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 dilemma1,2,3,4, 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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We thank the Egyptian Environmental Affairs Agency for permission to work at Ras Mohammed National Park, the Park Rangers and I. Riepl for local support, and M. Würth and A. Hubl for field assistance. We further thank the Lizard Island Research Station for their support concerning the experiments. R.B. was funded by the Natural Environment Research Council and by the Swiss Science Foundation. A.S.T.W. was funded by the Swiss Science Foundation. A.S.G. was funded by the Australian Research Council. O.L. was funded by the Swedish Research Council.
Author Contributions R.B. and A.S.G. were responsible for the experimental data; A.S.T.W. was responsible for the field data; O.L. was responsible for the model; and R.B., A.S.G. and O.L. contributed to the writing.
The file contains Supplementary Notes on the model of cleaner-client interactions. Equations (1) and (2) in the main text are derived and an important qualitative prediction of the model is demonstrated: cooperative pairs of cleaner fish provide higher service quality than singletons. (PDF 86 kb)
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Bshary, R., Grutter, A., Willener, A. et al. Pairs of cooperating cleaner fish provide better service quality than singletons. Nature 455, 964–966 (2008). https://doi.org/10.1038/nature07184
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