Bivalent impact of social networks on overarming: Insights on the alignment between social and individual interests

Drawing on evolutionary game theory, we present a stylized 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 others' choices. We show that the likelihood of confrontation affects the optimal societal arming rate and the arming rate that occurs in equilibrium. The latter rate quickly surpasses the former one 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. Results from our base model and its extensions highlight the importance of understanding how fundamental behavioral dynamics and network heterogeneity influence individual decisions to acquire firearms, informing empirical research for mitigating overarming.