Fig. 1

Probing persecutory ideation: inferring on others’ intentions experimental paradigm and computational model. a Participants took part in a face-to-face advice-taking task for monetary rewards and were randomly assigned to “player” and “adviser” roles. “Players” had to predict the outcome of a binary lottery draw, whereas “Advisers” gave Players suggestions on which option to choose. Both sets of participants received incentives and the pay-off structure differed to ensure the presence of both collaboration and competition between the two participants. Players profited from the Adviser’s recommendations as Advisers always received more information about the outcome of the lottery (constant probability of 80%), whereas Advisers gained from the Players’ compliance to take the advice into account. The Advisers’ motivation to provide valid or misleading information varied during the game as a function of their own incentive structure. Players were (truthfully) informed that the Adviser had his own (undisclosed) incentive structure and because of it, intentions could change during the game (volatility). The social learning task was adapted for fMRI or EEG recordings by using 2-sec video clips of the Advisers recorded during the interactive sessions. b According to the model, an agent infers on true hidden states in the world by continuously updating his/her predictions (or beliefs) via precision-weighted prediction errors (PEs). Assuming Gaussian distributions over beliefs, these can be described by their sufficient statistics, the mean (μ) and the variance/uncertainty (σ) or its inverse precision/certainty (π). Predictions about hidden states in the world (before observing an outcome) are denoted with a hat symbol (e.g.,\(\hat \pi\)). At each hierarchical level i, belief updates (updates of the posterior means \(\mu _i^{(k)}\)) on each trial k are proportional to precision-weighted PEs. The belief update is the product of the PE from the level below \(\delta _{i - 1}^{(k)}\), weighted by a precision ratio. The ratio is composed of \(\hat \pi _{i - 1}^{\left( k \right)}\) and \(\pi _i^{\left( k \right)}\), which represent estimates of the precision of the predicted input from the level below (sensory precision) and precision of the belief at the current level, respectively