Bivalent Impact of Social Networks on Overarming: Model-Based Insights on the Alignment between Social and Individual Interests

Abstract Drawing on evolutionary game theory, we present a stylized, conceptual model of gun acquisition for individuals in a society where all have the right to bear arms. In our dynamic model, pairwise confrontations with attendant payoffs take place between individuals who are either armed or unarmed. Individual payoffs depend on the probability of confrontation, the choice to arm, and the choices of others. We show that the likelihood of confrontation affects the optimal societal arming rate and the arming rate that occurs in equilibrium. The latter quickly surpasses the former as the probability of confrontation increases, a phenomenon we call overarming. This reflects a misalignment of individual and societal interests. We further show that spatial structures can exacerbate overarming, especially when individuals perceive a deteriorating social environment. Our modeling results highlight the importance of understanding how fundamental behavioral dynamics and network heterogeneity influence individual decisions to purchase firearms. Our work offers a theoretical, proof-of-concept framework -- demonstrated through analytical and simulation-based results -- that can inform future empirical research for understanding the dynamics of gun ownership and overarming and help identify potential avenues for effective intervention and policy-making.