## Introduction

Prosocial behaviour requires people to balance their own interests against others’ welfare. Faced with such conflicts, people sometimes altruistically sacrifice self-interest to help others1,2,3,4,5, but debates about why and how have preoccupied philosophers, economists and psychologists for centuries6,7. Recent work has tried to explain altruistic choices using dual-process models, which assume these choices result from competing dispositional preferences that evolve over time8,9. This suggests that one of the keys to enhancing prosociality may lie in understanding whether prosocial dispositions derive from intuition (which arises rapidly and automatically) or controlled reflection (which emerges slowly and only under optimal processing conditions). Resolving this debate would identify fundamental psychological processes that sustain social life, as well as practical approaches to increase prosocial behaviour.

Unfortunately, work on this question has led to conflicting results and conclusions. Using response times as a proxy for automaticity and control has suggested both that prosociality may be rapid and intuitive8,9,10 and that it requires lengthy deliberation11,12,13,14. Although recent work has called into question inferences drawn from deliberation times15,16,17, stronger causal manipulations that attempt to interfere with controlled processing using time pressure or instructions to respond intuitively have also led to conflicting conclusions, with people sometimes becoming more selfish18,19 and sometimes becoming more generous8,9,20,21,22. More recently, some researchers have proposed that some individuals have intuitively generous dispositions, while others are more intuitively selfish15,21,23. Yet other work suggests that changes in choices may not necessarily reflect differences in preferences, but rather differences in choice precision24,25,26. Thus a crucial set of questions remains unanswered despite more than a decade of work: when choosing to act altruistically, does generosity or selfishness come first, and if so, why15,21,22,23,26?

Here, we propose a simple mechanistic alternative to dual-process models: when making choices involving conflict between self and others, decision-makers are not simply driven by the fixed and sequential activation of intuitive and controlled processes. Instead, they use a single process—the serial, prioritised deployment of attention—to actively and strategically gather information about their own and others’ outcomes according to their dispositional social preferences. Such a model is consistent with research showing that selfish individuals attend more to self-relevant information while prosocial individuals attend more to other-relevant information27, but goes a step further in suggesting that time pressure (which may force individuals to make fast rather than fully informed choices) should amplify the strategic deployment of attention towards information prioritised by the individual28,29. For example, a selfish individual with little time to decide should first ascertain a choice’s consequences for herself, and only shift to processing its consequences for others if sufficient time remains. For someone who cares more about others, the order of priorities should be reversed. This strategic deployment of attention could thus lead to changes in choice under time pressure, since research suggests that attended information receives more weight during evaluation30,31,32,33,34,35. While these dynamics might produce patterns that appear on surface to support dual-process models of choice, they would actually stem from this fundamentally different set of mechanisms.

Our model makes three empirical predictions. First, time pressure should result not only in systematic changes in prosociality, but also systematic shifts in attention-allocation towards self- and other-relevant information. Second, these attentional changes should reflect individual differences in how much an individual cares about others’ welfare relative to self-interest. Finally, these attentional shifts, combined with time pressure’s constraints on serial processing, should better account for changes in generosity under time pressure than intuition-driven changes in social preferences.

To test these hypotheses, we experimentally constrained processing using time pressure and measured the influence of this manipulation on participants’ generosity and eye-gaze within a modified dictator game paradigm. We found that time pressure neither consistently increased nor decreased generosity. Rather, supporting our hypotheses, individuals appeared to strategically deploy their attention under time pressure, which in turn predicted changes in generosity. Determining whether changes in gaze were driven by underlying preferences (which might represent a core individual difference present under both time pressure and free response conditions) requires some way to measure those preferences. However, if social preferences drive attention and attention drives the very choices used to infer preferences, this leads to a circularity of inference that makes causal analysis difficult. Thus, to identify underlying preferences independent of attention’s effect on choice, and determine how those preferences might shape eye-gaze, we developed an extension of attentional drift-diffusion models (ADDMs)30,34,35 to simultaneously incorporate and account for real-time eye-movements during choice. As expected, our computational model showed that individuals exhibit stable social preferences that predicted generosity across both conditions. Importantly, we found that the model predicted both early attentional biases and how these biases changed under time pressure. Further confirming our hypotheses, individual differences in attention interacted with time pressure and dispositional social preferences to predict changes in generosity, while potential markers of intuition-driven preferences did not. Finally, forcing individuals to look at others’ outcomes rather than their own increased generosity, but only under time pressure, illustrating both the power and limits of attention’s causal influence on choice. Thus, our model suggests that altruistic choice dynamics result from dynamic attentional selection as opposed to the sequential activation of intuitive and controlled processes8,21.

## Result

### Attentional shifts drive changes in generosity

Having observed that time pressure may alter both the weights assigned to self-interest and other-focused concerns, and the attention paid to them, we sought to determine how such alterations, as well as default social response biases21, influence changes in generosity. We thus conducted stepwise regression on changes in generosity under time pressure (N = 50, see Supplementary Table 4). The most parsimonious model revealed only a significant main effect of average wother (b = −6.077, SE = 2.881, t38 = 2.109, p < 0.05, semi-partial R2 = 0.105), and three-way interaction between early gaze-biases, their change under time pressure, and average wother (b = 33.228, SE = 14.773, t38 = −2.249, p < 0.05, semi-partial R2 = 0.117). We observed no effect of changes in weights or default social biases.

In other words, for people who cared about others’ outcomes (i.e., +1SD in wother), inattention to those outcomes was detrimental to generosity under time pressure: becoming more self-focused in their early gaze tended to reduce generosity under time pressure, given that average early gaze was not already highly self-biased (two-way interaction: b = 0.385, SE = 0.195, t38 = 1.975, p = 0.056; simple effect of change in early gaze-biases at −1 SD early gaze-bias: b = −0.231, SE = 0.128, t38 = −1.802, p = 0.080). When early gaze-biases were already highly self-biased (mean or +1 SD), further biasing of early gaze towards self-outcomes did not change generosity (simple effect at mean: b = −0.056, SE = 0.071, t38 = −0.788, p = 0.436; at +1 SD: b = 0.120, SE = 0.096, t38 = 1.245, p = 0.221). For those who placed little weight on others’ outcomes (i.e., mean or −1 SD in wother), early attention did not matter (simple effects of average and change in early gaze and their two-way interaction, ps > 0.05) Thus, early attentional biases robustly drive changes in generosity under time pressure and provide a parsimonious account of choice dynamics.

### Forced attention biases generosity under time pressure

Our model thus far suggests a causal account wherein attention, driven by social preferences, influences the choices people make under time pressure. However, to directly test attention’s causal influence on altruistic choice, we conducted a second, on-line study where we manipulated participant’s attention to $Self and$Other. In this study, participants (N = 200) completed similar dictator games under high and low time pressure (see “Methods”), using mouse clicks to reveal choice attributes ($Self or$Other). Importantly, on some trials, they could choose which attribute to click on first. On other trials, they were forced to click on either $Self or$Other first. For parallelism with Study 1, we use the term fixation to describe when participants clicked on an attribute. If early attention derives its influence on choice only through its relationship with dispositional social preferences, first-fixations should have little to no effect when they are exogenously controlled. However, if attention has a direct causal influence on choice, then it should influence behaviour even when determined by outside forces.

Replicating Study 1, participants in Study 2 were more likely to choose selfishly if they freely looked first at $Self, specifically under time pressure (interaction: b = 0.648, SE = 0.259, z = 2.504, p = 0.012; simple effect of first-fixation under high time pressure: b = −1.016, SE = 0.209, z = −4.855, p < 0.001; low time pressure: b = −0.368, SE = 0.180, z = −2.048, p = 0.041, Fig. 7a). Moreover, generosity in forced-attention trials (which provides a measure of dispositional social preferences controlling for attention) predicted how selfishly oriented participants’ freely chosen first-fixations were, especially under time pressure (interaction: b = 0.710, SE = 0.258, z = 2.748, p = 0.006; simple effect of generosity under high time pressure: b = −2.636, SE = 0.559, z = −4.718, p < 0.001; low time pressure: b = −1.926, SE = 0.557, z = −3.461, p < 0.001). These findings corroborate results from Study 1 suggesting that dispositional social preferences drive attentional priorities, particularly under time pressure, and that these attentional priorities predict choice. Finally, we confirmed a causal effect of attention on choice independent of social preferences: generosity was strongly influenced by whether participants were forced to fixate on$Self or $Other first, but only under time pressure (interaction: b = 0.664, SE = 0.184, z = 3.601, p < 0.001; simple effect of first-fixation under high time pressure: b = −0.833, SE = 0.144, z = −5.766, p < 0.001; low time pressure: b = −0.169, SE = 0.117, z = −1.444, p = 0.149, Fig. 7b). Thus, even when holding dispositional social preferences constant, directing participants’ attention towards their own or others’ outcomes made them more selfish or more generous, respectively. ## Discussion Do preferences for acting generously evolve over time? Our results suggest they do but point to a markedly different explanatory mechanism than extant dual-process models: the serial, prioritised deployment of attention to preferred information during information-search. Three pieces of evidence support this interpretation. First, we found that individuals differ systematically in the extent to which they focused first on self- or other-relevant information under time pressure. Second, a sophisticated, gaze-informed computational model of choice suggested that underlying social preferences drive these initial attentional biases, particularly under time pressure. Third, these attentional biases causally predicted changes in generosity under time pressure. Our findings help to make sense of the growing body of literature suggesting that time pressure neither consistently increases nor decreases generosity8,19,22, but instead reveals individual differences in social preferences21,23. Moreover, while some of our findings hint at the possibility of fast and slow systems of processing8,13,21,42,43, they point firmly to the importance of attentional priorities in the face of processing constraints. Our results suggest an important insight into human prosociality: individuals tend to prioritise information about self-interest over information about others’ welfare. They demonstrated a tendency to look first at their own outcomes, particularly under time pressure, and the model-estimated influence of this information on choice, even after accounting for attention, was significantly higher. Yet these results appear to contradict the idea that individuals often default to pro-social responses (social heuristic hypothesis)8,15,44. What might reconcile such findings? Two possibilities are immediately apparent. First, much of the research demonstrating intuitive biases uses single-shot games in which participants self-generate monetary splits, whereas our study used repeated presentation of specific, experimenter-determined payouts. Perhaps response-modality, or the repeated exposure to games of this sort9 results in different decision processes. However, in supplementary analyses, we incorporated a series of one-shot games into our measure of prosociality and found that generosity in one-shot and repeated binary choices were strongly correlated, suggesting that they both tap into a common set of processes (see Supplementary Note 5). Instead, we think a second explanation is more likely. Much of the literature demonstrating default pro-social biases has emerged during the study of strategic cooperative behaviour, such as the Ultimatum or Public Goods Game, rather than purely altruistic behaviour8,9,15,17. We suspect that when one’s own outcomes are more clearly predicated on the behaviour or outcomes of others (as in the Ultimatum Game), attention shifts more decisively toward social information, yielding pro-social biases under time pressure. Future work using eye-tracking could test such a hypothesis by comparing the pattern of eye-gaze during Dictator and Ultimatum games. Examining whether people flexibly direct attention towards self-relevant information in a context-sensitive manner may also unveil the mechanism that drives the emergence of attentional biases under time pressure. Based on the relationship between model-identified underlying preferences and changes in attentional bias, we speculate that strategic goal-directed mechanisms are at play; people might be able to look in anticipation toward self-relevant information given salient cues about where it appears. However, it is also possible that components of these early attentional biases are intuitive expressions of social preferences27,45, driven by well-established characteristics of the automatic attention system46,47. Such an interpretation would be consistent with studies showing that previously rewarding stimuli capture attention automatically, regardless of the current goal context48. In our paradigm, the location of self-relevant information was constant throughout. Thus, to the extent that selfish individuals disproportionately value self-outcomes, the screen location signalling this value might come to draw attention in an automatic and habitual fashion. Future work manipulating the location of self- and other-relevant information from trial to trial in a predictable way might help to determine the relative automaticity or strategic goal-directedness of attentional prioritisation. However, effects of strategic deployment and reward-based attention-capture need not be mutually exclusive. Careful consideration of how these distinct processes support and dynamically shape the twin tasks of attention-allocation and choice-comparison may help to resolve important inconsistencies in the literature. Furthermore, the exact mechanisms of attention’s influence on the evidence-accumulation process remains unclear. Some work suggests that attention supports the initial construction of the choice-set while others posit that attention amplifies the value of evidence in real-time. While we have included both these possibilities as attentional mechanisms in our computational model, the field continues to debate the relative contributions of these mechanisms during choice32,35,49. Future work should seek to characterise and disambiguate between these mechanisms and their downstream effects on choice. We suspect that neurocomputational models like the one we have developed here will be key for resolving such issues. Importantly, these general cognitive mechanisms (attention and its multiple interactions with valuation) likely extend beyond altruistic and cooperative decision-making to other domains such as risky decision-making50 and dietary choices51,52. Our model clearly reveals the importance of considering dynamic, reciprocal connections between externally directed attention and valuation. Future work will need to explore how other dynamic processes, including internally directed attention53,54, memory55,56 and affective responding57 shape and interact with value-construction during social behaviour and beyond. ## Methods ### Study 1 Participants (N = 60) completed 160 trials of the modified dictator game (Fig. 2). To manipulate time pressure, participants had to make these choices either within 1.5 s after trial onset (high time pressure, 80 trials) or within 10 s (low time pressure, 80 trials). In the low time pressure condition, participants were also probabilistically notified they had responded fairly quickly and reminded to take their time to make the best choice if they responded before 2 s after trial onset. Supplementary analyses suggest that these prompts to delay responding did appear to encourage more extensive deliberation before choice (see Supplementary Note 6). Participants alternatingly encountered the low time pressure condition before high time pressure trials in blocks of 20 trials. Additional analyses revealed consistent patterns of effects across all blocks and no effects of block ordering (see Supplementary Note 7). Stimuli were presented and responses collected using MATLAB and the Psychophysics Toolbox58,59 on a 23-in. display monitor (100-Hz refresh rate, resolution 1920 × 1080 pixels). For eye-tracking purposes, participants sat in front of the computer screen at a distance of approximately 60 cm, with their head in a chin-rest to minimise head movements. At the end of the study, a random trial was selected from the participant’s choice set and the participant and their partner received the monetary outcomes of their choice on that trial. These outcomes were paid to the participant immediately, and to another participant in the study completing a subsequent experimental session. Thus, most participants completed the task once as the decision maker, receiving the outcome of their choice, and once as a recipient of the outcome of a previous participant’s randomly implemented choice. Participants discovered their passive participation as a recipient only at the end of the study. Monetary payoffs presented during the study ranged from$0 to $100 and were converted to real payouts using an exchange rate of 5:1. Participants learned that there would be an exchange rate in the instructions prior to the task but were not informed of the precise ratio until the end of the study. All participants provided informed consent in manners approved by the Research Ethics Board at the University of Toronto. ### Study 2 Study 2 was designed to examine the causal influence of attention on choice, independent of dispositional social preferences. Towards this end, we recruited participants from Amazon mechanical TURK (Final N = 200, 196 preregistered exclusions) and compensated$5 for their time, plus an amount determined by their choices in the study. Participants first completed a series of five one-shot dictator game where they were given varying amounts of money and asked how much they would like their partner to have on a continuous scale (see Supplementary Note 5). In the main task, participants completed 136 trials of a modified online version of the dictator game in Study 1 (see Supplementary Fig. 1) using Inquisit Web. To measure attention analogous to eye-gaze in Study 1, participants had to click on the location of $Self or$Other to reveal it, and could only view one piece of information at a time. To manipulate time pressure, participants had to make these choices either within 3 s after trial onset (high time pressure, 68 trials) or only after 3 s had elapsed but within 10 s (low time pressure, 68 trials). Subjective reports of time pressure on a single-item scale from 1 (Not at all) to 7 (Extremely) (“How rushed did you feel in trials where you had only 3 s to respond?”) provided confirmation for a manipulation check on this modified paradigm (Mpressure = 5.082, SD = 1.697). In 22 trials of each of the time pressure conditions, participants could choose to click on either their own outcomes or the other person’s outcomes first. In another 23 trials, participants were forced to click on their own outcomes (self-outcomes) first. In the last 23 trials, participants were forced to click on the other person’s outcomes (other-outcomes) first. Participants always encountered a low time pressure block followed by a high time pressure block in the practice and beginning of the main experiment but all following high and low time pressure blocks were randomly interleaved.

To signal free vs. forced-click trials, a visual border around the attributes cued what information was available for access (i.e., only self-outcomes, only other-outcomes, or both). Upon clicking, the selected information ($Self/$Other) appeared briefly, after which participants were prompted to access the non-selected piece of information. The duration of each attribute exposure were designed to mimic durations from Study 1. Participants were forced to oscillate between these pieces of information until they made a choice, or the time limit had elapsed. We recorded the number and order of clicks on each trial and defined each instance of information access as a fixation for subsequent analyses.

At the end of the study, a random trial was selected from the participant’s choice set and the participant and their partner received the monetary outcomes of their choice on that trial. These outcomes were paid to the participant immediately, and to another participant in the study completing a subsequent experimental session. Thus, most participants completed the task once as the decision maker, receiving the outcome of their choice, and once as a recipient of the outcome of a previous participant’s randomly implemented choice. Participants discovered their passive participation as a recipient only at the end of the study. Monetary payoffs presented during the study ranged from $0 to$100 and were converted to real payouts using an exchange rate of 50:1. All participants provided informed consent in manners approved by the Research Ethics Board at the University of Toronto. All details on experimental design and analyses of Study 2 were preregistered on the Open Science Framework (OSF) with the identifier CHWM3 [https://doi.org/10.17605/OSF.IO/CHWM3].

### Generous choices

We defined generous choices as trials where the participant accepted (rejected) a smaller (larger) amount of money for themselves compared to the default, in order to help their partner receive a larger amount. Choices were defined as selfish otherwise. Proportions of generous choices were calculated as the number of generous choices a participant made over the number of trials in which a response was recorded. Missed response trials (mean percentage of trials: high time pressure: Mstudy1 = 4.67%, MREP1 = 3.03%, MREP2 = 2.29%, Mstudy2 = 1.03%; low time pressure: Mstudy1 = 0.33%, MREP1 = 0.03%, MREP2 = 0.39%, Mstudy2 = 0.03%) were excluded from choice analyses.

### Eye tracking

In Study 1, we recorded eye-movements from the right eye (Pupil-CR tracking mode) using an EyeLink 1000 plus Desktop Mount (SR Research, Ontario, Canada) with a sampling rate of 1000 Hz. Before starting the experiment, the eye tracker was calibrated and validated to ensure tracking accuracy. For the calibration, participants fixated nine random dots on the screen; the eye tracker was then adjusted until the average tracking error of the visual angle was less than 0.5°. Following calibration, a nine-point validation phase was performed. The validation procedure measured the difference between the computed fixation position and the fixation position for the target obtained during calibration using the same nine random dots to ensure that the calibration was accurate and eye position errors were acceptable (average gaze-position error: 0.36° ± 0.01). To analyse the eye-movement data, we defined two (300 × 370 pixels) non-overlapping areas of interest (AOIs) around the two attributes ($Self and$Other), positioned at an equal distance from the centre cross, centred at (x = 320px, y = 540px) and (x = 1280px, y = 540px) from the left and top of the screen. Attribute positions (left or right) of $Self and$Other were counterbalanced across subjects to mitigate leftward reading biases. Eye-movement data were analysed between proposal onset and the response. We excluded three participants due to technical difficulties with the eye-tracking equipment during data collection, leaving a total of 57 eligible participants for remaining eye-tracking analyses.

We first extracted unfiltered eye-position data from all eligible participants using the Eyelink Data Viewer 3.1 with millisecond precision, classifying eye-gaze position as within the Self AOI, Other AOI or neither. To identify overall effects of time pressure, we then analysed gaze position across participants using univariate logistic mixed-effect models at every time point until 837 ms, the point at which >50% of trials had terminated under the high time pressure condition. The range of median reaction times under time pressure across subjects varied from 528 to 1084 ms with more than 50% of individuals’ median reaction times between 727 and 935 ms. To correct for multiple comparisons across the time points, we performed cluster-based permutation testing using the maximum cluster-level mass statistic, tmax60,61. Clusters were defined as time periods with at least two adjacent, significant time points.

For individual difference analyses, we extracted early gaze-biases, measured as the average proportion of time individual participants spent fixating on the Self vs. Other AOI in the first 286 ms of the trial (the time period of significant self-focused bias identified by the permutation analysis). For 15 of 9120 trials, in which participants responded before 286 ms, we calculated the proportion bias of early gaze with respect to their reaction time. Measures of later gaze-biases were computed as the proportion of time spent in the Self vs. Other AOI for the remaining trial duration (i.e., overall trial duration—286 ms). In these analyses, we included trials where participants failed to response before the time limit, given that these trials still provide information about individual participants’ attentional deployment. Excluding missed response trials (230 of 9120) yielded similar effects across all analyses.

In addition to continuous gaze data, we also conducted all analyses using measures based on first fixation position. In these analyses we excluded all fixations that were shorter than 100 ms and removed trials where participants failed to fixate on either of the two AOIs. These analyses revealed similar results to those using continuous measures of gaze, including the effect of attention on generous choice (see Supplementary Note 3).

To investigate the effects of early attention on choice, we adapted the ADDM30, constraining it by millisecond-by-millisecond trial-specific gaze position for each participant, and combined it with a multi-attribute extension of the DDM for altruistic choice26. Evidence for accepting the proposal on each trial (relative to the default) accumulated over time as a function of samples of the expected value (V). We defined the momentary expected value V(t) as the weighted sum of three attributes: self-interest ($Self), concern for others ($Other) and inequality (|$Self −$Other | ), with weights on $Self and$Other discounted by a factor θ when not the focus of visual attention, as shown in Eqs. (13).

$$V(t) = \,A(t)_{{\mathrm{self}}} \times {w}_{{\mathrm{self}}} \times \ {\mathrm{Self}} + A(t)_{{\mathrm{other}}} \times {w}_{{\mathrm{other}}} \times \ {\mathrm{ Other}} \\ + {w}_{{\mathrm{fairness}}} \times \left| \ {{\mathrm{ Self}} - \{\mathrm{ Other}}} \right| + \epsilon (t),$$
(1)
$$A(t)_{{\mathrm{self}}} = \left\{ {\begin{array}{*{20}{c}} {1,}\hfill & {\rm{if}}\,{\rm{gaze}}\,{\rm{on}}\,{\rm{Self}}\,{\rm{AOI}} \\ {1 - \theta ,} & {\rm{otherwise}.} \end{array}} \right.$$
(2)
$$A(t)_{\rm{other}} = \left\{ {\begin{array}{*{20}{c}} {1,}\hfill & {\rm{if}}\,{\rm{gaze}}\,{\rm{on}}\,{\rm{Other}}\,{\rm{AOI}} \\ {1 - \theta ,} & {\rm{otherwise}.} \end{array}} \right.$$
(3)

We further assumed that weights for a given attribute were 0 if the participant had not yet fixated on the information necessary to compute it (e.g., wother = 0 and wfairness = 0 if the participant had not yet fixated on $Other at any point prior to t). In other words, we assumed ignorance of a particular attribute until visual fixations confirmed acquisition of the necessary information ($Self for wself, $Other for wother,$Self and \$Other for wfairness).

Individual samples of the value V(t) accumulate over time, until they hit one of two choice-defining thresholds, determined by two parameters: an initial height parameter b, as well as a collapse-rate parameter d, capturing the exponential decay of the boundaries towards 0 over time within the trial24,26,39. We also employed two response bias parameters: a genbias parameter capturing intuitive social response biases predisposing people towards generous or selfish responses21, and a starting bias parameter stbias capturing a bias to reject or accept the proposal. These parameters summed together, such that the overall bias, z, towards accepting the proposal on any given trial was defined as shown in Eq. (4).

$$z = \left\{ {\begin{array}{*{20}{c}} {\rm{stbias}} + {\rm{genbias}}, {\rm{if}}\,\ {\rm{Self}}\, < \,\ {\rm{Other},} \\ {\rm{stbias}} - {\rm{genbias}},{\rm{if}}\,\ {\rm{Self}}\, > \, \ {\rm{Other}.} \end{array}} \right.$$
(4)

We fit these 8 parameters [wself, wother, wfair, b, d, stbias, genbias, θ] for each of both time pressure conditions simultaneously to quantify the unobservable dynamics of the decision process. Thus, we obtain two values per parameter that capture individual stability (mean) and contextual effects (change), resulting in 16 parameter values.

Additionally, to account for perceptual and motor processing that adds to response time without influencing the decision process itself, we included two separate percept and motor non-decision parameters, fixing each at 0.08 s based on neurobiological evidence about visual62 and motor processing times63. We added a single instance of the motor latency to simulated RTs of the model following termination of evidence at one of the two boundaries for choice. We added one instance of the percept latency to the final RT for the first instance of fixation on each unique piece of information (i.e., once if the participant only fixated on either Self or Other throughout the course of the trial, or twice if participant fixated on both). We further assumed that the value V(t) during this percept period was a function only of the previously available information, discounted by attention as shown in Eq. (5).

$$V(t) = \left\{ {\begin{array}{*{20}{c}} {0,} \hfill & {\rm{if}}\,{\rm{no}}\,{\rm{previous}}\,{\rm{fixation}}\,{\rm{in}}\,{\rm{AOIs},}\hfill \\ {(1 - \theta) \times w_{\rm{self}} \times \ {\rm{Self}} + \epsilon (t),} \hfill & {\rm{if}}\,{\rm{only}}\,{\rm{sampled}}\,{\rm{Self}}\,{\rm{AOI},} \hfill \\ {(1 - \theta) \times w_{\rm{other}} \times \ {\rm{Other}} + \epsilon (t),} & {\rm{if}}\,{\rm{only}}\,{\rm{sampled}}\,{\rm{Other}}\,{\rm{AOI}.}\hfill \end{array}} \right.$$
(5)

### The multi-attribute DDM

For comparison to the gaze-informed ADDM, we also fit a static multi-attribute DDM21. This model was identical to the gaze-informed model, with the exception that it did not include a discount parameter θ or information about eye fixations, and collapsed motor and percept parameters into a single non-decision parameter, ndt, that was estimated from the data. Thus, the model estimated 16 free parameters: 8 parameters related to average wself, wother, wfairness, b, d, stbias, genbias, and ndt and 8 related to change in these parameters due to time pressure.

### Model estimation

To examine overall effects of time pressure, as well as individual differences, we identified the best-fitting values of free parameters for each participant’s data separately, obtaining estimates of their posterior distributions using the differentially evolving Monte-Carlo Markov Chain (DEMCMC) sampling method41,64. In brief, this method simulates the likelihood of the observed data (i.e., choices and RTs) given a specific combination of parameters, and uses this likelihood to construct a Bayesian estimate of the posterior distribution of the likelihood of the parameters given the data. To maximise the data in estimating our model, we included missed responses by estimating the probability that simulations would fail to result in a choice prior to the time constraints imposed in the high and low time pressure conditions. Missed trials constituted 4% and 0.3% of all trials in the high and low time pressure conditions, respectively.

For each subject fit, we ran 3 × k chains in parallel65, where k is the number of free parameters, using uninformative priors. To preserve within-individual consistency in parameter values, we fitted data for both conditions simultaneously. In addition, to minimise the effects of parameters changing across individual fits of participants, we constrained possible parameter values as shown in Table 1, in accordance with values derived from previous model fits26 and theoretical bounds.

Given these constraints, we employed a transformation in parameter sampling to ensure the prior distributions of the model parameters were truly uniform (noninformative) across the specified range in each condition. For a diffusion model with k parameters (k/2 parameters for each of the 2 time pressure conditions), the DEMCMC sampler sampled k MCMC model parameters comprising of k/2 individual predispositions (Μparams) and k/2 effects of time pressure (change in parameters across conditions, δparams). The sum of these MCMC model parameters: Μparams + δparams × Condition (effect-coded as high time pressure: 1; low time pressure: −1) is then transformed using an inverse probit transformation. The priors for the MCMC model parameters were specified as normal distributions with mean 0 and variance of 0.5, N(0, 0.5) since inverse probit transformations of the sum of two normal distributions with mean 0 and variance of 0.5, N(0, 0.5), yields a uniform distribution across values of [0, 1] for parameters in both conditions. These transformed values were then scaled by their respective functions, fsc(x), to the range of values as seen in Table 1 to derive the diffusion model parameter values.

To construct the estimated posterior distributions of each parameter, we sampled 500 iterations per chain after an initial burn-in period of 500 samples. For each iteration, the DEMCMC algorithm41,64 proposes a new set of parameter estimates for each chain based on the scaled difference between the current parameter estimates of two other randomly sampled chains. The new parameter estimates are then evaluated by the Metropolis-Hastings algorithm for inclusion in the posterior distribution64,66. However, we included three additional features to our sampling method. Firstly, we implemented a probabilistic migration step, α = 0.1, with every MCMC step in place of the differential evolution to improve chain-mixing and convergence towards the high probability density region of the posterior distribution of parameters. The migration step cycles the positions of a subset of chains (Nmigrate uniformly sampled from the total number of chains) such that the positions of chains {i, i + 1.… j − 1, j} were compared against {i + 1, i + 2,…, j, i} and evaluated based on the Metropolis-Hastings algorithm64,66. Secondly, we resampled likelihoods of the current parameter set of the chain, if proposals were rejected thrice consecutively, to avoid stuck chains and improve chain acceptance rates41. Lastly, we also reset MCMC chain positions halfway through the burn-in period (iteration 250) if they fell outside of the 95% confidence interval of the chain means. All chains were assessed to have converged to the posterior distribution with the Gelman-Rubin statistic, R-hat < 1.167, and the overall acceptance rate of proposals for each model ranged between [0.120 and 0.299].

To evaluate the likelihood of each parameter combination proposed by the DEMCMC given the observed choice data, we conducted 10,000 simulations of the candidate model given participant-specific proposal values and (for the gaze-informed ADDM) trial-specific fixation data. We then obtained the probability of observed choices (Yes/No) and RTs from these simulations using kernel density estimation techniques with a Gaussian kernel68,69, obtaining smoothing bandwidths using Silverman’s rule of thumb70 multiplied by a factor of 0.5 to preserve the non-continuous nature of eye-movements, since saccades between AOIs could dramatically change the value evidence sampled, resulting in disjointed probability density distributions. Participant’s parameters were estimated as the mean of the posterior distributions. To ensure adequate fits, we excluded the 3 participants with technical difficulties in eye-tracking and an additional seven participants who provided the same response more than 90% of the time (i.e., accepting or rejecting >90% of trials) leaving a final sample for model-fitting of N = 50.

To evaluate the fits of extracted model parameters in predicting the variability in behaviour within an individual participant, we conducted 10,000 simulations of each trial for each participant with the fitted diffusion model parameters to obtain the model-predicted average acceptance rate and reaction time of every choice trial. To visualise and quantify these fits, we quantised both the choice data and reaction time data for each individual into 10 quantiles based on the model-predicted values of those measures per condition. We then computed each quantile mean of both observed and predicted values. Finally, we correlated the observed and predicted quantile means for both choice and reaction times for each of the time pressure conditions for each subject and performed a one-sample t test on these correlation coefficients across subjects to evaluate the model’s ability to capture variability in choice and reaction times within an individual.

### Model cross-validation

To conduct cross-validation, we fitted versions of both the gaze-informed ADDM and a multi-attribute DDM to half of the data (odd trials) and tested model generated predictions on the other half of the data (even trials). To generate these predictions for testing, we conducted 10,000 simulations of each trial for each participant with the fitted diffusion model parameters to obtain the model-predicted average. We then evaluated whether the various models were able to capture the inter-individual variability in out-of-sample generosity under high time pressure, low time pressure and the observed relative change in generosity using correlations. To compare between models, we used Fisher’s t test of dependent correlations to identify models that were significantly more accurate in predicting the interindividual variability in the out-of-sample data.

### Software

Continuous eye-tracking analyses were conducted using MATLAB (v2017b) and custom computational model fitting was conducted in Python (v3.6) based on kernel density estimation with SciPy (v1.4.1), parallelised with the native MATLAB Distributed Computing Server and the concurrent futures module in the Python Standard Library. All other statistical analyses were conducted in R 3.6.0. General linear mixed effects modelling was conducted using the lme4 package (v1.1-21) with degrees of freedom estimated using the Satterthwaite method. We conducted stepwise regression as implemented using the stepAIC function from the MASS package (v7.3-51.4). Effect size statistics of R2 and partial R2 were computed using the r2beta function from the r2glmm package (v0.1.2) using standardised general variances.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.