Dopamine and Temporal Discounting: Revisiting Pharmacology and Individual Differences.

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Learn more: PMC Disclaimer | PMC Copyright Notice J Neurosci . 2025 Oct 24;45(49):e0786252025. doi: 10.1523/JNEUROSCI.0786-25.2025 Dopamine and Temporal Discounting: Revisiting Pharmacology and Individual Differences Elke Smith 1, ✉ , Hendrik Theis 2, 3 , Thilo van Eimeren 2, 3 , Kilian Knauth 1, 4 , Deniz Tuzsus 1 , Lei Zhang 5 , David Mathar 1 , Jan Peters 1 Author information Article notes Copyright and License information 1 Department of Psychology, Biological Psychology, University of Cologne, Cologne 50969, Germany 2 Departments of Nuclear Medicine, Faculty of Medicine and University Hospital Cologne, University of Cologne, Cologne 50937, Germany 3 Neurology, Faculty of Medicine and University Hospital Cologne, University of Cologne, Cologne 50937, Germany 4 Department of Psychiatry and Psychotherapy, University Hospital Bonn, Bonn 53127, Germany 5 Centre for Human Brain Health, School of Psychology, University of Birmingham, Birmingham B15 2TT, United Kingdom Author contributions: E.S. and J.P. designed research; E.S., H.T., T.v.E., K.K., and D.T. performed research; E.S., H.T., T.v.E., K.K., L.Z., D.M., and J.P. contributed unpublished reagents/analytic tools; E.S. analyzed data; E.S. wrote the paper. This work was funded by the German Research Foundation (DFG; Grant Number, PE1627/5-1 awarded to J.P.). E.S. received support from the EUniWell Abroad Fellowship (2023, Centre for Human Brain Health, School of Psychology, University of Birmingham). H.T. was supported by the Cologne Clinician Scientist Programme (CCSP) funded by the DFG (Project Number, 4135431). We thank Lea Kemalides, Hannah Hacker, and Emily Burlon for helping with study organization and data collection. The authors declare no competing financial interests. ✉ Correspondence should be addressed to Elke Smith at e.smith@uni-koeln.de . This paper contains supplemental material available at: https://doi.org/10.1523/JNEUROSCI.0786-25.2025 ✉ Corresponding author. Received 2025 Apr 22; Revised 2025 Aug 11; Accepted 2025 Oct 3; Issue date 2025 Dec 3. Copyright © 2025 the authors SfN exclusive license . PMC Copyright notice PMCID: PMC12677122  PMID: 41136339 Abstract Disorders characterized by changes in dopamine (DA) neurotransmission are often linked to changes in the temporal discounting of future rewards. Likewise, pharmacological manipulations of DA neurotransmission in healthy individuals modulate temporal discounting, but there is considerable variability in the directionality of reported pharmacological effects, as enhancements and reductions of DA signaling have been linked to both increases and reductions of temporal discounting. This may be due to meaningful individual differences in drug effects and/or false-positive findings in small samples. To resolve these inconsistencies, we (1) revisited pharmacological effects of the DA precursor l -DOPA on temporal discounting in a large sample of N = 76 healthy participants ( n = 44 male) and (2) examined several putative proxy measures for DA to revisit the role of individual differences in a randomized, double-blind placebo–controlled preregistered study ( https://osf.io/a4k9j/ ). Replicating previous findings, higher rewards were discounted less (magnitude effect). Computational modeling using hierarchical Bayesian parameter estimation confirmed that the data in both drug conditions were best accounted for by a nonlinear temporal discounting drift diffusion model. In line with recent animal and human work, l -DOPA reliably reduced the discount rate with a small effect size, challenging earlier findings in substantially smaller samples. We found no credible evidence for effects of putative DA proxy measures on model parameters, calling into question the role of these measures in accounting for individual differences in DA drug effects. Keywords: dopamine, impulsive choice, individual differences, l -DOPA, temporal discounting Significance Statement Dopamine (DA) is involved in valuing future rewards and influences how individuals weigh immediate versus delayed rewards—a phenomenon known as temporal discounting. Understanding the role of DA is crucial, since disorders characterized by changes in DA neurotransmission, including substance-use disorders and behavioral addictions, are linked to changes in temporal discounting. There is evidence from pharmacological studies that manipulating DAergic neurotransmission modulates temporal discounting. However, the findings are highly mixed and suggest that this may be due to individual differences in baseline DA. To address this, we assessed effects of the DA precursor l -DOPA on intertemporal choice in healthy volunteers and examined several putative proxy measures for baseline DA to discern the role of individual differences in modulating drug effects. Introduction When choosing between options with an immediate benefit and options with a delayed, greater benefit, individuals commonly devalue future rewards, a phenomenon known as temporal discounting ( Mazur, 1987 ; Bickel et al., 2014 ). This tendency is stronger in substance-use disorders (SUDs) and behavioral addictions ( Peters and Büchel, 2011 ; Bickel et al., 2014 ), with altered dopamine (DA) neurotransmission proposed to underlie impulsive decision-making ( Volkow et al., 2004 ; Diana, 2011 ). Human and animal studies link DAergic frontal and striatal pathways to reward valuation ( Enomoto et al., 2011 ; Sands et al., 2023 ), while impulsivity and SUDs are linked to reduced DA function ( Volkow et al., 2004 ). Pharmacological studies reported mixed effects on temporal discounting ( D’Amour-Horvat and Leyton, 2014 ). A highly cited study reported increased temporal discounting after enhancing DA via its precursor l -DOPA ( Pine et al., 2010 ). Others reported decreases ( de Wit et al., 2002 ; Kayser et al., 2012 ; Wagner et al., 2020 ; Erfanian Abdoust et al., 2024 ), no effects ( Acheson and de Wit, 2008 ; Hamidovic et al., 2008 ), or moderating effects of impulsivity ( Petzold et al., 2019 ). Studies attenuating DA neurotransmission also provided mixed results ( Kelm and Boettiger, 2013 ; Arrondo et al., 2015 ; Weber et al., 2016 ; Soutschek et al., 2020 ). Interpretation is limited by small samples ( N = 10–14; Hamidovic et al., 2008 ; Pine et al., 2010 ; Arrondo et al., 2015 ), few trials, and delay-probability confounds ( Arrondo et al., 2015 ). Furthermore, drugs used to manipulate DA in above studies impact on different DAergic mechanisms, which likely lead to different neurocognitive effects ( Beeler and Mourra, 2018 ). Mixed effects may also result from differences in baseline DA. The relationship between DA levels and cognitive function is proposed to follow an inverted-U-shaped function ( Cools and D’Esposito, 2011 ), where enhancement impairs or improves cognition, depending on the individual baseline level. Data support this for working memory (WM), cognitive control ( Cools and D’Esposito, 2011 ), sensation seeking ( Gjedde et al., 2010 ), and impulsivity ( Petzold et al., 2019 ). However, direct tests linking DA function to cognitive performance are rare. One study examined a relatively large sample ( N = 50; Westbrook et al., 2020 ), while some applied the model to explain variability without directly testing the inverted-U shape ( Petzold et al., 2019 ). To address this, we tested how l -DOPA affects temporal discounting in a large healthy sample and whether putative baseline DA proxies, including spontaneous eyeblink rate (sEBR; Jongkees and Colzato, 2016 ), WM capacity ( Cools and D’Esposito, 2011 ), and impulsivity ( Petzold et al., 2019 ), influence drug effects. SEBR is indirectly linked to DAergic striatal activity ( Kaminer et al., 2011 ; Jongkees and Colzato, 2016 ), WM depends on prefrontal D1/D2 receptor modulation ( Braun et al., 2021 ; Matzel and Sauce, 2023 ), and impulsive choice relates to corticostriatal DA balance ( Buckholtz et al., 2010 ; Kayser et al., 2012 ; London, 2020 ). Despite these links, recent PET studies found no association between DA synthesis capacity and these measures ( Sescousse et al., 2018 ; van den Bosch et al., 2023 ). For drug effects, we predicted an inverted-U-shaped relationship with DA proxies ( https://osf.io/a4k9j/ ). More precisely, this hypothesis refers to the relationship between baseline DA and performance ( Cools and D’Esposito, 2011 ). DAergic drugs would shift individuals along this curve, improving performance in those with low baseline DA and impairing it in those with high baseline DA, implying a linear relationship between drug effects and DA proxies, which is the hypothesis tested here. For completeness, we also tested for a nonlinear relationship. We extended prior work by assessing DA's impact on the magnitude effect for temporal discounting ( Vanderveldt et al., 2017 ; Smith and Peters, 2022 ). Using a temporal discounting drift diffusion model (DDM), we jointly modeled choices and response times (RTs; Peters and D’Esposito, 2020 ; Wagner et al., 2020 ; Smith and Peters, 2022 ) and tested preregistered hypotheses regarding DA effects on response vigor (reduced nondecision times; Wagner et al., 2020 ; Westbrook et al., 2020 ) and caution (reduced boundary separation; Mathar et al., 2022 ). Materials and Methods Procedure The study was realized as repeated-measure within–subject design (see also preregistration at https://osf.io/a4k9j/ ). After passing a medical assessment to check for contraindications (see below, Sample) by a physician, eligible participants were invited to three separate testing sessions. First, the participants underwent a baseline screening, involving the recording of sEBR (using a webcam, followed by manual rating); testing of WM capacity, including digit span ( Wechsler, 2008 ), listening span ( van den Noort et al., 2008 ), and operation span ( Foster et al., 2015 ); a comprehensive psychometric assessment (reported previously; see also preregistration at https://osf.io/a4k9j/ ) including impulsivity (Barratt Impulsiveness Scale, BIS-15; Spinella, 2007 ; Meule et al., 2011 ); and the collection of demographic information. Following the baseline screening, the participants took part in two double-blind placebo–controlled testing sessions during which they received either l -DOPA or placebo. The measurements were carried out at 1 week intervals at a similar time of day and not during the pill break (i.e., the 7 d period in the monthly cycle of hormonal contraceptive use when the user stops taking the contraceptive pill). In individual cases, the interval was shortened or extended due to health or organizational reasons. The participants were instructed to fast for at least 2 h prior to testing. Before each drug session, they were tested for pregnancy and alcohol and drug consumption (THC, cocaine, MDMA, amphetamine, benzodiazepine, barbiturate, methamphetamine, morphine/heroin, methadone, and tricyclic antidepressants) and excluded if tested positive. Thirty minutes prior to testing (to ensure maximum plasma concentration during the testing phase), the participants received a tablet containing either 150 mg l -DOPA (plus 37.5 mg benserazide) or placebo (maize starch). Physiological parameters and well-being were monitored throughout the entire experimental session. In a follow-up query, the participants could not guess the current drug condition ( χ 2 [1, N = 76] = 0.47; p = 0.49). After the waiting period, the participants performed an incentivized intertemporal choice task, a reinforcement learning task (with eye tracking, to be reported elsewhere), and a visual pattern perception task ( Smith et al., 2024 ). The participants were financially reimbursed for participation and received an additional variable bonus depending on task choice. The study was approved by the local ethics committee of the Faculty of Medicine of the University of Cologne. Sample We included healthy male and female volunteers aged 25–40 who met the following criteria: normal weight as determined by a body mass index (BMI) between 19 and 25 ±2 (since the BMI does not account for body composition ( Provencher et al., 2018 ), right-handedness, normal or corrected-to-normal vision, German as first language (or profound German language skills), and for women hormonal contraception (to prevent pregnancy and reduce hormonal fluctuations). The participants were recruited via university bulletins and mailing lists and by word-of-mouth recommendation. General contraindications were as follows: intake of common and prescription drugs, participation in other studies involving medication, alcohol or drug intoxication or abuse, strongly impaired vision or strabismus, acute infections, pregnancy, strong emotional burden or physical stress during the study period, past or current psychiatric disorders, neurological disorders, metabolic disorders, internal diseases, chronic pain syndrome, and complications of anesthesia (according to self-report). Contraindications specifically regarding the intake of l -DOPA were hypersensitivity to l -DOPA or benserazide; intake of nonselective monoamine oxidase inhibitors; metoclopramide or antihypertensive medication (e.g., reserpine); disorders of the central DAergic system, e.g., parkinsonian syndromes; increased intraocular pressure (glaucoma); and breastfeeding. We initially aimed for a target sample size of N = 100; however, due to COVID-19–related restrictions and challenges, we were unable to reach the final recruitment goal. In total, 85 participants were invited to participate in the study. Nine participants did not complete the study ( n = 3 due to side effects such as nausea, and n = 6 for other reasons such as illness and organizational reasons). This resulted in a final sample of N = 76 participants ( n = 32 female), with a mean age of 28.26 (SD = 3.19; range 25–40), on average 16.43 years of education (SD = 2.30; range 10–18), a mean BMI of 22.54 (SD = 1.90; range 18–26), and average BIS-15 scores of 30.87 (SD = 5.03; range 17–41). For the assessment of a modulation of the drug effect on temporal discounting by the putative DA proxy measures, n = 75 participants were included in the regression analysis, since data for the BIS-15 was missing for one participant due to technical issues. Temporal discounting task The temporal discounting task consisted of 192 trials of intertemporal choices, i.e., choices between smaller-but-sooner (SS) and larger-but-later (LL) rewards, interspersed with two short breaks. The task comprised two magnitude conditions (half of the trials each), such that the SS reward was either low (10 €, low-magnitude condition) or high (20 €, high-magnitude condition). The SS reward was always available immediately (“now”) and remained unchanged throughout the experiment. The LL reward consisted of combinations of 16 multiples of the SS reward value, with separate sets of multiples and delays for each session (counterbalanced across participants; first drug session, multiples, [1.01 1.02 1.05 1.10 1.15 1.25 1.35 1.45 1.65 1.85 2.05 2.25 2.65 3.05 3.45 3.85]; delays (days), [1 7 13 31 58 122]; second drug session, multiples, [1.011.03 1.08 1.12 1.20 1.30 1.40 1.50 1.60 1.80 2.00 2.20 2.60 3.00 3.40 3.80]; delays. [2 6 15 29 62 118]). This was done to rule out the possibility that participants in the second session remembered specific decisions made in the first session, which, although unlikely, may have affected our ability to detect drug effects. The options were presented in white color against a black background. An option was selected via button press (“left arrow” or “right arrow” of keyboard) using the right hand, with a RT limit of 4 s. If no button was pressed within this time window, the participant was reminded to decide faster. The chosen option was highlighted with a white frame for 1 s. The trial order and side of option presentation (left/right side of the screen) were randomized. The trials were interspersed with intertrial intervals of random duration drawn from the interval between 0.5 and 1 s. The task was incentivized, i.e., the participants were informed beforehand, that upon completion of the task, they would receive the payout from one randomly selected trial, with a delay of the respective choice as a monetary voucher. The task was implemented with MATLAB (The MathWorks) and the Psychophysics Toolbox extension ( Brainard and Vision, 1997 ; Kleiner et al., 2007 ). Analysis Temporal discounting model We modeled intertemporal choice behavior using the hyperbolic discounting model ( Mazur, 1987 ; Green et al., 2005 ). To model the choices in the low- and high-magnitude condition within a single model, we fitted a subject-specific parameter k reflecting the discounting rate in the low-magnitude condition and a subject-specific parameter me reflecting the change of the discount rate from the low- to the high-magnitude condition. The subjective (discounted) value ( SV ) of the delayed reward on a given trial t was then modeled as follows: SV ( LL t ) = A t 1 + e k + I t * me * D t . ( 1 ) A is the amount of the LL reward on trial t . Here, k is the discount rate (in logarithmic space) for the low-magnitude condition, and me models are the change in log ( k ) from the low- to the high-magnitude condition. I serves as an indicator variable for the respective condition (zero for low-magnitude trials, one for high-magnitude trials). D specifies the delay of reward receipt. Softmax choice rule First, we applied the softmax choice rule ( Miedl et al., 2012 ) to model the probability of choosing the LL reward on trial t as follows: P ( LL t ) = e β * SV ( LL t ) e β * SV ( LL t ) + e β * SV ( SS t ) . ( 2 ) β is an inverse temperature parameter, describing the stochasticity of the choices (random choices are described by β = 0 , while stronger value-dependent choices are described by higher positive β values). SV is the subjective value of the LL reward on trial t . We implemented a single hierarchical Bayesian softmax model (see below, Parameter estimation) including the data from both drug conditions, in which the single-subject parameters were drawn from group-level Gaussian distributions. We assigned uniform priors covering numerically plausible values for the group-level means and standard deviations of log ( k ) , me , and β , and normal priors for parameters modeling changes from the low- to the high-magnitude condition, and changes from the placebo to drug condition, centering these priors at zero to ensure theoretically unbounded drug effects in the model, with nonetheless higher prior probability densities around zero. DDM as choice rule Furthermore, following several recent studies ( Wagner et al., 2020 ; Mathar et al., 2022 ; Smith and Peters, 2022 ), we applied the DDM to jointly model the participants’ choices and RTs. For the model's boundary definitions, the lower boundary was defined as choosing the SS reward and the upper boundary defined as choosing the LL reward. For this purpose, choices toward the lower boundary were multiplied by −1. Since single fast trials may lead to parameter adaption to these trials and hence to a poor model fit at the single-subject level, we excluded the slowest and fastest 2.5% of each participant's choices from the analysis ( Peters and D’Esposito, 2020 ). The RT on a trial t is then modeled using the Wiener first passage time (WFPT): R T t ∼ wfpt ( α , τ , z , υ ) . ( 3 ) The parameter α denotes the boundary separation (speed-accuracy trade-off), τ reflects the nondecision time (processing time unrelated to the decision process), z reflects the starting-point bias (bias toward one of the two boundaries, with z ∈ [ 0 , 1 ] , i.e., z = 0.5 reflects a neutral bias, and values z ≥ 0.5 reflect a bias toward choosing the LL reward), and υ denotes the drift rate (the rate of evidence accumulation). We fitted three different types of hierarchical DDMs to address different modeling questions, as outlined in the following sections. Condition-specific multivariate DDMs . First, condition-specific multivariate DDMs were fitted to the data from each drug condition separately. These models differed in the way in which the trial-wise subjective values modulated the drift rate and were used for model comparison. For perceptual decision-making, the drift rate varies relative to the strength of evidence ( Ratcliff et al., 2018 ). For value-based decision–making, numerous studies have shown that the drift rate is modulated by decision conflict, i.e., the value difference between available options ( Peters and D’Esposito, 2020 ; Smith and Peters, 2022 ). To begin with, we examined a null model (DDM null ) in which all parameters ( α , τ , z , and υ ) were held constant across trials. Next, to link the hyperbolic discounting model ( Eq. 1 ) to the DDM, we implemented two DDMs using different mapping functions linking trial-by-trial variability in the drift rate to trial-wise differences in subjective values as per Equation 1 . The first of these models was a linear model (DDM linear ; Pedersen et al., 2017 ): υ t = υ coeff * ( SV ( L L t ) − SV ( S S t ) ) . ( 4 ) The parameter υ coeff maps the value differences linearly onto the drift rate υ and converts them to the scale of the DDM ( Pedersen et al., 2017 ; Kutlikova et al., 2023 ). The second model entailing a value difference modulation was a sigmoid model (DDM sigmoid ), applying a nonlinear transformation of the scaled value differences using an S -shaped function ( Fontanesi et al., 2019 ): υ t = S ( υ coeff * ( SV ( L L t ) − SV ( S S t ) ) ) , ( 5 ) S ( m ) = 2 * υ max 1 + e − m − υ max . ( 6 ) S denotes a sigmoid function centered at zero with slope m and asymptote ± υ max . All models were implemented as hierarchical Bayesian models, in which the single-subject parameters were drawn from multivariate group-level Gaussian distributions (see below, Parameter estimation), with two means corresponding to the magnitude condition (low-magnitude and high-magnitude). The group-level means and standard deviations for the parameters α , τ , z , υ max , υ coeff , and log ( k ) were assigned uniform priors covering numerically plausible ranges. The parameter z (starting-point bias) was estimated in standard normal space but was backtransformed to the interval [0,1] at the trial level using the Φ -transform (standard normal cumulative distribution). These three DDMs (DDM null , DDM linear , and DDM sigmoid ) were compared based on approximate leave-one-out (LOO) cross-validation (using Pareto smoothed importance sampling; Vehtari et al., 2017 ), separately for the two drug conditions. Full multivariate DDM . Second, after confirming that the model ranking (see above) was not affected by the drug condition, we fitted a full multivariate DDM including the full covariance matrix of all parameters across all conditions for the best-fitting model. This model was used to obtain posterior estimates of test–retest (i.e., Session 1 and Session 2, corresponding to placebo and l -DOPA) correlation coefficients for each model parameter to verify the degree of reliability of each model parameter across drug conditions. Here, each parameter was drawn from a multivariate Gaussian distribution, with four means and four standard deviations for all drug and magnitude conditions (placebo-low, placebo-high, l -DOPA-low, l -DOPA-high) and the full covariance matrix. Drug-effect DDM . Third, we fitted a (univariate) drug-effect DDM for the best-fitting model identified using the condition-specific DDMs (see above), in which the placebo condition was modeled as the baseline, and for each parameter, drug effects were modeled as additive condition-effect parameters. The purpose of this model was to directly quantify the magnitude of drug-induced changes in each model parameter. Regression model . Lastly to analyze the effect of the putative proxies of DA function (BIS-15 score, sEBR and WM capacity) on the model parameters, we tested for linear and quadratic modulations of the drug-effect parameters from the full model across drug and magnitude conditions via Bayesian regression. WM capacity was operationalized as principal component (PC) across all three WM tasks ( Text S1 ; Fig. S1 ). As preregistered for the case of correlated WM measures, we used PC analysis (PCA) to obtain a compound score reflecting WM capacity. Since BIS-15 scores, sEBR, and the first PC of WM capacity were only weakly correlated (−0.08 < r < 0.16; see also Text S1 of the Supplementary Material), we then used each of these proxy measures as individual regressor instead of a compound score. As an example, the regression model is shown below for the drug effect on log ( k ) as outcome and the putative DA proxies BIS-15 score, sEBR, and the first PC of WM capacity as predictors: log ( k ) drug − shift = ι + ω 1 * BIS + ω 2 * sEBR + ω 3 * WM + ω 4 * BI S 2 + ω 5 * sEB R 2 + ω 6 * W M 2 + ϵ , ( 7 ) where ϵ ∼ N ( μ , σ ) . ( 8 ) The parameter ι denotes the intercept; ω 1 − 6 represent the regression coefficients for the three linear and squared proxy measures BIS-15 score (BIS), sEBR, and WM capacity, respectively. Note that to avoid the double use of parameter names, the conventional naming of the intercept as α and regression coefficients as β s was changed ( β denotes the temperature parameter of the softmax model; α denotes the boundary separation parameter of the DDM). Analysis of posterior distributions . To quantify the evidence for effects of drug and magnitude on model parameters, as well as effects of the putative DA proxy measures on model parameters, we examined the highest posterior density intervals (HDI) of the posterior distributions of the drug-effect DDM and of the regression coefficients for linear and quadratic terms from the regression model. Here, effects were considered credible if zero fell outside the 95% HDI. Parameter estimation Parameter estimation of all models (softmax and DDMs) was performed with Markov chain Monte Carlo simulation, as implemented in Stan (version 2.26.1; Carpenter et al., 2017 ), using R (version 4.3.1; R Core Team, 2023 ) and the R interface to Stan RStan (version 2.26.23; Stan Development Team, 2024 ). For the softmax model, sampling was performed with 4,000 iterations for four chains (2,000 warmup samples). For the condition-specific DDM and full multivariate DDMs, sampling was performed with 8,000 iterations for four chains (6,000 warmup samples). For the drug-effect DDM, sampling was performed with 12,000 iterations for four chains (10,000 warmup samples, no thinning). For the regression model, sampling was performed with 2,000 iterations for four chains (1,000 warmup samples). The convergence of the chains for the single-subject and group-level parameters was assessed by inspecting the traces such that R ^ ≤ 1.01 ( Gelman and Rubin, 1992 ; Vehtari et al., 2021 ). For the condition-specific multivariate DDMs, as well as for the drug-effect DDM, we slightly relaxed criteria with regard to R ^ as compared with the preregistration (for the drug-effect DDM, two rather peripheral parameters, the standard deviations of υ coef f s and m e s , had an R ^ of 1.03 and 1.01, respectively). Inspecting the posteriors confirmed that in all cases, distributions were clearly peaked. We previously performed parameter recovery analyses for the temporal discounting DDMs used in this study, demonstrating accurate recovery of model parameters ( Peters and D’Esposito, 2020 ; Wagner et al., 2020 ). Posterior predictive checks To ensure that the best-fitting model captures the characteristics of the observed data well, we conducted posterior predictive checks ( Palminteri et al., 2017 ; Zhang et al., 2020 ). For the softmax model, we ran 4k simulations per trial and overlaid the predicted onto the observed choices. For each of the condition-specific multivariate DDMs, we simulated 1k datasets based on the respective posterior distributions. For each participant, we then overlaid the predicted onto the observed RT distributions and LL choice proportions across five LL value bins to capture the associations between choices, RTs, and subjective discounted values. Results Descriptive statistics and results from model-agnostic analyses are shown in Text S2 and Table S1 of the Supplementary Material, respectively. Numerically, participants made more LL choices under l -DOPA compared with placebo, but this difference was not significant ( Text S2 ). Softmax choice rule Modeling the choices with the softmax choice rule, we found reduced discounting for higher rewards (magnitude effect), as indicated by the negative effect of value magnitude on l o g ( k ) ( me parameter, the 95% HDI of the posterior distribution not including zero), and reduced discounting under l -DOPA compared with placebo, as indicated by a negative drug effect on log ( k ) [ log ( k ) s parameter]; see Table 1 and Figure 1 , the 95% HDI of the posterior distribution not including zero. The drug effect on the magnitude effect was not reliably different from zero (the 95% HDI of the posterior distribution including zero). Table 1. Group-level means and 95% HDIs of the posterior distributions from the softmax model MD 95% HDI β 1.75 [1.26, 2.31] β s 0.05 [−0.29, 0.38] log( k ) −4.76 [−5.31, −4.24] log( k ) s −0.24 [−0.48, −0.02] me −0.59 [−0.69, −0.49] me s 0.02 [−0.13, 0.15] Open in a new tab HDI, highest posterior density interval; β , inverse temperature parameter; β s , drug effect for β ; log( k ), discount rate; log( k ) s , drug effect for log( k ); me, magnitude effect; me s , drug effect for magnitude effect. Figure 1. Open in a new tab Posterior distributions of the group-level parameter means of the softmax model. The horizontal solid line indicates the 95% highest posterior density interval; the vertical dashed line indicates x = 0. Parameters in the placebo condition (top row, gray distributions) were modeled as the baseline, and changes from placebo to l -DOPA (bottom row, pink distributions) were modeled as additive shift ( s ) parameters. β , inverse temperature parameter; β s , drug effect for β ; log( k ), discount rate; log ( k ) s , drug effect for log ( k ) ; me , magnitude effect; m e s , drug effect for magnitude effect. DDM comparison Comparing the condition-specific multivariate DDMs with regard to predictive accuracy using LOO cross-validation ( Vehtari et al., 2017 ) confirmed that the data were best accounted for by a DDM including a nonlinear, i.e., sigmoid, scaling of the drift rate by the subjective value differences (DDM sigmoid ). This was the case for both drug conditions ( Table 2 ). Table 2. Model comparison for the condition-specific multivariate DDMs Model Drift rate value scaling LOO score Placebo l -DOPA DDM null None 25,324.20 23,877.22 DDM linear Linear 20,436.01 19,297.99 DDM sigmoid Sigmoid 16,922.39 15,800.42 Open in a new tab DDM, drift diffusion model; LOO, leave-one-out cross-validation score. Lower LOO scores indicate a better model fit. Posterior predictive checks Softmax model To verify that the softmax model can account for the observed choices, we conducted posterior predictive checks. We simulated 4k datasets based on the posterior distributions of the hierarchical softmax model and overlaid the predicted onto the observed choices. This demonstrated that the softmax model accounted well for the observed LL choice proportions ( Fig. 2 ). Figure 2. Open in a new tab Observed (teal) and predicted (orange) proportions of LL choices from the softmax model across participants split by magnitude and drug condition. Model-predicted choices were obtained by averaging over 4k simulations per trial from the posterior distribution. The scaling of the x -axis has been changed to “factor” for better readability. Points, means; bars, standard deviations. DDM Posterior predictive checks for the condition-specific multivariate DDMs confirmed that the DDM sigmoid provided a good account of the relationship between RT and LL choice proportions and subjective value ( Figs. 3 , 4 ) in individual participants across the full range of log ( k ) values observed. Furthermore, the DDM sigmoid predicted the choices with the highest accuracy ( Table 3 ). In line with the model comparison, this was the case for both drug conditions. Next, we implemented a DDM sigmoid including both magnitude and drug conditions, by including additive drug-effect parameters for capturing changes in parameter values from the low- to high-magnitude and from the placebo to l -DOPA condition. All further analyses are based on the drug-effect DDM sigmoid . Figure 3. Open in a new tab Posterior predictive RT plots for the condition-specific multivariate DDM variants [null, DDM null (orange); lin, DDM linear (blue); sig, DDM sigmoid (green)] for three example participants with a discount rate close to the median (Participant #4; top row, k = −5.10), a high discount rate (Participant #14, middle row, k = −2.64), and a low discount rate (Participant #16, bottom row, k = −6.77; discount rate from DDM sigmoid ). Trials were binned into five bins of equal sizes according to the subjective value of the LL option for each participant (based on hyperbolic discounting, see Materials and Methods, Temporal discounting model). The y -axis depicts the observed mean RTs per bin (data, gray solid line) and model-predicted mean RTs per bin for the different DDMs (colored dashed lines). Model-predicted RTs were generated by averaging over 1k datasets simulated from the posterior distribution of each hierarchical model. Figure 4. Open in a new tab Posterior predictive choice plots for the condition-specific multivariate DDM variants [null, DDM null (orange); lin, DDM linear (blue); sig, DDM sigmoid (green)] for three example participants with a discount rate close to the median (Participant #4, top row, k = −5.10), a high discount rate (Participant #14, middle row, k = −2.64), and a low discount rate (Participant #16, bottom row, k = −6.77; discount rate from DDM sigmoid ). Trials were binned into five bins of equal sizes according to the subjective value of the LL option for each participant (based on hyperbolic discounting, see Materials and Methods, Temporal discounting model). The y -axis depicts the observed LL choice proportion per bin (data, gray solid line) and model-predicted LL choice proportions per bin for the different DDMs (colored dashed lines). Model-predicted choices were generated by averaging the proportion of LL choices over 1k datasets simulated from the posterior distribution of each hierarchical model. Table 3. Accuracy of the choice predictions for the condition-specific multivariate DDMs Placebo l -DOPA Low High Low High DDM null 0.63 0.65 0.63 0.65 DDM linear 0.74 0.75 0.73 0.75 DDM sigmoid 0.83 0.84 0.82 0.84 Open in a new tab Model-predicted choices were generated by averaging the proportion of LL choices over 1k datasets simulated from the posterior distribution of each hierarchical model. DDM, drift diffusion model. Effects of reward magnitude and drug on model parameters As predicted, higher rewards were discounted less, as indicated by more LL choices in the high- compared with low-magnitude condition (see Text S2 of the Supplementary Material for results on model-agnostic analyses) and a negative effect of reward magnitude on log ( k ) ( me ) parameter in the drug-effect DDM sigmoid ( Table 2 ; Fig. 3 ). This magnitude effect on log ( k ) was credibly different from zero (the 95% HDI of the posterior distribution of me did not include zero). Likewise, the directional BF me <0 versus >0 = Inf provided extreme evidence for values smaller than zero versus greater than zero. The posterior distributions of the drug-effect DDM sigmoid , in which the placebo condition was modeled as the baseline and drug effects as additive changes from the baseline, revealed that enhancing DA transmission reduced discounting, as indicated by a negative drug effect on log ( k ) ( log ( k ) s ) parameter in the DDM sigmoid ( Table 4 ; Fig. 5 , bottom row), substantiated by the observation that the 95% HDI of the posterior distribution did not include zero and BF log( k ) s <0 versus >0 = 49.15 provided substantial evidence for values smaller than zero versus greater than zero. Recall that these effects were reproduced using the softmax choice rule ( Table 1 ; Fig. 1 ). Table 4. Summary of model parameters of the drug-effect DDM (parameter group means and 95% HDIs of the posterior distributions) for the drug-effect DDM sigmoid with parameters in the placebo condition modeled as the baseline and changes from placebo under l -DOPA modeled as additive shift ( s ) parameters Baseline Drug effect M 95% HDI M 95% HDI α 2.15 [2.08, 2.24] α s −0.06 [−0.16, 0.03] τ 0.76 [0.72, 0.81] τ s 0.03 [−0.01, 0.07] z −0.02 [−0.06, 0.01] z s 0.02 [−0.01, 0.06] υ coeff 50.43 [35.01, 66.84] υ coef f s 0.91 [−1.17, 2.79] υ max 1.87 [1.74, 2.00] υ ma x s 0.01 [−0.12, 0.13] log ( k ) −4.86 [−5.40, −4.33] log ( k ) s −0.20 [−0.40, −0.01] me −0.66 [−0.75, −0.56] m e s 0.08 [−0.03, 0.19] Open in a new tab HDI, highest posterior density interval; α , boundary separation; τ , nondecision time; z , starting-point bias; υ coeff , drift rate scaling factor; υ max , asymptote for υ coeff ; log ( k ) , discount rate; me , magnitude effect for log ( k ) ; log ( k ) s , drug effect for log ( k ) ; m e s , drug effect for me . Figure 5. Open in a new tab Posterior distributions of the group-level parameter means for the core DDM parameters and discounting parameters of the drug-effect DDM sigmoid . Parameters in the placebo condition (top row, gray distributions) were modeled as the baseline, and changes from placebo to l -DOPA (bottom row, pink distributions) were modeled as additive shift ( s ) parameters. The horizontal solid line indicates the 95% highest posterior density interval; the vertical dashed line indicates x = 0. α , boundary separation; τ , nondecision time; z , starting-point bias; υ coeff , drift rate scaling factor; υ max , asymptote for υ coeff ; log ( k ) , discount rate; me , magnitude effect for log ( k ) ; log ( k ) s , drug effect for log ( k ) ; m e s , drug effect for me . In contrast, the drug effect on the magnitude effect ( m e s parameter) was not credibly different from zero in both the softmax model and DDM (the 95% HDI of the posterior distribution included zero in both cases). For the remaining DDM parameters ( α , z , τ , and υ max ), we found no credible evidence for drug effects, since in all cases, the 95% HDI of the posterior distributions included zero (BF α s <0 vs >0 = 8.83; BF τ s >0 vs <0 = 17.35; BF z s >0 vs <0 = 7.06; BF υ coeff- s >0 vs <0 = 4.45; BF υ coeff-max >0 vs <0 = 1.28). This suggests that these parameters were not credibly modulated by the drug manipulation ( Table 4 ; Fig. 5 , bottom row). Effects of individual differences To test for a modulation of the drug effects by individual measures of putative DA proxies, we regressed the drug-effect parameters of the drug-effect DDM sigmoid onto sEBR, the first PC of a PCA across the WM tasks (digit span, Wechsler, 2008 ; listening span, van den Noort et al., 2008 ; operation span, Foster et al., 2015 ) and impulsivity (BIS-15 score, Spinella, 2007 ; Meule et al., 2011 ). We found no credible evidence that any of the drug effects were substantially modulated by the DA proxy measures, since for all posterior distributions of the regression coefficients, the 95% HDIs included zero. See Figure 6 for Bayesian regression coefficients for drug-effect parameters for the discount rate and magnitude effect and Table S2 and Fig. S2 of the Supplementary Material for a full summary of all regression coefficients for all drug-effect parameters. See Figure 7 for associations between DA proxy measures and individual drug effects across DDM parameters. Supplementary analyses testing linear associations between WM, EBR, and BIS-15 and behavioral measures (the percentage of LL choices and RTs) and model parameters under placebo revealed no strong relationships ( Fig. S3 ). Figure 6. Open in a new tab Posterior distributions of the linear regression coefficients (℧) for the DA proxies impulsivity (BIS-15 scores), sEBR, and WM capacity (WM), regressing the drug-shift (s) parameters for the discount rate log ( k ) and the magnitude effect me of the drug-effect DDM sigmoid onto the proxies. The posterior distribution of the intercept is not depicted. The horizontal solid line indicates the 95% highest posterior density interval; the vertical dashed line indicates x = 0. log ( k ) s , drug effect for log ( k ) ; m e s , drug effect for me . Figure 7. Open in a new tab Relationship between the putative DA proxy measures impulsivity (BIS-15 scores), sEBR, and WM capacity (WMC) and the drug effects (means of single-subject posterior distributions for the drug-effect parameters of the drug-effect DDM sigmoid ). Points, single-subject values; solid black line, regression line; gray ribbon, standard error. s , drug effect (additive shift) parameter; α , boundary separation; τ , nondecision time; z , starting-point bias; v coeff , drift rate scaling factor; v max , asymptote for v coeff ; log( k ), discount rate; me, magnitude effect. Reliability of drift diffusion parameter estimates To estimate the test–retest reliability, we implemented the best-fitting DDM, i.e., the DDM sigmoid , as a model spanning both drug sessions (full multivariate DDM). The model parameters of each individual were drawn from group-level multivariate Gaussian distributions, with means and covariance matrices for all parameters, setting uniform priors from −1 to 1 for the test–retest correlation coefficient parameters (see Materials and Methods, Parameter estimation, for details on parameter estimation). Test–retest reliability was excellent for υ coeff (drift rate scaling parameter) and log ( k ) (discount rate) for both magnitude conditions ( Table 5 ; Fig. 8 ). For α , test–retest reliability was poor for both magnitude conditions. For τ and υ max , test–retest reliability was moderate. Furthermore, while test–retest reliability was good for z (starting-point bias) for the low-magnitude condition, it was poor for the high-magnitude condition. This suggests that the magnitude effect (see section “Effects of reward magnitude and drug on model parameters”) is mediated by the starting-point bias only in some individuals. While in the low-magnitude condition, the starting point appeared to be consistently biased toward SS rewards, this was not the case in the high-magnitude condition. Table 5. Means and 95% HDIs of the posterior distributions of the correlation coefficients from the full multivariate DDM between placebo–low magnitude and l -DOPA–low magnitude and placebo–high magnitude and l -DOPA–high magnitude, respectively Low magnitude High magnitude M 95% HDI M 95% HDI α 0.28 [0.05, 0.52] 0.27 [0.02, 0.51] τ 0.55 [0.39, 0.70] 0.56 [0.40, 0.71] z 0.76 [0.60, 0.90] 0.24 [−0.04, 0.53] υ coeff 0.98 [0.95, 1.00] 0.97 [0.93, 1.00] υ max 0.47 [0.25, 0.68] 0.60 [0.42, 0.78] log ( k ) 0.93 [0.89, 0.96] 0.93 [0.88, 0.96] Open in a new tab DDM, drift diffusion model; HDI, highest posterior density interval; α , boundary separation; z , starting-point bias; τ , nondecision time; υ coeff , coefficient mapping the value differences onto the drift rate using a sigmoid function S ; υ max , asymptote for S ; log( k ), discount rate. Figure 8. Open in a new tab Test–retest (placebo vs l-DOPA) reliability of the parameter estimates from the full multivariate DDM. Posterior distributions of the correlations between placebo–low magnitude and l -DOPA–low magnitude (yellow) and placebo–high magnitude and l -DOPA–high magnitude (green), respectively. Vertical dashed line, ρ = zero . Α , boundary separation; τ , nondecision time; z , starting-point bias; υ coeff , coefficient mapping the value differences onto the drift rate using a sigmoid function S ; υ max , asymptote for S ; log( k ), discount rate. Discussion Here, we revisited the effect of DA on temporal discounting and the role of individual differences in putative DA proxies, including impulsivity, WM capacity, and sEBR. Previous pharmacological studies yielded mixed results ( D’Amour-Horvat and Leyton, 2014 ; Castrellon et al., 2021 ), likely due to baseline DA differences or small-sample noise. Using temporal discounting DDMs, we dissociated effects of reward magnitude, l -DOPA, and individual differences on decision-making. As predicted and replicating previous work ( Green et al., 1997 ; Smith and Peters, 2022 ), higher rewards were discounted less (magnitude effect), supported by model-agnostic analysis and computational modeling. l -DOPA did not credibly affect the magnitude effect—if anything, l -DOPA slightly attenuated it. Furthermore, we found no credible effects of l -DOPA on the drift rate value scaling or starting point. Centrally, l -DOPA credibly reduced temporal discounting, with log( k ) decreasing from −4.86 (placebo) to −5.06 ( l -DOPA), corresponding to a 20% decrease (in the raw discount rate from 0.0078 to 0.0063), yielding a small effect size (Cohen's d ≈ −0.26; M log ( k ) s = − 0.20 ; S D log ( k ) s = − 0.76 ). Detecting this effect with 80% power at α = 0.05 would require ∼116 participants, though hierarchical Bayesian estimates may underestimate between-subject variability due to partial pooling. Although small, this effect challenges earlier findings of increased discounting under l -DOPA in N = 13 participants ( Pine et al., 2010 ) and aligns with more recent animal ( Heyer-Osorno and Juárez, 2020 ; Magnard et al., 2024 ) and human studies ( Kayser et al., 2012 ; Wagner et al., 2020 ; Erfanian Abdoust et al., 2024 ), suggesting DA reduces temporal discounting. DA may influence cost–benefit trade-offs by increasing cost tolerance or facilitating overcoming costs ( Kurniawan et al., 2011 ; Beeler, 2012 ; Michely et al., 2020 ). Thus, DA would reduce waiting costs, increasing the preference for LL over SS rewards, consistent with our findings. l -DOPA's reduction of temporal discounting aligns with findings in Parkinson's patients showing reduced discounting ON versus OFF DAergic medication ( Foerde et al., 2016 ). Similarly, DA increases have been linked to improved model-based control in healthy individuals ( Wunderlich et al., 2012 ; but see Kroemer et al., 2019 ) and PD patients ( Sharp et al., 2016 ). DA may enhance cognitive functions supporting both model-based control and temporal discounting, including planning ( Mehta et al., 2005 ) and executive control ( Cai et al., 2022 ). Striatal DA may contribute to decision-making by regulating the balance of striatal “go” and “no-go” pathways ( Maia and Frank, 2011 ; Collins and Frank, 2014 ; Maia et al., 2017 ). Increased striatal DA levels may also boost the signal-to-noise ratio of value representations ( Wagner et al., 2020 ), increasing the likelihood that LL rewards reach prefrontal cortical processing. Mixed earlier findings may also stem from individual differences in DA-related traits such as impulsivity ( Buckholtz et al., 2010 ; Petzold et al., 2019 ; Keidel et al., 2021 ). Following the inverted-U-shaped hypothesis of DA function, DAergic drugs would produce opposite effects depending on baseline DA levels ( Williams and Castner, 2006 ; Cools and D’Esposito, 2011 ), leading to the highly cited assumption that the relationship between WM capacity and DA level follows an inverted-U-shaped function, such that depending on baseline DA levels, DAergic drugs may elicit opposing effects (for a review, see Floresco, 2013 ). However, we found no credible association between DA drug effects and individual differences in sEBR, WM capacity, or impulsivity. Possibly, the inverted-U model is not appropriate—we tested linear and quadratic effects but not other functions ( Floresco, 2013 ). Second, some studies supporting an inverted-U-shaped model had comparatively small-sample sizes ( N = 10–22; Acheson and de Wit, 2008 ; Hamidovic et al., 2008 ; Landau et al., 2009 ; Gjedde et al., 2010 ; Pine et al., 2010 ; Kayser et al., 2012 ) or inferred quadratic effects for subgroups without direct tests ( Petzold et al., 2019 ). Several PET studies provide no evidence for an inverted-U-shaped relationship between D2 receptor availability and sEBR, WM capacity, or impulsivity ( Dang et al., 2017 ; Sescousse et al., 2018 ; van den Bosch et al., 2023 ). This suggests that heterogeneous earlier findings may reflect noise from underpowered studies. Nonetheless, other measures may better reflect baseline DA, or effects may depend on DA release or D2/D3-receptor availability instead ( van den Bosch et al., 2023 ). Although we did not measure DA directly, the absence of DA proxy effects in our N = 76 sample challenges their validity as direct baseline DA indicators. Moreover, if these measures reflect baseline DA, they would be expected to correlate, which they did not. While capturing individual differences, these measures did not explain variance in individual differences in DA drug effects on temporal discounting. Of note, disparate findings may further stem from different drugs used (buproprion, d-amphetamine, pramipexol, tolcapone, l -DOPA, haloperidol; Pine et al., 2010 ; Kayser et al., 2012 ; Petzold et al., 2019 ; Wagner et al., 2020 ), which act via distinct receptor mechanisms. For instance, haloperidol, a DA antagonist, which, at lower doses, increases striatal DA transmission, reduced delay discounting in two recent studies ( Wagner et al., 2020 ; Erfanian Abdoust et al., 2024 ). Regarding overall effects on remaining model parameters, we expected l -DOPA to increase response vigor (reduce RTs and nondecision times; Wagner et al., 2020 ) and to lower the decision threshold (reduce boundary separation; Mathar et al., 2022 ; Chakroun et al., 2023 ). Model-agnostic analysis revealed no significant RT difference between l -DOPA and placebo. Numerically, l -DOPA reduced the boundary separation, but the effect was small, and the 95% HDI overlapped with zero. The baseline (placebo) estimate of the nondecision time was consistent with our previous studies ( Peters and D’Esposito, 2020 ; Wagner et al., 2020 ). However, if anything, l -DOPA slightly increased nondecision times, although the 95% HDI overlapped with zero. This contrasts with studies using other DAergic drugs ( Wagner et al., 2020 ; Mathar et al., 2022 ). One explanation may be that our task, though time-limited, did not impose strong time pressure, allowing ample deliberation. Thus, decision dynamics like boundary separation may have been less sensitive to DAergic modulation than in tasks requiring rapid decisions or noisy value estimations (e.g., in reinforcement learning; Mathar et al., 2022 ; Chakroun et al., 2023 ). Posterior predictive checks confirmed that the DDM sigmoid accounted best for associations between RT, LL choice proportions, and subjective value. Both the DDM linear and DDM sigmoid reproduced the subjective value-related reductions in RTs; however, the DDM linear over- and underestimated RTs for small and large LL values, respectively. Both the DDM linear and DDM sigmoid reproduced the observed increases in LL choice proportions with increasing LL value; however, the former model underestimated the effect. Comparing the linear and sigmoid DDM, it is notable that their performance varied across data regions. The sigmoid mapping constrains the drift rate, preventing it from becoming disproportionately large for high value differences. For intermediate value differences, both models generated similar predictions, whereas for more extreme differences, the DDM linear under- or overpredicted RTs and LL choice proportions. This pattern is evident in the posterior predictive checks, e.g., for Participant #4 and #14 in Figure 1 and Participant #4 and #16 in Figure 2 . Overall, the DDM sigmoid best predicted choices across drug conditions, with posterior predictive checks showing it accounted for the full range of observed data at the individual-participant level. Given variability across participants, such differences in model fit would be obscured in group-level predictions. Limitations This study has several limitations. First, we did not assess hormonal cycle effects on drug effects. As ovarian hormones interact with DA signaling ( Yoest et al., 2018 ), decision-making fluctuates with the cycle phase ( Lazzaro et al., 2016 ), and future studies should address this. Furthermore, DA proxies may not have modulated drug effects due to limited variance in these measures. In data from healthy controls, extreme values, such as high impulsivity, are underrepresented. Lastly, our modeling did not account for potential nonlinear utility effects (e.g., valuing the two SS rewards differently). Estimating these would require a broader SS range. Future studies may explore DA's role in nonlinear utility transformations. Conclusion In this study, we investigated the effects of the DA precursor l -DOPA on temporal discounting and the role of putative DA proxies. Temporal discounting DDMs showed that choices and RTs were best explained by a nonlinear, sigmoid drift rate value scaling. Contrasting with earlier small-sample studies ( Pine et al., 2010 ), l -DOPA credibly reduced temporal discounting across models, supporting the notion that enhancing DA transmission decreases temporal discounting ( Kayser et al., 2012 ; Wagner et al., 2020 ; Erfanian Abdoust et al., 2024 ). Inconsistent with the inverted-U hypothesis, sEBR, WM capacity, and impulsivity did not modulate drug effects, questioning their proposed role as direct proxies for baseline DA ( Gjedde et al., 2010 ; Cools and D’Esposito, 2011 ), a conclusion supported further by weak intercorrelations. Data Availability All the model code is openly available on the Open Science Framework at https://osf.io/5fkjy/ . The fitted models are openly available at https://zenodo.org/records/13378364 (DOI: 10.5281/zenodo.13378364). The data cannot be shared publicly, since the participants did not provide consent to public data access. 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