Domestic violence is a global crisis with severe human, emotional, and economic consequences, affecting an estimated 30% of women worldwide. Despite international commitments to eliminate it, prevention and services remain inadequate. Community mobilization interventions, involving local collaboration to address ill-health, have shown promise in reducing domestic violence, particularly in contexts of severe poverty and inequality. However, the mechanisms driving their impact remain poorly understood. Existing theoretical frameworks often lack nuance, overlooking complexities and potential unintended consequences. This study uses a game-theoretic model to formalize hypothesized processes involved in challenging unequal gender norms within community mobilization interventions. The aim is not to create a perfectly predictive model, but rather to provide explanatory clarity and identify core uncertainties in the evidence. The model analyzes the conditions under which domestic violence prevention becomes a social dilemma, where individual inaction, though rational, leads to negative collective consequences. The role of altruism in overcoming this dilemma will be explored.

The socio-ecological framework highlights the interplay of individual, relationship, community, and societal factors contributing to domestic violence. This framework is adapted to center the role of patriarchal ideology, male entitlement, and household gender roles. Feminist theories, such as the theory of Hegemonic Masculinity and Male Peer Support Theory, provide mechanisms by which societal ideologies manifest at the individual level, showing how men are rewarded for conforming to stereotypically masculine roles and how violence is used to punish female partners for non-conformity. Qualitative and quantitative studies demonstrate a correlation between societal acceptance of wife-beating and the experience of violence. Individual behavior change interventions often fail in contexts where social norms condone male violence. Community mobilization interventions, characterized by their open-ended approach and active community involvement, aim to challenge these norms, but their unpredictable nature necessitates a more rigorous understanding of their mechanisms. Existing theories of change emphasize community-driven attitude and social norm change as key drivers of reduction in domestic violence. The role of "organized diffusion," or active dissemination of anti-violence messages by community members, is highlighted in process evaluations. Game theory, a framework for analyzing interactive decision-making, is applied here to model trust, cooperation, and collective action in the context of domestic violence prevention.

The authors develop a game-theoretic model to formalize the dynamics of collective action to prevent domestic violence. The model involves a two-stage multiplayer game with women and men as players. The model incorporates several key assumptions: 1. **Attitudes Matter:** Men with more pro-violent attitudes are more likely to perpetrate violence. 2. **Social Norms Matter:** Men reward or punish peers for violent behavior. 3. **Perpetration of Violence Incurs Costs:** Violence is not cost-free for perpetrators. 4. **Costly Preventive Action is Possible:** Women's actions can change men's attitudes, but this involves effort and cost. 5. **Violence Creates Suffering for Survivors:** Women experience disutility from violence. 6. **Women's Welfare Should Be Assessed Assuming Zero Tolerance for Violence:** Adaptive preferences, where women accept conditions of oppression, are considered. The game unfolds in two stages: (1) Women choose their effort levels in changing men's attitudes; and (2) Men choose their level of violence. The model's utility functions for women and men consider the interplay of attitudes, social norms, violence, efforts, and costs. A Nash equilibrium is sought, representing the outcome of rational decision-making in the absence of interventions. The impact of parameter changes (e.g., increased costs of violence, reduced tolerance for violence) on equilibrium violence levels, women's effort, and welfare is analyzed. Social dilemmas are identified, where individual rationality leads to collective suboptimality. The authors then introduce scenarios to illustrate the model's predictions and evaluate potential solutions to the social dilemmas. The concept of altruism (process-based, empathetic, and reciprocal) is incorporated to explore its role in motivating collective action and overcoming the social dilemma.

The model demonstrates that under certain conditions, women's collective action to prevent domestic violence constitutes a social dilemma. Individually rational behavior leads to suboptimal collective outcomes, leaving all women worse off than if they had collectively acted. The authors show that simply making it easier for women to take action (reducing cost or increasing effectiveness of effort) is unlikely to solve the dilemma. Interventions that reduce women's tolerance for violence or increase the cost of perpetrating violence may have negligible or even counterintuitive effects. Increased cost of perpetration can lead to higher violence if women anticipate the deterrent effect and reduce their own efforts. Introducing altruism into the model offers potential solutions. The findings indicate that process-based (intrinsic motivation to act), empathetic (concern for others' suffering), and reciprocal (matching others' efforts) altruism can significantly reduce violence levels and improve women's welfare. Simulations show even small amounts of altruism drastically improve outcomes compared to self-motivated individual action. The positive impact of altruism is particularly significant when coupled with homogeneity in the population, meaning women are similarly situated and share similar experiences, promoting equal benefits for all from collective action. Introducing heterogeneity into the model reveals a larger range of outcomes for women, but the median effects still align with previous findings. Altruism appears to be most effective in communities characterized by strong social norms that reinforce or punish violent behaviors, while in contexts with weak social norms, community mobilization might be less effective.

The findings highlight the critical role of social dilemmas in understanding the challenges of collective action to prevent domestic violence. The model demonstrates why conventional interventions focusing solely on individual behavior change or external punishments may prove insufficient. The incorporation of altruism suggests a potential avenue for fostering collective action and overcoming the inherent barriers. The model's results are consistent with empirical observations of successful community mobilization interventions, supporting the significance of collective identity, empathy, and reciprocal support in driving social change. However, the model also reveals the complex interactions between individual behavior, social norms, and altruism, emphasizing the need for targeted interventions tailored to specific contexts and the importance of carefully measuring the externalities related to time and effort investments in community mobilization efforts.

This paper provides a novel game-theoretic framework for understanding collective action in domestic violence prevention. The model demonstrates that social dilemmas are crucial to consider, and that interventions must account for these challenges. Process-based, empathetic, and reciprocal altruism emerge as key mechanisms for mobilizing collective action and reducing violence. Future research should focus on empirically testing the model’s predictions, exploring the interplay between different forms of altruism, and developing tailored interventions to foster collective action in diverse communities. The study emphasizes the need for interdisciplinary collaboration between game theorists, gender scholars, and public health researchers to design and evaluate effective violence prevention strategies.

The model relies on simplifying assumptions, including the rational utility-maximization of individuals. While the model incorporates social and psychological factors, it does not explicitly model beliefs or belief updating, which could influence individual decisions. The model focuses primarily on women's collective action, neglecting men's roles. The choice of parameter values in the illustrative scenarios is for explanatory purposes and not based on empirical data from real-world contexts. Further research incorporating these factors and empirically validating the model's predictions is needed.