2.1 Participants and materials

109 participants (35% female; M age = 23.4 years, SD = 3.5) were recruited using the Online Recruitment System for Economic Experiments (ORSEE; Greiner Reference Greiner2015) at Linköping University, Sweden. A sample-size calculation based on means and standard deviations from a previous study from our lab (Kirchler et al. in press) and with 70% power showed that 50 participants were needed in each condition. Data collection continued until all scheduled experimental sessions for the week of the 100th participant had been completed. All participants gave their informed consent prior to participation. Individuals were not allowed to participate if they were taking anxiolytic, antidepressive, or pain relieving medication. Participants were paid 100 SEK (approx. 12 USD) as a show-up fee plus or minus the amount from one randomly selected decision. Delayed payoffs from the intertemporal choice task were paid using Swish, a free, popular smartphone app that facilitates immediate money transfers between bank accounts. Participants who had not already installed Swish on their phone were required to do so before participating in the study. Two male participants were excluded due to technical problems during the experiment, leaving 107 participants in the final sample.

Painful heat stimulation was delivered to the distal part of participants’ left dorsal forearm using a 3 × 3 cm Thermal Stimulator Probe (Q-sense, Medoc). Prior to the experiment, participants’ pain threshold for heat was determined by a procedure following Perini et al. (Reference Perini, Bergstrand and Morrison2013), in which the thermode had a baseline temperature of 32 °C and increased at a speed of 1 °C/s. Participants’ task was to press a mouse button positioned in their right hand when the stimulation reached the border between painful and too painful. For safety reasons, the temperature never exceeded 50 °C. After they had pressed, the temperature returned to baseline. The procedure was repeated four times. The highest achieved temperature was selected as the pain threshold (max. 49 °C). Participants then completed a 1 min trial block in which the temperature varied between their pain threshold and 2 °C below the threshold, just as it would during the experimental trials (see below). Participants were told that the stimulation was meant to be painful but endurable and were allowed adjust to a lower or higher temperature if they perceived the stimulation as too painful or not painful enough, respectively. Pain thresholds after adjustments ranged between 40 °C and 49 °C (M = 48.07, SD = 1.38). Fifty-four participants had the maximum pain threshold of 49 °C. Pain thresholds did not differ as a function of the order in which participants were in the pain and control conditions, t(105) = .80, p = .425. A manipulation check was conducted on the last 56 participants, who indicated how painful they perceived the stimulation on a scale from 1 (not at all painful) to 10 (extremely painful). This confirmed that the stimulation was perceived as very painful (M = 8.43, SD = 1.36) and that the subjective experience of the stimulation did not differ as a function of the order of conditions, t(54) = .56, p = .578.

2.2 Experimental design

We used a crossover design in which participants performed three decision-making tasks twice: once with pain and once without pain. Participants thus served as their own controls. The order of the tasks was the same for all participants, but the order of the pain and control conditions was randomized between participants so that about half the participants (n = 57, 32% female) were in the pain condition first and the other half (n = 50, 40% female) were in the control condition first. In the pain condition, painful heat stimulation as described above was delivered to participants’ left forearm continuously for 60 s while they completed each task. In the control condition, the thermode was placed on participants’ forearm but the temperature remained at baseline (32 °C). Everything else was identical between conditions. Each task lasted for 60 s and was followed by a break of at least 30 s during which the thermode was removed from participants’ arm. Thus, pain was only delivered during the decision phase. General instructions were given before the experiment started and task-specific instructions were given before each task. Participants were informed that one of their decisions would be randomly selected for actual payment. The tasks were presented on a computer screen and were programmed in Qualtrics. A translation of the complete instructions for the experiment is provided in the Supplemental Materials.

2.3 Data analysis

We first performed paired samples t-tests to investigate whether the proportion of risky and impatient choices, compared to the total number of trials in each task, was greater in the pain condition than in the control condition. We then performed regression analyses in order to confirm the results from the t-tests while also controlling for age and gender. Our regression model for the risky choice tasks was specified as follows:

(1) $y_{ik}={\beta }_0+{\beta }_{1}Pain+{\beta }_{2}Round+{\beta }_{3}Ratio+{\beta }_4{X}_i+{\in }_{ik}$

where the dependent variable $y_{ik}$ is a dummy variable indicating whether participant i chose the risky option in trial k. Pain is a dummy for the pain condition and Round is a dummy for the second round of the tasks, i.e. the second time participants performed the tasks. An alternative model also included the interaction term Pain × Round, which allows the effect of pain to differ across the two task rounds. Ratio is the ratio between the expected value of the risky option and the expected value of the safe option on each trial (standardized). X _i is the control variables age and gender. The model was estimated using OLS and standard errors were corrected for clustering on the individual level.

Our regression model for the intertemporal choice task was identical to the model above except the dependent variable $y_{ik}$ was a dummy variable indicating whether participant i chose the immediate option in trial k and Ratio was replaced with Delay, which denotes the difference in days (one or five) between the immediate and the delayed reward. Thus, the regression model for the intertemporal choice task was specified as follows:

(2) $y_{ik}={\beta }_0+{\beta }_{1}Pain+{\beta }_{2}Round+{\beta }_{3}Delay+{\beta }_4{X}_i+{\in }_{ik}$

For all choice tasks, we also investigated whether the effect of pain differed between male and female participants. To do this, we performed regression analyses using the models specified above where we included the interaction term Pain × Female, which allows the effect of pain to differ across genders.

We also estimated risk aversion and discounting parameters for the pain and control conditions. For the estimation of risk aversion, we assumed constant relative risk aversion (CRRA) and the following utility function:

(3) $u\left(x\right)=\left(\begin{array}{c}\frac{x^{1-r}}{1-r}\text{if}x\ge 0\\ -\frac{{\left(-x\right)}^{1-r}}{1-r}\text{if}x<0\end{array}\right)$

where r is the coefficient of relative risk aversion and x is the monetary outcome. With this parameterization, r = 0 denotes risk-neutral behavior, r > 0 denotes risk aversion (risk-seeking behavior), and r < 0 denotes risk-seeking behavior (risk aversion) for gains (losses). Using this utility function, we denoted the expected utility of each alternative (A) as:

(4) $EU\left(A\right)=\sum _{x\in A}p\left(x\right)u\left(x\right)$

We calculated the difference in expected utility between the safe option (S) and the risky option (R) using:

(5) $\Delta EU=EU\left(S\right)-EU\left(R\right)$

The likelihood function is:

(6) $L=\left(\begin{array}{cc}\Phi \left(\Delta EU\right)& \text{if}\text{Safe}\\ 1-\Phi \left(\Delta EU\right)& \text{if}\text{Risky}\end{array}\right)$

where Φ is the cumulative distribution function of the standard normal distribution. The likelihood function was estimated using maximum likelihood with the Broyden-Fletcher-Goldfarb-Shanno algorithm. We estimated the average risk factor for the whole sample in the pain and control conditions in the following way (allowing for heterogeneity in risk preferences):

(7) $\hat{r}=r_0+{\alpha }_{0}Pain+{\alpha }_{1}Round$

where $r_0$ represents the estimate of the constant, Pain is a dummy for the pain condition, and Round is a dummy for the second round of the task. An alternative model also included the interaction term Pain × Round, which allows the effect of pain to differ across the two task rounds. Standard errors were clustered at the individual level. Estimates were provided separately for gains and losses in order to allow for different curvature of the utility function for positive and negative outcomes.

For the discount factor, we assume exponential discounting and the following function for discounted utility:

(8) $u\left(\text{x}\right)={\delta }^t{u}_t\left(\text{x}\right)$

where $\delta$ denotes the discount factor and t denotes the number of days until the outcome will be realized. In function (8) we assume that the utility function at time t, $u_t\left(x\right)$ , takes form as in (3) with estimated average risk factor as described above. Using (8) we calculated discounted utility separately for the immediate and the delayed reward. We then calculated the difference in discounted utility between the delayed (D) and the early (E) options using:

(9) $\Delta U=U\left(D\right)-U\left(E\right)$

We can then describe the likelihood function as:

(10) $L=\left(\begin{array}{cc}\Phi \left(\Delta U\right)& \text{if}\text{Delayed}\\ 1-\Phi \left(\Delta U\right)& \text{if}\text{Early}\end{array}\right)$

where Φ is the cumulative distribution function of the standard normal distribution. We used the same estimation method as for risk preferences. Similarly, we estimated the average discount factor for the whole sample in the pain and control conditions, allowing for heterogeneity in time preferences:

(11) $\hat{\delta }={\delta }_0+{\alpha }_{0}Pain+{\alpha }_{1}Round$

where ${\delta }_0$ represents the estimate of the constant, Pain is a dummy for the pain condition, and Round is a dummy for the second round of the task. An alternative model also included the interaction term Pain × Round, which allows the effect of pain to differ across the two task rounds. Standard errors were clustered at the individual level.

We finally considered data at the individual level by investigating whether pain had the same effect on all individuals in each task and whether individuals who changed their behavior in response to pain on one task also changed their behavior in a similar fashion on the other tasks. For the latter, we calculated the difference in the proportion of risky and impatient choices in the pain condition compared to the control condition, for each individual and task. We then performed Pearson correlations of the difference scores to explore the relationship between choices in the three tasks.