Significance: Polarization is rising while political debates are moving to online social platforms. In such settings, algorithms are used to recommend new connections to users, through so-called link recommendation algorithms. Users are often recommended based on structural similarity (e.g., nodes sharing many neighbors are similar). We show that preferentially establishing links with structurally similar nodes potentiates opinion polarization by stimulating network topologies with well-defined communities (even in the absence of opinion-based rewiring). When networks are composed of nodes that react differently to out-group contacts—either converging or polarizing—connecting structurally dissimilar nodes enhances moderate opinions. Our study sheds light on the impacts of social-network algorithms in opinion dynamics and unveils avenues to steer polarization in online social networks.

Mitigating climate change effects involves strategic decisions by individuals that may choose to limit their emissions at a cost. Everyone shares the ensuing benefits and thereby individuals can free ride on the effort of others, which may lead to the tragedy of the commons. For this reason, climate action can be conveniently formulated in terms of Public Goods Dilemmas often assuming that a minimum collective effort is required to ensure any benefit, and that decision-making may be contingent on the risk associated with future losses. Here we investigate the impact of reward and punishment in this type of collective endeavors — coined as collective-risk dilemmas — by means of a dynamic, evolutionary approach. We show that rewards (positive incentives) are essential to initiate cooperation, mostly when the perception of risk is low. On the other hand, we find that sanctions (negative incentives) are instrumental to maintain cooperation. Altogether, our results are gratifying, given the a-priori limitations of effectively implementing sanctions in international agreements. Finally, we show that whenever collective action is most challenging to succeed, the best results are obtained when both rewards and sanctions are synergistically combined into a single policy.

Indirect reciprocity (IR) is a key mechanism to understand cooperation among unrelated individuals. It involves reputations and complex information processing, arising from social interactions. By helping someone, individuals may improve their reputation, which may be shared in a population and change the predisposition of others to reciprocate in the future. The reputation of individuals depends, in turn, on social norms that define a good or bad action, offering a computational and mathematical appealing way of studying the evolution of moral systems. Over the years, theoretical and empirical research has unveiled many features of cooperation under IR, exploring norms with varying degrees of complexity and information requirements. Recent results suggest that costly reputation spread, interaction observability and empathy are determinants of cooperation under IR. Importantly, such characteristics probably impact the level of complexity and information requirements for IR to sustain cooperation. In this review, we present and discuss those recent results. We provide a synthesis of theoretical models and discuss previous conclusions through the lens of evolutionary game theory and cognitive complexity. We highlight open questions and suggest future research in this domain. This article is part of the theme issue ‘The language of cooperation: reputation and honest signalling’.