Introduction

Social animals have evolved sophisticated mechanisms for cooperation. To coordinate, individuals exchange information, enabling independent and group regulation (Emerson, 1956; Wheeler, 1911). Interaction provides the self with insights about others and, simultaneously, about its own state within the environment. In humans, this psychological differentiation begins in utero (Ciaunica et al., 2021) and continues into adulthood. This prolonged differentiation facilitates the distinction between self and others, allowing grounded social orientation and flexible adaptation. Early psychological theorists highlighted the importance of healthy social exchange in humans for integrating constructive relational blueprints, noting that disruptions during sensitive periods can impair the formation of safe social bonds (e.g., Fairbairn, 1952; 1994) and foster less adaptable interpersonal beliefs (Young et al., 2006).

At the individual level, humans must manage information exchange to navigate and reduce relational uncertainty. When faced with external uncertainty about others’ characteristics, prior knowledge can swiftly and effectively guide predictions. Indeed, to reduce uncertainty about others, theories of the relational self (Anderson & Chen, 2002) suggest that the self is the most extensive and well-grounded representation available, leading to a readily accessible initial belief that can be projected or integrated when learning about others (self-insertion; Allport, 1924; Kreuger & Clement, 1994). When uncertainty arises regarding one’s own internal state, external cues can provide anchoring information to support self-through-other calibration. Therefore, individuals can generalize information from others to themselves. contagion has been observed across economic (Suzuki et al., 2016), intertemporal (Garvert et al., 2015), effort discounting (Devaine & Daunzieu, 2017), and moral choice behaviour (Yu et al., 2021). Social contagion is hypothesised to facilitate adaptation to social groups (Deutsch & Gerard, 1955; Toelch & Dolan, 2015), and as a crucial component of interpersonal cohesion that relies on trust (Frith & Frith, 2012).

Insights into healthy self-other relations can be gained from their frequent absence, a common and distressing reality for those with a diagnosis of Borderline Personality Disorder (BPD). BPD is characterized by interpersonal sensitivity and instability, emotional dysregulation, impulsivity, paranoia, and severe fear of abandonment (e.g., Gunderson et al., 2018; Euler et al., 2021). It is strongly associated with early childhood adversity, such as psychological, physical, and sexual abuse or neglect (Afifi et al., 2011; Bateman et al., 2023), and inconsistent parenting experiences (Crawford et al., 2009), particularly during sensitive developmental periods (Fonagy & Bateman, 2008). Early adversity interacts with pre-existing variations in stress-homeostasis mechanisms, exacerbating interpersonal disruptions (Pratt et al., 2017), underpinned by difficulties in mentalizing, leading to disruptions in social learning (e.g., Fonagy & Luyten, 2009; Nolte et al., 2023) and representations of self and other (Hanegraaf et al., 2021). The mechanisms connecting early life adversity and relational instability are elusive, making it harder to find a path to rehabilitation.

Critical questions persist concerning both typical and disrupted interaction: What computational mechanisms support efficient generalisation from self-to-other and other-to-self? Do processes operate globally or locally based on outcome (e.g. individual vs. joint reward)? Can such formal models explain observations of social learning changes in diagnoses like BPD? Understanding the processes and representations humans use in social exchange has broad implications for theories of development, group cohesion, reputation management, interpersonal synchrony, and the breakdown of social bonds.

Formal models of healthy (non-clinical) exchange posit forms of interaction between self and other representations which can reduce uncertainty during learning (whilst potentially introducing biases). As such, self-insertion accounts demonstrate that integrating self-preferences into initial predictions about others causally increases reaction times and can increase predictive accuracy when predictions are correct (Tarantola et al., 2017; Barnby et al., 2022). Social contagion has been framed as convergence to a common latent state shared by oneself and another, calibrated by self and other uncertainty (Moutoussis et al., 2016; Thomas et al., 2022). By comparison, in mental ill-health, computational models have almost exclusively probed social processes during observational learning without fully integrating self and other into future beliefs. The BPD phenotype has been associated with a potential over-reliance on social versus internal cues (Henco et al., 2020), ‘splitting’ of social latent states that encode beliefs about others (Story et al., 2023), negative appraisal of interpersonal experiences with heightened self-blame (Mancinelli et al., 2024), inaccurate inferences about others’ irritability (Hula et al., 2018), and reduced belief adaptation in social learning contexts (Siegel et al., 2020). Associative models have also been adapted to characterize ‘leaky’ self-other reinforcement learning (Ereira et al., 2018), finding that those with BPD overgeneralize (leak updates) about themselves to others (Story et al., 2024). Altogether, there is currently a gap in the direct causal link between insertion, contagion, and learning (in)stability.

Our present work sought to achieve two primary goals. 1. Extend prior computational theories to formalise and test the interrelation between self-insertion and social contagion in learning and choice to probe self-other generalisation, and 2. Test whether previous computational findings of differences in social learning in people with BPD can be explained by disruptions to self-other generalisation. Here, our formal hypotheses concerning self-other generalisation (Barnby et al., 2023) make clear a priori predictions about its relationship with observational learning that can be empirically interrogated. Exploring these factors within models can uncover algorithmic biases that healthy volunteers and people with BPD either do or do not share. We accomplish these goals using a dynamic, sequential economic paradigm called the Intentions Game. The Intentions Game builds upon the well-known Social Value Orientation framework (Murphy & Ackerman, 2011), which captures innate motivational variation in reward allocation to self and other.

We discover that healthy participants employ a mixed process of self-insertion and contagion to predict and align with the beliefs of their partners. In contrast, age, sex, and education, and social deprivation matched individuals with BPD exhibit distinct, disintegrated representations of self and other, despite showing similar average accuracy in their predictions about partners. Our model and data suggest that the previously observed computational characteristics in BPD arise from a failure of information transfer, first from self to other, and then from other to self, an under rather than over generalisation. By integrating separate computational findings, we provide a foundational model and a concise, dynamic paradigm to investigate uncertainty, generalisation, and learning in social interactions.

Results

Healthy participants (CON; n=53) and participants diagnosed with BPD (n=50), matched on age, gender, education, and social deprivation indices (Table 1), were invited to participate in a three-phase social value orientation paradigm—the Intentions Game (Figure 1A)—with virtual partners. In phase 1, participants made forced choices between two options for splitting points with an anonymous partner. In phase 2 participants learned to predict the decisions of a new anonymous partner using the same forced-choice setup, receiving feedback on the accuracy of their successive predictions. Notably, using a novel server architecture (Burgess et al., 2023), partners in phase 2 were configured to be approximately 50% different from the participants in terms of their choices, ensuring that all participants had to learn about their partners. Phase 3 mirrored the first, with participants informed that they were matched with a third anonymous partner, unrelated to those in phases 1 and 2. Detailed descriptions of the task can be found in the methods section and Figure 1. All participants also self-reported their trait paranoia, childhood trauma, trust beliefs, and trait mentalizing (see Methods).

Psychometric and Behavioural Results

Participants with BPD, compared to CON, retrospectively reported significant childhood trauma, epistemic disruptions (including mistrust and credulity), elevated referential and persecutory beliefs, and demonstrated ineffective trait mentalizing (Table 1). The groups did not differ in trait measures of certainty regarding self and others’ mental states, nor in epistemic trust.

We analysed the ‘types’ of choices participants made in each phase (Supplementary Table 1). The interpretation of a participant’s choice depends on both values in a choice. For example, a participant could make prosocial (self=5; other=5) versus individualistic (self=10; other=5) choices, or prosocial (self=10; other=10) versus competitive (self=10; other=5) choices. There were 12 of each pair in phases 1 and 3 (individualistic vs. prosocial; prosocial vs. competitive; individualistic vs. competitive).

In phase 1, both CON and BPD participants made prosocial over competitive choices with similar frequency (CON=9.67[3.62]; BPD=9.60[3.57]; t=-0.11, p=0.91). However, CON participants made significantly fewer prosocial choices when individualistic choices were available (CON=2.87[4.01]; BPD=5.22[4.54]; t=2.75, p=0.007). Both groups favoured individualistic over competitive choices with similar frequency (CON=11.03[1.95]; BPD=10.34[2.63]; t=-1.52, p=0.13). For a reaction time assessment see Supplementary Text 1).

Each group showed good predictive accuracy (CON=77.2%[13.9%]; BPD=72.7%[15.6%]). There was no difference in overall predictive accuracy between BPD and CON (linear estimate=2.44, 95%CI: −0.67, 5.54; t=1.56; p=0.12), nor on a trial-by-trial basis (linear estimate=0.26, 95%CI: −0.06, 0.59; z=1.61, p=0.11). All participants showed an effect of time on accuracy, such that participants became more accurate in predicting their partner over the course of phase 2 (linear estimate=0.013, 95%CI: 0.008, 0.017; z=6.01; p<0.001). Server matching between participant and partner in phase 2 was successful, with participants being approximately 50% different to their partners with respect to the choices each would have made on each trial in phase 2 (mean similarity=0.49, SD=0.12).

In phase 3, both CON and BPD participants continued to make equally frequent prosocial versus competitive choices (CON=9.15[3.91]; BPD=9.38[3.31]; t=-0.54, p=0.59); CON participants continued to make significantly less prosocial versus individualistic choices (CON=2.03[3.45]; BPD=3.78 [4.16]; t=2.31, p=0.02). Both groups chose equally frequent individualistic versus competitive choices (CON=10.91[2.40]; BPD=10.18[2.72]; t=-0.49, p=0.62).

Table 1.

Figure 1.

Computational Analysis

Over all three phases, we assumed participants and their partners used a Fehr-Schmidt utility function (Fehr & Schmidt, 1999) to calculate the utility of two options , based on the joint rewards available for both the participant, R_ppt = and their partner, R_par = . The utility of each option was weighted based on absolute-reward gain α (how much participants care about self-earnings, irrespective of the other) and relative-reward β along a prosocial-competitive axis (how much participants care about equality of outcomes); β < 0 is prosocial, whereas β > 0 is competitive.

We then constructed four models to explain how participants used their own preferences ( = {, }) and uncertainty over these preferences ( = {, }) to predict and learn about the preferences of their partner (θ_par; Figure 1B; see methods). Model M1 (Figure 1C) suggests that participants initially use their own preferences as a prior belief about their partner (self-insertion), which is gradually diminished during the learning process in phase 2. M1 also posits that, following learning, the inferred beliefs about a partner will influence participants’ own preferences, making them more similar to their partner’s preferences following observation (social contagion). According to this model, participants shift towards their partner based on their uncertainty about self and others (Figure 1E): greater uncertainty over self-preferences and increased precision in representing the other cause stronger social contagion effects.

Model M4 (Figure 1D), on the other hand, suggests that participants do not engage in these generalization processes: predictions about others are not grounded in the self, and observing others does not alter self-preferences. Models M2 and M3 allow for either self-insertion or social contagion to occur independently. Consistent with prior research, we also constructed a model that assumes the same insertion and contagion processes as M1, but along a single prosocial-competitive axis (‘Beta model’; Barnby et al., 2022). The ‘Beta model’ is equivalent to M1 in its causal architecture (both self-insertion and social contagion are hypothesized to occur) but differs in its utility function: participants might only consider a single dimension of relative reward allocation, which is typically emphasized in previous studies (e.g., Hula et al., 2018).

All computational models were fitted and compared using a Hierarchical Bayesian Inference (HBI) algorithm which allows hierarchical parameter estimation while assuming random effects for group and individual model responsibility (Piray et al., 2019; see Methods for more information). We report individual and group-level model responsibility, in addition to exceedance probabilities between-groups to assess model dominance.

Table 2.

Model Comparison – BPD Participants Hold Disintegrated Self-Other Beliefs

We found that CON participants were best fit at the group level by M1 (Frequency = 0.59, Exceedance Probability = 0.98), whereas BPD participants were best fit by M4 (Frequency = 0.54, Exceedance Probability = 0.86; Figure 2A). We first analyse the results of these separate fits. Later, in order to assuage concerns about drawing inferences from different models, we examined the relationships between the relevant parameters when we forced all participants to be fit to each of the models (in a hierarchical manner, separated by group). In sum, our model comparison is supported by convergence in parameter values when comparisons are meaningful (see Supplementary Materials). We refer to both types of analysis below.

Generative Accuracy and Recovery

We simulated data for each participant using their individual parameters from the winning model within each group and refitted our models using this simulated data. Model comparison yielded very similar results (Figure 3A): CON synthetic participants best fit at the group level by M1 (Frequency = 0.58, Exceedance Probability = 0.98) and BPD synthetic participants best fit by M4 (Frequency = 0.57, Exceedance Probability = 0.85). The simulated data closely matched the actions of participants across all three phases (median accuracy = 0.8, SD = 0.12). In phase 2, the model-predicted total correct scores were not significantly different from observed scores (Figure 3E). Both model responsibility and common parameters within each dominant model were significantly associated (model confusion p = 0.46–0.97, p < 0.001; parameter recovery p = 0.70–0.94, p < 0.001; Figure 3C). , preferences in phase 1 were negatively correlated with prosocial versus competitive choices (r=-0.77, p<0.001) and individualistic versus competitive choices (r=-0.59, p<0.001); was positively correlated with individualistic versus competitive choices (r=0.53, p<0.001) and negatively correlated with prosocial versus individualistic choices (r=-0.69, p<0.001). Given the very good to excellent performance of the models, we analysed individual parameters and simulations between groups.

Figure 2.

Phase 1 – BPD Participants Are More Certain About Themselves

We first examined self-representations of participants in phase 1. CON participants (under model M1) and BPD participants (under M4) were equally prosocial (CON mean[] = −7.50; BPD mean[] = −6.59; Δμ[] = 0.92, 95%HDI: −1.24, 3.12) – both groups valued equal allocation of reward between themselves and their partners. BPD participants had lower preferences for earning higher absolute rewards (CON mean[]=18.41; BPD mean[] = 10.57; Δμ[] = −7.83, 95%HDI: −11.06, −4.75). BPD participants were also more certain about both self-preferences for absolute and relative reward (Δμ[] = −0.89, 95%HDI: −1.01, −0.75; Δμ[] = −0.32, 95%HDI: −0.60, −0.04) versus CON participants (Figure 2B).

These differences were replicated when considering parameters between groups when we fit all participants to the same models (M1-M4; see Table S2).

Phase 2 – BPD Participants Use Disintegrated and Neutral Priors

We next assessed how participants generated their prior beliefs about a partner in phase 2. CON participants were best fit by M1 which assumes the same median belief participants use in phase 1 is identical to their median prior belief about their partners. In contrast, BPD participants were best fit by M4 and so generated a new median prior belief about their partners. Assessing by individual models show this was driven by expectations about a partner’s prosocial-competitive preferences (relative reward; see Table S2).

In BPD participants, only new beliefs about the relative reward preferences of partners differed (see Fig 2E) – new median priors were larger than median preferences in phase 1 (mean[] = −0.47; Δμ[ – ] = −6.10, 95%HDI: −7.60, −4.60). BPD priors about their partner’s relative preferences were also centred closely around 0 (Δμ[0 − ] = −0.39, 95%HDI: −0.77, −0.05), suggesting that BPD participants entered into the interaction with very neutral priors about their partner’s preferences for relative reward.

BPD participants were equally flexible around their prior beliefs about a partner’s relative reward preferences (Δμ[] = −1.60, 95%HDI: −3.42, 0.23), and were less flexible around their beliefs about a partner’s absolute reward preferences (Δμ[]=- 4.09, 95%HDI: −5.37, −2.80), versus CON (Figure 2B). Median belief change (from priors to posteriors) in phase 2 was lower in BPD versus CON (Δμ[] = −5.53, 95%HDI: −7.20, −4.00; Δμ[Δ] = −10.02, 95%HDI: −12.81, −7.30). Posterior beliefs about partner were more precise in BPD versus CON (Δμ[] = −0.94, 95%HDI: − 1.50, −0.45; Δμ[] = −0.70, 95%HDI: −1.20, −0.25). This is unsurprising given the disintegrated priors of the BPD group in M4, meaning they need to ‘travel less’ in state space. Even under assumptions of M1-M4 for both groups, BPD versus CON showed smaller posterior standard deviation in phase 2 over after learning (see Table T2). These results converge to suggest those with BPD form rigid posterior beliefs about prosocial-competitiveness.

We checked that these conclusions about self-insertion did not depend on the different models, we found that under M1 and M2 were consistently larger in BPD versus CON. This supports the notion that new central tendencies for BPD participants in phase 2 were required for expectations about a partner’s relative reward (see Fig S10 & Table S2). and parameters under assumptions of M1 and M2 were strongly correlated with median change in belief between phase 1 and 2 under M3 and M4, suggesting convergence in model outcome (Fig S11).

Analysing belief updating on a more granular trial-by-trial basis using M1 for CON and M4 for BPD revealed preference type and between-group differences in belief refinement over the course of phase 2 (Figure 2D). We examined this by analysing the Kullback-Leibler divergence (D_KL) – expected informational surprise – on each trial in Phase 2.

Across both groups and belief types informational surprise reduced over time (linear estimate[D_KL] = −0.007, 95%CI: −0.008, −0.005; t = −7.60, p < 0.001). Beliefs about a partner’s relative reward preferences were updated more than absolute reward preferences (linear estimate= 0.54, 95%CI: 0.47, 0.62; t = 14.00, p < 0.001). These interacted, updating over relative vs. absolute beliefs reduced over the course of phase 2 (linear estimate = −0.013, 95%CI: −0.015, −0.011; t = −10.81, p < 0.001). These findings were supported under M1-M4 only assumptions (see Table T3).

BPD informational surprise is restricted over beliefs about absolute reward versus CON. CON participants remained more flexible than BPD participants along both types of preference (linear estimate [D_KL()] = 0.40, 95%CI: 0.29, 0.51, t = 7.18, p < 0.001; linear estimate [D_KL()] = 0.17, 95%CI: 0.29, 0.51, t=3.06, p=0.002). There was a group by time interaction, such that the difference between groups, and the magnitude of belief updates decreased over time (linear estimate [D_KL()] = −0.009, 95%CI:-0.012,-0.006, t = −5.30, p < 0.001; linear estimate [D_KL()] = −0.004, 95%CI:-0.008,-0.001, t = −2.78, p = 0.005) – CON participants and BPD participants eventually converged to an equivalent updating schedule (Figure 2D).

Assessing this same relationship under M1- and M2-only assumptions reveals a replication of this group effect for absolute reward, but the effect is reversed for relative reward (see Table S3). This accords with the context of each model, where under M1 and M2, BPD participants had larger phase 2 prior flexibility over relative reward (leading to larger initial surprise), which was better accounted for by a new central tendency under M4 during model comparison. When comparing both groups under M1-M4 informational surprise over absolute reward was consistently restricted in BPD (Table S3), suggesting a diminished weight of this preference when forming beliefs about an other.

We explored how beliefs and choices were associated with reaction times, showing that belief updates and reaction times were coupled over the course of phase 2 and related to participant-partner similarity (Figure S9).

Phase 3 – BPD Participants Are Less Influenced by Partners

In the dominant model for the BPD group—M4—participants are not influenced in their phase 3 choices following exposure to their partner in phase 2. To further confirm this we also analysed absolute change in median participant beliefs between phase 1 and 3 under the assumption that M1 and M3 was the dominant model for both groups (that allow for contagion to occur). This analysis aligns with our primary model comparison using M1 for CON and M4 for BPD (Figure 2C). CON participants altered their median beliefs between phase 1 and 3 more than BPD participants (M1: linear estimate = 0.67, 95%CI: 0.16, 1.19; t = 2.57, p = 0.011; M3: linear estimate = 1.75, 95%CI: 0.73, 2.79; t = 3.36, p < 0.001). Relative reward was overall more susceptible to contagion versus absolute reward (M1: linear estimate = 1.40, 95%CI: 0.88, 1.92; t = 5.34, p<0.001; M3: linear estimate = 2.60, 95%CI: 1.57, 3.63; t = 4.98, p < 0.001). There was an interaction between group and belief type under M3 (M3: linear estimate = 2.13, 95%CI: 0.09, 4.18, t = 2.06, p=0.041) but not M1. There was a main effect of belief type on precision under M3 (linear estimate = 0.47, 95%CI: 0.07, 0.87, t = 2.34, p = 0.02) but not M1; relative reward preferences became more precise across the board. Derived model estimates of preference change between phase 1 and 3 strongly correlated between M1 and M3 along both belief types (see Table S2 and Fig S11).

Figure 3.

Exploratory Parameter Associations

We explored whether social contagion may be restricted as a result of childhood trauma, paranoia, and less effective trait mentalizing. We collected psychometric data from participants prior to entering the task and asked participants to attribute explicit intentions to their partner after phase 2. For raw parameter correlations with all psychometric measures see Figure S7. All analyses were corrected for False Discovery Rate (FDR; p[fdr]).

We explored psychometric associations with social contagion under the assumption of M3 for all participants (where everyone is able to be influenced by their partner). We conducted partial correlation analyses to estimate relationships conditional on all other associations and retained all that survived bootstrapping (1000 reps), permutation testing (1000 reps), and subsequent FDR correction. Persecution and CTQ scores were both moderately associated with MZQ scores (RGPTSB r = 0.41, 95%CI: 0.23, 0.60, p=0.004, p[fdr]=0.043; CTQ r = 0.354 95%CI: 0.13, 0.56, p=0.019, p[fdr]=0.02). MZQ scores were in turn moderately and negatively associated with shifts in prosocial-competitive preferences (Δ) between phase 1 and 3 (r = −0.26, 95%CI: −0.46, −0.06, p=0.026, p[fdr]=0.043). CTQ scores were also directly and negatively associated with shifts in individualistic preferences (Δ; r = −0.24, 95%CI: −0.44, − 0.13, p=0.052, p[fdr]=0.065). This provides some preliminary evidence that trauma impacts beliefs about individualism directly, whereas trauma and persecutory beliefs impact beliefs about prosociality through impaired trait mentalising (Figure 4A). Social contagion under M3 was highly correlated with contagion under M1 (Fig S11).

We also tested parameter influences on explicit intentional attributions in Phase 2. Attributions included the degree to which they believed their partner was motived by harmful intent (HI) and self-interest (SI). According with prior work (Barnby et al., 2022), greater participant-partner disparity at the start of phase 2 was distinctly associated with HI and SI (Figure 4B), although associations did not survive FDR correction. Greater disparity of absolute preferences before learning was associated with reduced attributions of SI (ρ[| − |] = −0.23, p=0.02, p[fdr]=0.08), and greater disparity of relative preferences before learning exaggerated attributions of HI (ρ[| − |] = 0.21, p=0.04, p[fdr]=0.08). This is likely due to partners being significantly less individualistic and prosocial on average compared to participants (΄μ[α] = −5.50, 95%HDI: −7.60, −3.60; Δμ[β] = 12, 95%HDI: 9.70, 14.00); partners are correctly recognised as less selfish and more competitive.

Greater prior uncertainty (before interaction) over a partner’s relative preferences was associated with increased HI (ρ[] = 0.25, p=0.01, p[fdr]=0.04) but not SI, according with prior work (Barnby et al., 2022). There was no uncorrected association between prior uncertainty over absolute preferences with either attribution. This suggests that expectations of greater difference, irrespective of one’s true difference between self-other, may exaggerate beliefs about the intentional harm of others.

Figure 4.

Discussion

We built and tested a theory of interpersonal generalisation in a population of matched participants with (BPD) and without (CON) a diagnosis of borderline personality disorder using the Intentions Game, a three-phase social value orientation task. Both groups demonstrated equivalent behavioural accuracy but employed different strategies. CON participants used a process of self-other generalization to predict and align with their partners, while BPD participants maintained distinct representations of self and other, particularly over joint reward outcomes. As a whole, all participants were more sensitive to updates about joint versus absolute outcomes, with BPD participants particularly concerned with how outcomes relatively effected self and other. Our exploratory findings also indicate that retrospectively reported childhood trauma and persecutory beliefs were linked to reduced trait mentalising, which was subsequently associated with diminished self-change. Collectively, our results integrate prior findings in BPD and provide a formal account of social information generalisation in humans, alongside a concise social paradigm to test these processes.

The data replicate models of social generalisation that have focused on individual processes of self-insertion and contagion, extending these theories by demonstrating both processes in conjunction. Models of self-insertion directly map participant preferences onto prior beliefs about others, which has been used to explain increased reaction times in observational learning of others’ snack food preferences (Tarantola et al., 2017), as well as improved predictive accuracy when matched with individuals of similar social values (Barnby et al., 2022). Both findings are replicated in this study. Although we did not explicitly model reaction times, we observed an interaction between reaction time reductions over time and interpersonal similarity at baseline. In tandem, computational models of social contagion have focused on intertemporal discounting (Moutoussis et al., 2016) – with behavioural studies also focusing on effort-based reward (Devaine & Daunizeu, 2017) and moral preferences (Yu et al., 2021) – and explain shifts in self-preferences as a function of uncertainty regarding self and others. In both the dominant (M1) and sub-dominant (M3) models that best explained data in healthy participants, shifts in self-beliefs were also influenced by representational uncertainty of self and other: greater self-uncertainty and reduced other uncertainty led to larger shifts in social preferences.

The data also align with prior research on social impression formation, which suggests that humans form rapid evaluations of others that are refined over time (Bone et al., 2021; Moutoussis et al., 2023). This initial ‘heating’ and subsequent ‘cooling’ of beliefs corresponds to the computational complexity employed: model-based strategies are typically used early in interactions, transitioning to simpler, model-free computations once a partner’s behaviour becomes predictable (Gęsiarz & Crockett, 2015; Guennouni & Speekenbrink, 2022). Our findings support this framework, demonstrating initial variability early in interactions followed by steady updating.

Disruptions in self-to-other generalization provide an explanation for previous computational findings related to task-based mentalizing in BPD. Studies tracking observational mentalizing reveal that individuals with BPD, compared to those without, place greater emphasis on social over internal reward cues when learning (Henco et al., 2020; Fineberg et al., 2018). Those with BPD have been shown to exhibit reduced belief adaptation (Siegel et al., 2020) along with ‘splitting’ of latent social representations (Story et al., 2024a). BPD is also shown to be associated with overgeneralisation in self-to-other belief updates about individual outcomes when using a one-sided reward structure (where participant responses had no bearing on outcomes for the partner; Story et al., 2024b). Our analyses show that those with BPD are equal to controls in their generalisation of absolute reward (outcomes that only affect one player) but disintegrate beliefs about relative reward (outcomes that affect both players) through adoption of a new, neutral belief. We interpret this together in two ways: 1. There is a strong concern about social relativity when those with BPD form beliefs about others, 2. The absence of self-insertion when predicting relative outcomes may predispose to brittle or ‘split’ beliefs. In other words, those with BPD assume ambiguity about the social relativity preferences of another (i.e. how prosocial or punitive) and are quicker to settle on an explanation to resolve this. Although self-insertion may be counter-intuitive to rational belief formation, it has important implications for sustaining adaptive, trusting social bonds via information moderation.

Those with a diagnosis of BPD also show reduced permeability in other-to-self generalising. While prior research has predominantly focused on how those with BPD use information to form impressions, it has not typically been examined whether these impressions affect the self. In interactive trust paradigms, neural responses to monetary offers from others to the self were substantially blunted in individuals with BPD compared to those without (King-Casas et al., 2008). Similarly, in non-social reward tasks, those with BPD show reduced neural feedback-related negativity amplitudes, which obstructs feedback-related self-change (Stewart et al., 2019; Vega et al., 2013). Our results suggest a mechanistic basis for social contagion, indicating that self-rigidity prevents observed social behaviours from generalizing to the self, potentially exacerbated by childhood trauma, paranoia, and impaired mentalizing capabilities. Resistance to social influence may serve as a protective response but can also contribute to the pervasive loneliness experienced by individuals with BPD, even in the absence of social isolation (Liebke et al., 2017).

Notably, despite differing strategies, those with BPD achieved similar accuracy to CON participant. While all participants were more concerned with relative vs. absolute reward, those with BPD changed their strategy contingent on this focus. Practically this difference in BPD is captured either through disintegrated priors with a new median (M4) or very noisy, but integrated priors over partners (M1) if we assume M1 can account for the full population. In either case, the algorithm underlying the computational goal for BPD participants is far higher in entropy and emphasises a less stable or reliable process of inference. It is important to assess this mechanism alongside momentary assessments of mood to understand whether more entropic learning processes contribute to distressing mood fluctuation.

Clinical implications of our work underscore the importance of consistency and stability in clinical support for individuals with a diagnosis of BPD. Encouragingly, we found that those with BPD were not entirely impermeable to observed behaviour, suggesting that consistent external models of trust could be internalized over time. Restoring a stable sense of self through social learning and effective mentalizing (Nolte et al., 2023), along with a consistent focus on differentiating self from other (de Meulemeester et al., 2021), are central to mentalization-based therapies (Bateman & Fonagy, 2010; Smits et al., 2024) and other evidence-based treatments for BPD. We hope that our paradigm and model can offer insights into the effectiveness of these and other therapies in driving mechanistic psychological change. A key task for future work will be to assess whether generalisation principles may be restored in within-individuals with a diagnosis of BPD following intervention.

More broadly, our model bridges formal theories of associative learning and social cognition. Reinforcement learning approaches have effectively organized theories around uncertainty navigation in non-social contexts (Piray et al., 2021; Zika, 2023). However, humans do not function in isolation. Bayesian models of internal and external social beliefs are better suited to capture the dynamic nature of time, context, and uncertainty during interactions (FeldmanHall & Nassar, 2021; Velez & Gweon, 2021), where joint reward rather than individual reward may be particularly salient (Barnby et al., 2023). Our paradigm is concise, visually engaging, includes straightforward rules and instructions, and allows for tight experimental control over partner similarity. Our model and paradigm effectively capture core social psychological principles grounded in general computational approaches to learning and uncertainty, elucidating key aspects of human social interaction and exchange.

We note some limitations to our study. Primarily, we focused on the ability of individuals to integrate their self-concept into beliefs about others. It is also possible that humans possess strong, salient representations of others (or groups of others) that serve as dominant templates for learning. This may be particularly relevant for individuals with BPD, who will often have interpersonal experiences of abuse, neglect, or other forms of distress. The use of a salient, negative other-prior as a basis for learning was not measured in this study, but it may explain the ambivalent prior observed in phase 2, where a mixture of self and notional other influences belief formation, leading to rigid belief updating. Individuals with BPD may integrate priors from different sources as a mixture. We can simulate this by modelling a causal framework that incorporates priors based on both self and a strong memory impression of a notional other (Figure S3). However, a strength of our data is that we observed impression formation independent of valence—impressions were formed regardless of whether a partner was more or less prosocial or selfish than the participant (Figure S4). This supports our hypothesis that a vulnerable self-model and lack of self-insertion contribute to the formation of overly precise beliefs during learning as a means of rapidly reducing uncertainty. Even if a mixture model better explains the ambivalent prior in phase 2, it would still support a general hypothesis about the fractured concept of self and other in BPD.

Another strength of our work is demonstrating processes of self-insertion and contagion under minimal interaction conditions: simple observation alone was sufficient to elicit both processes. However, this is also a limitation. While we predict that these processes will apply in more naturalistic settings, this has yet to be tested, and it remains unclear whether these effects will persist in richer conditions, particularly when higher affective arousal and challenges to mentalising are present. Lastly, the action space and parameters governing choice in our study were quite simple—two actions influenced by two parameters. This was a deliberate computational choice to avoid overly complex action spaces that may be difficult to fit to real human data, and which might fail to capture how these mechanisms operate in the context of increasing action and model complexity. As a whole, our findings open new possibilities for testing how social uncertainty across the lifespan (e.g. in adolescence; Sebastian et al., 2008), and in the context of ill-health, may explain the formation and maintenance of healthy social bonds as well as their disruption.

Finally, a limitation may be that behaviour in tasks based on economic preferences may not have clinical validity. This issue is central to the field of computational psychiatry, much of which is based on generalising from tasks like that within this paper and discussing correlations with psychometric measures. Extrapolating economic tasks into the real world has been the topic of discussion for the many reviews on computational psychiatry (e.g. Montague et al., 2012; Hitchcock et al., 2022; Huys et al., 2016). We note a strength of this work is the use of model comparison to understand causal algorithmic differences between those with BPD and matched healthy controls. Nevertheless, we wish to further pursue how latent characteristics captured in our models may directly relate to real-world affective change.

Materials and Methods

Participants

We used a case-control, between-subjects design with 103 participants: a control group from the general population (N = 53) and a clinical group diagnosed with BPD (N = 50). Both groups were recruited for a larger study investigating social exchanges in BPD and Anti-Social Personality Disorder (approved by the Research Ethics Committee for Wales, 12/WA/0283). The control and clinical groups were matched on age, sex, years in education, and the English Indices of Deprivation based on the 2019 census (IoD 2019; Ministry of Housing, Communities & Local Government, 2019). Participants received £70 compensation for completing questionnaires and online tasks which included the Intentions Game. They also received a performance bonus if they were entered into the lottery for surpassing 1000 points over the course of the game.

Participants for the control group were recruited through an advertisement on the Call For Participants website (https://www.callforparticipants.com), local community services and adult schools. Inclusion criteria required control participants to have no pre-existing or current diagnoses of mental health disorders, neurological disorders, or traumatic brain injuries. Additionally, control participants must not have been currently in therapy or taking medication for any psychiatric disorders.

The majority of BPD participants were recruited through referrals by psychiatrists, psychotherapists, and trainee clinical psychologists within personality disorder services across 9 NHS Foundation Trusts in the London, and 3 NHS Foundation Trusts across England (Devon, Merseyside, Cambridgeshire). Four BPD participants were also recruited by self-referral through the UCLH website, where the study was advertised. To be included in the study, all participants needed to have, or meet criteria for, a primary diagnosis of BPD (or emotionally-unstable personality disorder or complex emotional needs) based on a professional clinical assessment conducted by the referring NHS trust (for self-referrals, the presence of a recent diagnosis was ascertained through thorough discussion with the participant, whereby two of the four also provided clinical notes). The patient participants also had to be under the care of the referring trust or have a general practitioner whose details they were willing to provide. Individuals with psychotic or mood disorders, recent acute psychotic episodes, severe learning disability, or current or past neurological disorders were not eligible for participation and were therefore not referred by the clinical trusts.

Psychometric Measures

Green et al. Paranoid Thought Scale (GPTS)

The GPTS assesses paranoid thoughts, including ideas of social reference (scale A) and persecution (scale B), in both general and clinical populations (Green et al., 2008). Each item is scored from 0 (not at all) to 5 (totally) concerning endorsement of each item. We retained items from the GPTS that were consistent with the revised version outlined in Freeman et al., 2021 (Revised GPTS; R-GPTS). The R-GPTS has demonstrated excellent psychometric properties (Freeman et al., 2021), making it a reliable and valid tool for assessing trait paranoid thoughts in non-clinical and clinical populations.

Childhood Trauma Questionnaire (CTQ)

The Childhood Trauma Questionnaire is used to screen for maltreatment history (Bernstein et al., 2003). Each item is scored from 1 (never true) to 5 (very often true). The CTQ has showed good internal consistency reliability across the five scales (Sacchi et al., 2018) and good construct validity based on significant associations with stress responsivity (McMahon et al., 2022), and dissociation (Nobakht et al., 2021).

Certainty About Mental States Questionnaire (CAMSQ)

The CAMSQ assesses one’s certainty in classifying the mental states of oneself and others at an abstract level (Müller et al., 2023), e.g. ‘I know what other people think of me’ and ‘I know my feelings’. Each subscale is scored from 1 (never) to 7 (always). In US and German samples, the CAMSQ showed high internal consistency for Self-Certainty (ω = .90/.88) and Other-Certainty (ω = .91/.89) subscales, and high two-week test-retest reliability for Self-Certainty (r = .85), Other-Certainty (r = .78), and Other-Self-Discrepancy (r = .82) scores (Müller et al., 2023).

Mentalisation Questionnaire (MZQ)

The MZQ is a 15-item questionnaire assessing an individual’s trait mentalizing, i.e., one’s ability to understand and interpret their own and others’ mental states (Hausberg et al., 2012). The MZQ demonstrated good internal consistency (α = .81) and test-retest reliability (r = .76), and was sensitive to change over a 6-month follow-up period and showed good criterion-related validity, distinguishing individuals with BPD from those without BPD (Hausberg et al., 2012). A higher score reflects worse trait mentalizing.

Epistemic Trust, Mistrust and Credulity Questionnaire

The ETMCQ is a 15-item measure calibrated to assess trust (e.g. ‘I usually ask people for advice when I have a personal problem), mistrust (e.g. ‘I’d prefer to find things out for myself on the internet rather than asking people for information), and credulity (e.g. ‘I am often considered naïve because I believe almost anything that people tell me’; Campbell et al., 2021). Each item is scored from 1(Strongly Disagree) to 7(Strongly Agree).

Paradigm, procedure and server architecture

The Intentions Game is a repeated social-value orientation paradigm with three phases.

In Phase 1 of the Intentions Game, participants take on the role of the decider with an anonymous partner over 36 trials. In each trial, participants choose between two options to distribute points between themselves and their partners. Participants make 12 choices each between prosocial and competitive (e.g. Option 1=[10,10], Option 2 = [10,5]) individualistic and competitive (e.g. Option 1=[10,5], Option 2=[8,1]), and prosocial and individualistic options (e.g. Option 1=[5,5], Option 2=[10,5]). Phase 1 choices allowed experimenters to classify participants’ social preferences as prosocial (preferring equal outcomes), individualistic (maximising own payoff), or competitive (maximising relative payoff difference at the cost of lower self-gain).

We included a task environment that balanced each type of choice pair (see Supplementary Table 1).

In phase 2 of the game, participants were matched with a new anonymous partner and played the role of the recipient over 54 trials. In this phase, the participants predicted which of the two options their partner would choose on each trial. Trial numerical values for self and other were identical to Phase 1. Partners’ decisions were determined via a dynamic algorithm (Burgess et al., 2023) to ensure partners were approximately ~50% different from the participants’ based on participants’ choices in phase 1. To surmise this architecture, we implemented a version of the client-server paradigm hosted on an Amazon Web Service (AWS) LightSail server, where the webbased behavioural task (implemented with JavaScript in Gorilla.sc) acted as the client and exchanged information with a remote AWS server. The server received all anonymised behavioural data following phase 1. The Application Programming Interface (API) to interact with the server used a customizable R script (v4.3) to process the received data from the participant, and additional R scripts were used to process and generate output for the participant. A function within the backend scripts first used Bayesian inference to approximate a participant’s parameters for phase 1. It then simulated what choices the participant would have made in phase 2 had the participant been in the role of the partner. The algorithm then sought to find parameters that would be at least 50% dissimilar from participant parameters with respect to the generated choices of those parameters. This allowed the task behaviour of phase 2 to be dynamically updated in response to participant choices in phase 1. This facilitated tight control over the state of the task and enabled advanced computations to be performed on participant data beyond the capabilities of a web browser.

Participants were incentivised in phase 2 to predict accurately, as accurate predictions would contribute to their total point scores (total correct answers were multiplied by 10 and added to their points) and determined their entry into the lottery to win an extra £20 Amazon voucher. After participants had made their predictions, they were given feedback informed on whether their predictions were accurate.

At the end of phase 2, participants were asked to rate (1) the extent to which they thought their partner was driven by the desire to earn points in this task overall (self-interest) and (2) the extent to which they thought their partner was driven by the desire to reduce the participant’s points in this task overall (attribution of harmful intent). The answers were presented using two separate sliders from 0 to 100; the sliders were initialised to be invisible until the participants made the first click.

Phase 3 was identical to phase 1 except that participants were matched with a new anonymous partner. Participants would take on the decider role similar to phase 1 which allowed experimenters to estimate whether the observation of their partner in phase 2 had an influence on participants in phase 3.

Behavioural Analysis

All analysis was conducted in R (v. 4.3.3) on a macbook pro (M2 Max; OS=Ventura13.5). All individual numeric values extraneous of statistical tests are reported with their mean and standard deviation (mean=KCWM8V2, SD=YY). All statistical tests where dependent variables mapped one value to one participant (e.g. trait psychometric scores) were conducted as linear models, with the regression coefficient, 95% confidence interval (95%CI), t-value and p-value reported like so (linear estimate=KCWM8V2, 95%CI:AA,BB; t=CC, p=DD). When dependent variables mapped multiple values to each participant (e.g. trial-by-trial accuracy or reaction time) random-effects linear modelling was used. All correlations used Pearson estimates (r) unless distributions were non-normal, in which case Spearman-ranked correlations (r) were performed.

Model space and Computational Analysis

We apply four computational hypotheses (M1-M4) which could explain the data collected from the Intentions Game (Figure 1), centred around formal principles of self-insertion and social contagion. Self-insertion states that a self inserts their own preferences into their beliefs about others (Anderson & Chen, 2002; Kreuger & Clement, 1994); Social Contagion states that a self’s preferences will change when exposed to the preferences of an other (Frith & Frith, 2012). In each case, cognitive representations of self and other are allowed to intermingle to form a new hybrid of the two for the purposes of computational efficiency and/or social bonding.

We note some important assumptions in our notation going forward. In dyadic social interaction, both parties are trying to estimate and predict the true state (θ) of the self (θ_S) and the other (θ_O). However, this estimation is inherently imperfect. Theories of social inference need to consider three sources of noisy estimation of this quantity: the self’s (s) metacognitive model of their own state, , their partner’s (O) state, , and finally the experimenter’s approximation of both quantities, , (Barnby et al., 2024). In this work we consider the experimenter’s approximation of the self’s state (phase1), the self’s approximation of their other (phase 2), and how exposure to a partner may influence (phase 3). We term the self the participant (ppt) and the other the partner (par) and assume θ_ppt = in phase 1, θ_par = in phase 2, and are the shifted participant preferences following exposure to the partner.

All models assumed a constricted Fehr-Schmidt utility function was used by participants and partners to calculate the utility of two options in each trial within the task.

In phase 1, participants made binary choices c^{t, t} = {1… T} about whether option 1 or option 2 should be chosen given the returns for each option pair, R^t = {R^t;1; R^t;2} = .

Here, α_ppt describes the weight a participant places on their own payoff (in one reduced model we set α_ppt = 1), and β_ppt, the weight a participant places on their payoff relative to the payoff of their partner. Large positive or negative values of β_ppt indicate respectively that participants like or dislike earning more than their partner. We can therefore describe these terms α and β as reflecting preferences for absolute and relative payoffs, respectively. For efficiency we discretised states of α_ppt from 030 (increments of 0.125) and β_ppt from −30 to 30 (increments of 0.25).

Over this state space we can construct a belief that participants are estimated to hold which generate their choices, C. Herein, we refer to this belief as θ_ppt, where θ_ppt is a matrix over a fixed grid of α_ppt and β_ppt values. In the models, θ_ppt is drawn from a normal distribution made from a central tendency, , and a standard deviation, . The standard deviation around the central tendency allows for stochastic choice behaviour consistent with random utility models (Block, 1974; McFadden, 1974). We invert the model to estimate θ_ppt based on a participant’s choices given their likelihood of choosing c^t = 1 :

When is larger, a participant’s choices in Phase 1 are estimated to be less deterministic and more stochastic – i.e. they are less sure about their preferences along each dimension. This consideration will become important for choices made in phase 3.

In phase 2, over 54 trials, we then model the participants binary predictions , t = {1… T} about whether option 1 or 2 would be chosen by their partner given the returns R^t = {R^t;1; R^t;2} = for each pair of options. They then were given feedback about the partner’s true decision which we note as d^f. We assumed the participant predict the partner in the same way they would themselves, ranging along two dimensions, α_par and β_par which was needed to be inferred through observation, using a likelihood for d^f of LL = log [p(d^t = 1|α_par, β_par, R^t)] using the same formula as phase 1. We note the belief about α_par and β_par together as θ_par, represented as a matrix over a fixed grid of α_par and β_par values.

The partner decisions, D^t = {d¹, d² …, d^T} are then used to update the participants beliefs about the partner, written as p(θ_par|D^f), starting with prior p(θ_par|D⁰). Both M1 and M2 assume participants use their own central tendency, , as a starting point for their prior beliefs about their partner as theoretically outlined as a self-insertion bias (Barnby et al., 2024) which draws from past computational work (Barnby et al., 2022; Tarantola et al., 2017). We also assumed participants used a new standard deviation which allowed for participants to believe their partner may be different from them (belief flexibility). Therefore we have:

In models M3 and M4, we assume participant’s may instead use a new central tendency (rather than their own) as prior beliefs over their partner. This are free parameters to be approximated, , .

In all cases, we assume participants update their beliefs about their partner’s social preferences given their partner’s decisions D along trials 1–54 according to Bayes rule:

We can then marginalise over to calculate the belief participants had over their participant’s social value preferences.

We assume that participants predict the partner’s decision in the next trial by calculating the probability determined by the utility differences ΔU_{α, β}(R^t+1) as in phase 1, summed over the joint distribution of partner parameters, :

And then performed probability matching, so that:

In the third phase participants are once again asked to make choices for themselves and a new anonymous partner over 36 trials with an assumed identical utility function as in phase 1. In model M1 and M3 we assume participants use a combination of their own preferences and the posterior beliefs about their partner to form a new distribution to select between the two options available on each trial. This draws from the same formulation used previously (Moutoussis et al. 2016). In essence, we state that participants know their true preferences in phase 1 but are unsure about them. The inferred partner beliefs provides information to the participant about some common preference distribution both share, which in turn informs the participant’s own choices , t = {1… T} in the form of an adjusted belief along each dimension for phase 3, and (eq. 7), using a log likelihood of LL = log[p( = 1|, , R^t)]. We refer to and together as for convenience, where is a matrix over a grid of fixed values of and . To note: models M2 and M4 do not assume participants undergo this change, and instead use their original phase 1 beliefs to make choices LL = log[p( = 1|α_ppt, β_ppt, R^t)].

Where and are the standard deviation and central tendency of the final posterior inference about the partner, .

All computational models were fitted using a Hierarchical Bayesian Inference (HBI) algorithm which allows hierarchical parameter estimation while assuming random effects for group and individual model responsibility (Piray et al., 2019). During fitting we added a small noise floor to distributions (2.22e⁻¹⁶) before normalisation for numerical stability. Parameters were estimated using the HBI in untransformed space drawing from broad priors (μ_M=0, σ²M = 6.5; where M={M1, M2, M3, M4}). This process was run independently for each group. Parameters were transformed into model-relevant space for analysis. All models and hierarchical fitting were implemented in Matlab (Version R2022B). All other analyses were conducted in R (version 4.3.3; arm64 build) running on Mac OS (Ventura 13.0). We extracted individual and group level responsibility, as well as the protected exceedance probability to assess model dominance per group.

To conduct model recovery we simulated synthetic participants (CON=53; BPD=50) using their fitted parameters from the dominant model of the group (CON=M1; BPD=M4). We then performed model fitting with an identical procedure to the real behavioural data. We tested associations between model responsibility and individual parameters for the real and recovered models, as well as the association between choices and predictions made by the model from simulation and the choices and predictions made by participants in each trial.

Differences between groups for individual-level parameters were estimated using hierarchical Bayesian t-tests (Bååth, 2014) and hierarchical general linear models in rStanArm. Differences in mean between groups (Δμ) are additionally reported with their corresponding posterior 95% High Density Interval (95%HDI). Belief updates were calculated as the Kullback-Leibler Divergence between probabilities (P) from trial t-1 to t, marginalised along all possible states, S={s¹, s², … , sⁿ}: D_KL(P^f||P^t-1) = .

Open data and code:

https://github.com/josephmbarnby/SocialTransfer_Barnby_etal_2024

Acknowledgements

We would like to greatly thank all participants who took part in the research.

Additional information

CRediT

JMB: Conceptualisation, Data Curation, Investigation, Formal Analysis, Methodology, Project Administration, Software, Supervision, Visualisation, Writing – Original Draft, Writing – Review and Editing. JN: Investigation, Methodology, Writing – Original Draft, Writing – Review and Editing. JG: Conceptualisation, Investigation, Project Administration, Resources, Writing – Review and Editing. MW: Project Administration. HB: Software, Writing – Review and Editing. LR: Resources, Writing – Review and Editing. GC: Validation, Writing – Review and Editing. JK: Supervision, Writing – Review and Editing. PRM: Resources, Writing – Review and Editing. PD: Conceptualisation, Formal Analysis, Writing – Review and Editing. TN: Conceptualisation, Project Administration, Resources, Supervision, Writing – Review and Editing. PF: Conceptualisation, Resources, Supervision, Writing – Review and Editing.

Funding

JMB is supported by a Wellcome Trust award (228268/Z/23/Z) and as a scholar within the FENS-Kavli Network of Excellence. Funding for PD was from the Max Planck Society and the Humboldt Foundation. PD is a member of the Machine Learning Cluster of Excellence, EXC number 2064/1 – Project number 39072764 and of the Else Kroner Medical Scientist College “ClinbrAIn: Artificial Intelligence for Clinical Brain Research”.

Supplementary Materials

Supplementary Figure 1.

Supplementary Figure 2.

Supplementary Figure 3.

Supplementary Figure 4.

Supplementary Figure 5.

Supplementary Figure 6.

Supplementary Figure 7.

Supplementary Figure 8.

Supplementary Figure 9.

Supplementary Figure 10.

Supplementary Figure 11.

Supplementary Table 1.

Supplementary Table 2.

Table T3

Supplementary Text 1. Reaction times in the Intentions Game

Phase 1

Examining reaction times (in milliseconds; ms) in phase 1 by choice type revealed that, compared to competitive choices, individualistic choices were made faster (linear estimate = −880.60, 95%CI: −1385.42, −376.2; t = −3.42, p < 0.001), and prosocial choices were made fastest (linear estimate = −1171.1, 95%CI: −1701.97, − 640.71; t = −4.32, p < 0.001) irrespective of the type of choice pair. Prosocial choices were made significantly faster than individualistic choices (linear estimate = −290.70, 95%CI: −548.50, −32.91; t = −2.21, p = 0.027).

Phase 2

All participants were slower at the start of phase 2 and sped up over time (linear estimate = −15.03, 95%CI: −21.06, −8.99; t = −4.88, p < 0.001). Baseline participant-partner similarity did not have an overall effect on reaction time but did interact with trial – as participant-partner similarity increased, reaction times early in phase 2 were significantly slower and this effect attenuated over time (linear estimate = −0.53, 95%CI: −0.75, −0.32; t = −4.91, p < 0.001; see Figure S9). Reaction time did not vary between groups: both BPD and CON participants displayed the same effect.

Reaction times and belief updates in phase 2 were significantly coupled, such that larger shifts in posterior beliefs along both axes were associated with larger reaction times (linear estimate [D_DL()] = 0.044, 95%CI: 0.027, 0.06, t = 5.01, p < 0.001; linear estimate [D_KL()] = 0.021, 95%CI: 0.005, 0.039, t = 2.49, p = 0.012).

Phase 3

Reaction times in phase 3 revealed that compared to competitive choices, individualistic choices were made faster (linear estimate = −528.50, 95%CI: −943.60, − 114.6; t=-2.50, p = 0.012), and prosocial choices were made fastest (linear estimate = −693.5, 95%CI: −1137.65, −250.39; t=-3.07, p = 0.002). Prosocial choices were no longer executed significantly faster than individualistic choices. All participants made faster choices in phase 3 compared to phase 1 (linear estimate = −242.02, 95% CI: − 332.64, −151.41; t=-5.24, p = 0.001).