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We examine how wealth inequality and diversity in the perception of risk of a collective disaster impact cooperation levels in the context of a public goods game with uncertain and non-linear returns. In this game, individuals face a collective-risk dilemma where they may contribute or not to a common pool to reduce their chances of future losses. We draw our conclusions based on social simulations with populations of independent reinforcement learners with diverse levels of risk and wealth. We find that both wealth inequality and diversity in risk assessment can hinder cooperation and augment collective losses. Additionally, wealth inequality further exacerbates long term inequality, causing rich agents to become richer and poor agents to become poorer. On the other hand, diversity in risk only amplifies inequality when combined with bias in group assortment—i.e., high probability that agents from the same risk class play together. Our results also suggest that taking wealth inequality into account can help to design effective policies aiming at leveraging cooperation in large group sizes, a configuration where collective action is harder to achieve. Finally, we characterize the circumstances under which risk perception alignment is crucial and those under which reducing wealth inequality constitutes a deciding factor for collective welfare.