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Collective action problems arise when cooperating individuals suffer costs of cooperation, while the benefits of cooperation are received by both cooperators and defectors. We address this problem using data from spotted hyenas fighting with lions. Lions are much larger and kill many hyenas, so these fights require cooperative mobbing by hyenas for them to succeed. We identify factors that predict when hyena groups engage in cooperative fights with lions, which individuals choose to participate and how the benefits of victory are distributed among cooperators and non-cooperators. We find that cooperative mobbing is better predicted by lower costs (no male lions, more hyenas) than higher benefits (need for food). Individual participation is facilitated by social factors, both over the long term (close kin, social bond strength) and the short term (greeting interactions prior to cooperation). Finally, we find some direct benefits of participation: after cooperation, participants were more likely to feed at contested carcasses than non-participants. Overall, these results are consistent with the hypothesis that, when animals face dangerous cooperative dilemmas, selection favours flexible strategies that are sensitive to dynamic factors emerging over multiple time scales.