforcement cost increasing from e=0 to e=5
• Figure 3b (Promotion x Cohesiveness x Incentive Value) animated with enforcement cost increasing from e=0 to e=5
• Figure 3c (Opposition x Cohesiveness x Incentive Value) animated with enforcement cost increasing from e=0 to e=5
  
• Figure 4 (Productivity x Rivalness x Incentive Value) animated with enforcement cost increasing from e=0 to e=5
• Figure 4b (Promotion x Rivalness x Incentive Value) animated with enforcement cost increasing from e=0 to e=5
• Figure 4c (Opposition x Rivalness x Incentive Value) animated with enforcement cost increasing from e=0 to e=5
  Increasing the cost of enforcement from 0 to 5 has an unsurprising dampening effect on enforcement behavior, but the overall qualitative patterns identified in the article (Figures 3 and 4) are robust over this entire range. As mentioned, if enforcement is so costly or difficult that no actor will ever enforce, we would obviously observe no informal control and thus productivity will be a straightforward function of selective incentives. This animation of Figure 3c shows the reason for the surprising curvilinear relationship between incentive value and antisocial norms, described in the article. As enforcement cost rises, second-order free riding may in some cases be a solution to the collective action problem identified in this article: Actors who would prefer antisocial norms in the most highly competitive environment nevertheless refrain from opposing work because the benefit of doing so does not exceed the cost of enforcement in those conditions.
  
  In the experiments presented in the article, subjective scope of influence is uniformly distributed in the range [0,9]. The following animations assign the same influence scope value to all group members, but vary the scope value from the minimum (θ=1) to the maximum (θ=N-1).
• Figure 3 (Productivity x Cohesiveness x Incentive Value) animated with influence scope increasing from θ=1 to θ=9
• Figure 3b (Promotion x Cohesiveness x Incentive Value) animated with influence scope increasing from θ=1 to θ=9
• Figure 3c (Opposition x Cohesiveness x Incentive Value) animated with influence scope increasing from θ=1 to θ=9
  
• Figure 4 (Productivity x Rivalness x Incentive Value) animated with influence scope increasing from θ=1 to θ=9
• Figure 4b (Promotion x Rivalness x Incentive Value) animated with influence scope increasing from θ=1 to θ=9
• Figure 4c (Opposition x Rivalness x Incentive Value) animated with influence scope increasing from θ=1 to θ=9
  As noted in the article, homogeneous θ<3 implies that no actor will promote work, given the enforcement cost. We see no promotion (and little opposition) in these conditions, where actors believe that their influence efforts will have negligible effect. The qualitative shape of the response surface presented in the article is robust over the rest of the range of influence scope.