Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread cooperation is often much more difficult. We show here that there exist strategies of `targeted punishment' whereby a small number of punishers can shift a population of defectors into a state of global cooperation. The heterogeneity of players, often regarded as an obstacle, can in fact boost the mechanism's effectivity. We conclude by outlining how the international community could use a strategy of this kind to combat climate change.

High-order, beyond-pairwise interdependencies are at the core of biological, economic, and social complex systems, and their adequate analysis is paramount to understand, engineer, and control such systems. This paper presents a framework to measure high-order interdependence that disentangles their effect on each individual pattern exhibited by a multivariate system. The approach is centred on the 'local O-information', a new measure that assesses the balance between synergistic and redundant interdependencies at each pattern. To illustrate the potential of this framework, we present a detailed analysis of music scores from J.S. Bach, which reveals how high-order interdependence is deeply connected with highly non-trivial aspects of the musical discourse. Our results place the local O-information as a promising tool of wide applicability, which opens new perspectives for analysing high-order relationships in the patterns exhibited by complex systems.