  Social dilemmas present a significant challenge in multi-agent cooperation
because individuals are incentivised to behave in ways that undermine socially
optimal outcomes. Consequently, self-interested agents often avoid collective
behaviour. In response, we formalise social dilemmas and introduce a novel
metric, the general self-interest level, to quantify the disparity between
individual and group rationality in such scenarios. This metric represents the
maximum proportion of their individual rewards that agents can retain while
ensuring that a social welfare optimum becomes a dominant strategy. Our
approach diverges from traditional concepts of altruism, instead focusing on
strategic reward redistribution. By transferring rewards among agents in a
manner that aligns individual and group incentives, rational agents will
maximise collective welfare while pursuing their own interests. We provide an
algorithm to compute efficient transfer structures for an arbitrary number of
agents, and introduce novel multi-player social dilemma games to illustrate the
effectiveness of our method. This work provides both a descriptive tool for
analysing social dilemmas and a prescriptive solution for resolving them via
efficient reward transfer contracts. Applications include mechanism design,
where we can assess the impact on collaborative behaviour of modifications to
models of environments.
