This is an interesting question. The short answer is yes, no, and maybe. Since anthropomorphizing is generally frowned upon by the scientific community, the subjectivity of the word "play" becomes more acute. If we assume that behavior we observe in other species occurs under the same motivation as our own, then applying our own term for it is less problematic. However, now the word "motivation" becomes an issue. So just think of the terms "stimulus and reward," and let's move on.
Do you own Tropheus duboisi? If so, you might be interested to know that a team of researchers has recently concluded that the species does play. If you can get your hands on a copy of the article "Highly Repetitive Object Play in a Cichlid Fish (Tropheus duboisi)," give it a read. It's pretty fascinating.
In fact, one of the co-authors, Gordon Burghardt, has outlined in the article his five criteria for defining play:
1. The behavior is incompletely functional in the behavioral context in which it is expressed
Interestingly enough, according to the authors, at the time of the article T. duboisi was the only cichlid species to have been studied and display behavior that met the "play" criteria above.
Burghardt, G. M. 2011: Defining and recognizing play. In: Oxford Handbook of the Development of Play (Pellegrini, A. D., ed.). Oxford University Press, Oxford, UK, pp. 9-18.
Burghardt, G. M., Dinets, V. and Murphy, J. B. (2015), Highly Repetitive Object Play in a Cichlid Fish (Tropheus duboisi). Ethology, 121: 38–44. doi:10.1111/eth.12312.
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