The ability to anticipate how another individual will behave is a critical skill in the animal kingdom. Humans typically deal with this problem using their Theory of Mind (ToM), i.e. the ability to decipher beliefs and intentions of others. Although non-human primates (apes in particular) exhibit elaborate social behavior, there is no established consensus on whether this mirrors some form of sophisticated ToM. We suggest that ToM sophistication can be operationally defined in terms of the depth of recursive beliefs, as in "I think that you think that I think...". Importantly, mutual social interactions may call for highly recursive beliefs: not only do I think that you think, but I also think that you think that I think... This study aims at comparing how primate species (including humans) differ with respect to this form of ToM sophistication. The main novelty of our experimental approach is to estimate each primate’s ToM sophistication from its performance in repeated interactive games that are calibrated using information theoretic models of (artificial) recursive ToM. We first validated our model in human subjects and then tested 6 species of captive non-human primates (3 species of great apes: orangutans, gorillas, chimpanzees, and 3 species of old-world monkeys: lion-tailed macaques, rhesus macaques and collared mangabeys) in an adaptation of the task used in the human study. Our paradigm consisted in a “hide and seek” game in which individuals played against a human opponent (a familiar zoo keeper). In each trial, the individual had to infer where food had been hidden by the experimenter opponent (either in his right or left hand). In fact, the location of the food was chosen by learning algorithms, some of which endowed with artificial ToM. Critically, we varied the sophistication of these algorithms, yielding three conditions, ranging from a control (a simple random biased sequence) to a mildly sophisticated ToM agent (1-ToM). The profile of primates’ performances against the different algorithms was then used to infer their ToM sophistication. Preliminary results show that the pattern of performance of nonhuman primates differ from those of humans. Although most nonhuman primates tended to win in the control condition, they lost against the 1-ToM agent, in contrast to the human group (that won). Surprisingly, comparing the performances between the non-human primates' species did not reveal any significant inter-species difference. Therefore, great apes did not perform better than monkeys in our task. Interestingly, variability in the performances actually seems more to rely on inter-individual differences rather than on inter-species differences. Moreover, in every species, at least one individual exhibited mild (but statistically significant) ToM sophistication. Taken together, these data indicate that the distribution of ToM sophistication within each of these non-human primate species is quite heterogeneous. Further analyses are in progress to identify predictive factors (e.g. familiarity with humans, age, motivation and frustration during the game) that could explain away inter-individual differences, thus eventually revealing (or not) inter‑species differences [Authors Aurore San‑Galli and Marie Devaine contributed equally to this work].