Abstract Theory of Mind (ToM) is the ability to attribute mental states (e.g., beliefs and desires) to other people in order to understand and predict their behaviour. If others are rewarded to compete or cooperate with you, then what they will do depends upon what they believe about you. This is the reason why social interaction induces recursive ToM, of the sort “I think that you think that I think, etc.”. Critically, recursion is the common notion behind the definition of sophistication of human language, strategic thinking in games, and, arguably, ToM. Although sophisticated ToM is believed to have high adaptive fitness, broad experimental evidence from behavioural economics, experimental psychology and linguistics point towards limited recursivity in representing other’s beliefs. In this work, we test whether such apparent limitation may not in fact be proven to be adaptive, i.e. optimal in an evolutionary sense. First, we propose a meta-Bayesian approach that can predict the behaviour of ToM sophistication phenotypes who engage in social interactions. Second, we measure their adaptive fitness using evolutionary game theory. Our main contribution is to show that one does not have to appeal to biological costs to explain our limited ToM sophistication. In fact, the evolutionary cost/benefit ratio of ToM sophistication is non trivial. This is partly because an informational cost prevents highly sophisticated ToM phenotypes to fully exploit less sophisticated ones (in a competitive context). In addition, cooperation surprisingly favours lower levels of ToM sophistication. Taken together, these quantitative corollaries of the “social Bayesian brain” hypothesis provide an evolutionary account for both the limitation of ToM sophistication in humans as well as the persistence of low ToM sophistication levels.

Citation: Devaine M, Hollard G, Daunizeau J (2014) Theory of Mind: Did Evolution Fool Us? PLoS ONE 9(2): e87619. https://doi.org/10.1371/journal.pone.0087619 Editor: Tiziana Zalla, Ecole Normale Supérieure, France Received: July 30, 2013; Accepted: December 26, 2013; Published: February 5, 2014 Copyright: © 2014 Devaine et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by the European Research Council (JD) and the French Ministère de l’Education Nationale (MD). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.

Introduction Theory of Mind (ToM) is the ability to attribute mental states (e.g., beliefs and desires) to other people in order to understand and predict their behaviour [1]. This ability lies at the core of human social cognition: it develops early in life [2], and its impairment is associated with severe neuropsychiatric disorders [3]–[4]. ToM endows us with highly adaptive social skills, such as teaching, persuading or deceiving [5]. Thus, natural selection should have promoted phenotypes that exhibit highly sophisticated forms of ToM [6]–[10]. In fact, behavioural economics has provided undisputable experimental evidence of people’s bounded rationality in strategic interactions [11]. In particular, we seem to be very limited in our ability to correctly guess the behaviour of others in games [12]–[14]. These results corroborate experimental psychology studies [15]–[16], as well as linguistic and even literary evidence [17]–[18] that all point towards a heterogeneous and limited ToM sophistication in humans. We may thus wonder why evolution has not made all of us smarter. In particular, what made it possible for low ToM sophistication phenotypes to persist in socially demanding environments? In this work, we test whether such apparent limitations may not in fact be proven to be adaptive, i.e. optimal in an evolutionary sense. In turn, this raises two challenging issues: (i) how do we formally define ToM sophistication phenotypes?, and (ii) how do we measure their adaptive fitness? We start with the premise that if others are rewarded to compete or cooperate with you, what they believe you will do is relevant for you to predict their behaviour. This is the reason why social interaction induces recursive thinking, of the sort “I think that you think that I think, etc.”. Critically, recursion is the common notion behind the definition of sophistication of human language [19]–[20] and strategic thinking in games [14], [21]. In line with Yoshida et al. [22], we define ToM sophistication as the depth of recursive thinking. Here, a 0-ToM agent learns (over the course of repeated interactions) how likely her opponent’s choices are. In contrast, a 1-ToM agent adopts the “intentional stance” [23], i.e. she tries to understand how 0-ToM updates his belief, from observing his behaviour. Hence, 1-ToM is defined in terms of her recursive belief, i.e. her belief about 0-ToM’s belief. A 2-ToM observer assumes she faces either a 1-ToM or a 0-ToM agent. This means she has to both recognize the sophistication of her opponent and understand how he learns. More generally, a k-ToM agent tries to understand how her opponent learns, under the assumption that he is less sophisticated than herself. In so doing, k-ToM forms high-order recursive beliefs, which may be highly uncertain. Thus, we model the impact of subjective uncertainty onto the mechanism of belief update using information theory (cf. the Bayesian brain hypothesis [24]–[26]). In the context of social interaction, we are left with the question of what prior information agents use to learn about how others learn. Here, we simply assume that the brain’s model of other brains presumes they are optimal too. By this we mean that people believe other conspecifics behave according to common sense (e.g., they make decisions that reveal their preferences and beliefs, which change as learning unfolds). The key idea here is to consider how such common sense notion impacts on the (Bayes-optimal) learning rules of agents interacting with each other. In this context, Bayes-optimality simply means that information processing suffers no distortion aside from potential prior biases. Agnostic priors on peoples’ choices (i.e. priors that do not involve the intentional stance) would yield Bayesian agents that track the descriptive statistics of others’ choices. This is essentially what 0-ToM learners do. Eventually, they arrive at uncertain estimates (beliefs) of, e.g., others’ choice frequency. However, Bayes-optimal forecasts of 0-ToM’s behaviour rely on the (ambiguous) identification of the covert beliefs and preferences that determine her overt decisions. This is the essence of 1-ToM’s learning rule, which relies on an informative prior assumption, namely: others are (agnostic) Bayes-optimal agents. Under this “social Bayesian brain” hypothesis, one can derive the learning rule of k-ToM agents recursively, starting with 0-ToM (see Models). Although k-ToM learners are all Bayes-optimal, they differ in terms of the depth of recursion of their beliefs. This difference in ToM sophistication changes the way k-ToM agents react to a given sequence of their opponent’s action. For example, 0-ToM will tend to act as if her opponent was more likely to pick the action that she had chosen most frequently in the past. In turn, 1-ToM will anticipate this and act accordingly. Since their respective behavioural response pattern will be different, 2-ToM is in a position to discriminate between 0-ToM and 1-ToM (and act accordingly). In brief, k-ToM will best-respond to her opponent’s past choices, under the constraint of limited sophistication. Thus, ToM sophistication phenotypes are characterized in terms of (formal) belief update rules that (i) are specific to the depth of their recursion, and (ii) shape their behavioural strategy over the course of repeated social interactions. We address the second challenge from the perspective of evolutionary game theory (EGT). In brief, EGT states that the reproductive and survival successes of any behavioural phenotype is determined by how well it performs when interacting with other alternative phenotypes [27]. Here, we extend this idea to evaluate the adaptive fitness of ToM sophistication. Current ethological debates highlight the importance of competitive versus cooperative types of reciprocal social interactions in the evolution of ToM [10]. We thus focused on a pair of two-players games that capture these two canonical forms of social interaction. In “hide and seek”, the gain of the winner is exactly balanced by the loss of the looser, which is the essence of competition. In contradistinction, agents playing “battle of the sexes” are most rewarded for coordinating their behaviour (see Models and Methods). Note that both games’ payoffs are contingent on players’ ability in predicting their opponent’s behaviour (there is no prior good decision).

Discussion In this work, we have proposed a quantitative evolutionary account of ToM sophistication in humans. This relies upon a meta-Bayesian formalism [26] for recursive ToM inferences that arise in the context of reciprocal social interactions. The key idea here is that meta-bayesian agents learn or recognize the subjective (potentially high-order) beliefs of other agents in a Bayes-optimal fashion. Here, ToM sophistication is defined as the level of recursion of such meta-bayesian agents. We have assessed the relative performance of ToM agents playing competitive or coordinative games with each other. Finally, we have identified what evolutionary forces could have led to the observed variability of ToM sophistication in humans. More precisely, we have shown that: (i) a non-trivial informational cost to sophistication limits the way one can exploit less sophisticated ToM agents, and (ii) one may benefit from engaging in a cooperative interaction with more sophisticated ToM agents. Eventually, these properties yield an evolutionary stable mixture of ToM phenotypes with a lower bound at k = 1 (agents without ToM get extinct) and an upper bound at k = 2. Our model was largely inspired by previous work from behavioural economics and experimental psychology on bounded rationality. More precisely, k-ToM shares with models such as “level k” [13] and the “cognitive hierarchy” [12] the notion of recursive thinking. These models have been typically used to explain people’s behaviour in non-repeated games such as the “beauty contest” (but see [14], [31]–[32] for nice extensions to repeated games). They prove useful in capturing inter-individual variability in peoples’ behaviour, in terms of the sophistication of their strategic thinking. For example, Camerer and colleagues [21] have reported the following distribution of levels: around 20% of level 0 players, 33% of level 1, 25% of level 2 and then a decreasing proportion of higher levels. Although not identical, such results are consistent with our EGT prediction (cf. the distribution peaks around level 1 and 2). Observed discrepancies may have three distinct causes. First, peoples’ behaviour is not unambiguously mapped onto levels of strategic thinking (cf. issues with levels’ stability across games, etc…). Second, we may not have included all the relevant evolutionary constraints on ToM sophistication (see comment below on comparing ToM across species). Third, there are conceptual differences between k-ToM (which deals with the sophistication of learning rules) and the cognitive hierarchy (which cares about the sophistication of behavioural policies). This theoretical difference is not trivial. On the one hand, one could argue that the basic cognitive resource that underlies both processes is the same, namely: the ability to form recursive beliefs. On the other hand, theory of mind is essentially inferential (cf. the intentional stance). That is, ToM is engaged when we identify mental states (beliefs, intentions, emotions, etc…) from social signals (decisions, facial expressions, etc…). In this perspective, ToM may have more to do with the way we adapt to others (through learning) than with the evaluation of the consequences of our actions (decision making). We will now discuss the limitations of our model. First, we did not account for social preferences or norms, such as fairness or inequity aversion. These are thought to explain people’s altruistic behaviour despite strong incentive for betrayal, as in the “prisoner’s dilemma” game [33]–[34]. However, it turns out that, in these games, meta-Bayesian agents choose the egoistic (dominant) strategy, irrespective of their ToM sophistication level. This means that ToM alone cannot explain people’s altruistic behaviour. Interestingly, a recent study [35] has used EGT with the iterated “prisoner’s dilemma” to explain the emergence of fairness through evolution. The captivating question of whether ToM’s adaptive fitness depends upon social preferences (and reciprocally) is beyond the scope of the present work. Addressing this would require modelling, e.g. inference on others’ fairness preferences. Second, our approach shares with similar hierarchical models (such as the “cognitive hierarchy” [13], [21]) the relative arbitrariness of the first level. This is critical, because the behavioural response of all subsequent levels in the hierarchy (recursively) rely on the definition of the first level [36]. Our definition of 0-ToM agents follows from the “Bayesian brain” hypothesis: there is no reason to consider 0-ToM agents that would not learn optimally, aside from their inability to take the “intentional stance”. We believe this is mandatory for evaluating ToM’s adaptive fitness. This is because we do not want the effect of ToM sophistication on behavioural performance to be confounded by differences in, e.g., the principles underlying the way agents learn and decide. Taken together, these considerations constrain the definition of 0-ToM agents. This deserves further comments. It seems to us that it would not make sense to define 0-ToM agents that would be insensitive to feedback (e.g., payoff). This is because there will always exist a broad class of social interactions, in the context of which any such feed-forward system would perform very poorly. In other terms, feed-forward 0-ToM agents would have no evolutionary adaptive fitness. Critically, the feedback’s source is twofold: context (i.e. nature of the interaction -cf. game payoff table-) and opponent (i.e. behavioural tendencies). This is important, because there are not many types of agents that would differ qualitatively in their response to such information. An example of an agent sensitive to the context but not to her opponent is the Nash policy. By construction however, the ensuing -ToM agents would be Nash players as well, and thus ToM sophistication would have no adaptive fitness. In contradistinction, imitative learners are sensitive to their opponent, but not to context. However, the adaptive fitness of such agents is similar to feed-forward agents. Yet another possibility is to consider agents that would respond to an aggregate context-opponent feedback, namely: reward. This is the essence of genuine reinforcement learning (RL) agents. Note that, in terms of behavioural performance, RL agents are comparatively closer to 0-ToM than to any other agent type we have considered (including Nash players; cf. Figure 7). In fact, this was expected, since there is a linear one-to-one mapping between the value of each option and the opponent’s choice probability. Additionally, -ToM agents (with ) have a clear tendency to identify RL players as 0-ToM, at least in a competitive context. This means that we expect our results to be robust to re-defining 0-ToM agents as RL agents. Note that any agent that would be differentially sensitive to context and opponent feedbacks would be formally very similar to our 0-ToM. Taken together, we believe our results would be very robust to admissible changes in the definition of 0-ToM agents. Third, one may invoke another line of work, which consists in considering that biological costs (such as brain size) induce additional evolutionary forces that eventually limited our cognitive skills [37]. The weakness of such studies is the lack of specificity: how global features such as brain size relate to different cognitive functions is unclear. In any case, what we have shown is that one does not have to appeal to biological costs to explain our limited ToM sophistication. More generally, one could challenge the very idea that natural selection acted upon ToM sophistication. For example, a radical non-adaptationist scenario would consider that such cognitive phenotypes evolved from random genetic drift. Alternatively, one could argue that ToM sophistication is a by-product of constraints imposed by other cognitive traits (such attention or working memory) that were under selective pressure. Debates about whether or not a given phenotype has been shaped by natural selection are not uncommon in evolutionary biology (cf. e.g., [38]). In our context, we would appeal to the importance of social cognitive skills in shaping humans’ adaptive fitness [7], [8]. However, we believe that, if properly extended, our work could provide a more satisfactory answer to this question. This is because EGT can be used to predict a specific relationship between features of the ecological niche (here, we considered the proportion of cooperative interactions and the typical amount of learning) and the distribution of ToM sophistication. The key point is that such features can vary across different species. Thus, provided one appropriately captures the critical differences between ecological niches, one could then test the induced variability in ToM sophistication (across species) against the null. We will pursue this in subsequent publications. Last, one could challenge the fact that we have neglected developmental (and, to a lesser extent maybe, pathological) aspects of ToM [39]. This is related to the notion of “proximal constraints” of evolution, which relate to the ability of individuals to gradually adopt behavioural strategies that have local adaptive fitness, and are thus positively reinforced by their environment [40]. Applying the principles of such reinforcement learning theories of motivation [41] would advocate for considering agents that could change their ToM sophistication level at will. Here, we have rather assumed that ToM sophistication is a phenotype that can hardly be changed or learned over the course of the agent’s life time. However, another way of looking at ToM phenotypes is in terms of an informative prior belief on the population profile of ToM sophistication. Effectively, k-ToM phenotypes can be thought of as agents with unbounded ToM sophistication, who a priori believe that their conspecifics’ level of ToM sophistication cannot exceed k-1. This has two implications: (i) one could relax this prior and effectively allow agents to adapt their effective ToM sophistication level, and (ii) one could think of evolution as selecting a very specific form of prior that defines classes of meta-Bayesian agents [42]. To conclude, our meta-Bayesian approach unravelled non-trivial properties of inferential aspects of ToM. In particular, the informational cost to sophistication is a key determinant of ToM’s adaptive fitness. Note that this cost might in fact induce strong evolutionary forces for most cognitive processes that can be viewed as inferential in nature, as is the case for, e.g., learning or perception [24], [43]. This is because, as any ill-posed problem, inference heavily relies upon some form of prior information or belief [44]. Critically, we speculate that the sophistication of such prior eventually matches the complexity of the agent’s ecological niche, because of its inevitable evolutionary cost/benefit ratio.

Supporting Information Text S1. This note provides technical details about the derivation of the learning rule of ToM agents and our application of Evolutionary Game Theory (EGT) to ToM sophistication phenotypes. https://doi.org/10.1371/journal.pone.0087619.s001 (DOCX)

Author Contributions Conceived and designed the experiments: JD MD. Performed the experiments: JD MD. Analyzed the data: JD MD. Contributed reagents/materials/analysis tools: JD MD. Wrote the paper: JD MD GH.