1. University of Neuchâtel, Department of Zoology, Rue Emile-Argand 11 Case postale 158, 2009 Neuchâtel, Switzerland
2. University of Queensland, School of Integrative Biology, St Lucia, Queensland 4072, Australia
3. Stockholm University, Department of Zoology, SE-10691 Stockholm, Sweden

Correspondence to: Redouan Bshary¹ Correspondence and requests for materials should be addressed to R.B. (Email: redouan.bshary@unine.ch).

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^{1, 2, 3, 4}, 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 theorem⁵, 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 ectoparasites⁶ off clients but actually prefer to cheat and eat client mucus⁷. 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.

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