Pairs of cooperating cleaner fish provide better service quality than singletons.

Service providers may vary service quality depending on whether they work alone or provide the service simultaneously with a partner. The latter case resembles a prisoner's dilemma, in which one provider may try to reap the benefits of the interaction without providing the service. Here we present a game-theory model based on the marginal value theorem, which predicts that as long as the client determines the duration, and the providers cooperate towards mutual gain, service quality will increase in the pair situation. This prediction is consistent with field observations and with an experiment on cleaning mutualism, in which stable male-female pairs of the cleaner wrasse Labroides dimidiatus repeatedly inspect client fish jointly. Cleaners cooperate by eating ectoparasites off clients but actually prefer to cheat and eat client mucus. Because clients often leave in response to such cheating, the benefits of cheating can be gained by only one cleaner during a pair inspection. In both data sets, the increased service quality during pair inspection was mainly due to the smaller females behaving significantly more cooperatively than their larger male partners. In contrast, during solitary inspections, cleaning behaviour was very similar between the sexes. Our study highlights the importance of incorporating interactions between service providers to make more quantitative predictions about cooperation between species.