The Role of Psychological and Physiological Factors in Decision Making under Risk and in a Dilemma

Different methods to elicit risk attitudes of individuals often provide differing results despite a common theory. Reasons for such inconsistencies may be the different influence of underlying factors in risk-taking decisions. In order to evaluate this conjecture, a better understanding of underlying factors across methods and decision contexts is desirable. In this paper we study the difference in result of two different risk elicitation methods by linking estimates of risk attitudes to gender, age, and personality traits, which have been shown to be related. We also investigate the role of these factors during decision-making in a dilemma situation. For these two decision contexts we also investigate the decision-maker's physiological state during the decision, measured by heart rate variability (HRV), which we use as an indicator of emotional involvement. We found that the two elicitation methods provide different individual risk attitude measures which is partly reflected in a different gender effect between the methods. Personality traits explain only relatively little in terms of driving risk attitudes and the difference between methods. We also found that risk taking and the physiological state are related for one of the methods, suggesting that more emotionally involved individuals are more risk averse in the experiment. Finally, we found evidence that personality traits are connected to whether individuals made a decision in the dilemma situation, but risk attitudes and the physiological state were not indicative for the ability to decide in this decision context.


HRV OVERVIEWS
summarizes the HRV of all observations during these periods, LF HF indiv.means the HRV measures averaged by framework for each individual (the second of which was used for the analysis).

EXTENSION BEYOND EUT
We also looked at results beyond an EUT framework by allowing for probability weighting and assuming a utility function of U i (x, p) = w i (p) · v i (x) where w i (p) represents a probability weighting function, assigning objective probabilities a subjective weight, and v i (x) the utility from receiving outcomes. We used functional forms of w i (p) = Supplementary Figures 1 (a) and (b) illustrate the distributions of individual r i and γ i estimates for the HL method. 1 For this overview and in the following analysis we have restricted our sample to 45 individuals that had a single switching point (SSP) in both periods of HL to make the graphs readable and to ensure convergence of our maximum likelihood models. We further investigated how demographics, personality traits and physiological states were related to r and γ. Supplementary Table 3 includes the results from our analysis, showing potential personality and gender effects for r and γ, respectively, which are however not robust to alternative specifications. The same is true for the role of HRV in r. However, there is a significant relationship between HRV and probability weighting suggesting that more stressed individuals are more likely to display inverse S shape-type probability weighting. This could indicate that the relationship observable before in the EUT-based analysis could be driven by probability weighting. *** indicates significance at the 1% level, ** 5% significance and * 10 % significance. Standard errors (in brackets) are clustered by individuals. The availability of HRV data has reduced the sample between estimations (due to missing or unreadable data).

Introduction
The following part, or game, of this session is an economic experiment. This means that the amount of your final payment will depend on the decisions you take in the following stages. I.e., your decisions taken on the next screens, together with the random outcome of an external probability distribution, will directly translate into how much you will be paid at the end of the experiment. Please follow the instructions carefully, and please raise your hand if you have a question: an experiment administrator will come to you. During the experiment, any talking or other communication between participants is forbidden.
You will make decisions during this experiment by responding to questions displayed on the computer screen in front of you. After you have completed your responses for the decisions on each screen, please press the Continue button at the bottom of the screen to proceed to the next screen. Your decisions in this experiment are anonymous, and you are identified solely by your participant number. The payment you will receive at the end of the experiment will be kept confidential from all other participants.
This experimental game will be continued over two rounds. You will receive instructions for each step of the experimental game on your screen. At the conclusion of the experiment, the computer will randomly select one decision from Type One and one decision from Type Two to be played to determine the amount that you will be paid. This means that you (or the administrator) do not know which decision will be selected. Therefore, it would be reasonable to treat each decision as if it were the decision that will be selected for determining your final payoff.

HL example instructions
Please make sure to read all instructions very carefully. This is an instruction screen. You do not have to make any decisions on this screen. On the NEXT screen you will have to make nine decisions between two lotteries. For each of the nine decisions you MUST select either option A or option B. Each lottery is characterized by the probability of receiving one of two payoffs. Below is an EXAMPLE of only two of the nine decisions that you will be required to make In decision 1 you have to choose between lottery A1 and lottery B1. In lottery A1 you either receive $1 with probability 0.3 and $3 with probability 0.7. In Lottery B1 you get $0 with probability 0.5 and $5 with probability 0.5.
Remember, at the end of the experiment one decision will be selected at random. This decision will then be played out and will then contribute to your final payment. Because the decision that is played is selected randomly you do not know which decision will be selected and hence it would be reasonable to answer all decisions as if they were the decision that determined your final payment. When you select an option, an X will indicate your choice. You can revise your choice as many times as you like. After you have made all nine choices, click the Continue button to move to the next screen.

HL choice list
Supplementary

AH example instructions
In this part of the experiment you will consider many options of gambles. The gambles will differ according to the amount of money at stake and the chances of winning that money. An option of gambles might look like this. Notice, you see all available gambles in the option by moving the slider bar back and forth, GIVE IT A TRY! The pie chart represents the probability of winning while the bar chart represents the possible gain. See how there is a tradeoff between these two variables as you move the slider.
Maximum gain is $10.00. Each 1 percent increase in the pie decreases possible earnings by $0.10. Each 1 percent decrease in the pie increases possible earnings by $0.10 Supplementary Figure 2. AH picture Notice that in this example, every time you try to increase the chance of winning by 1 percentage point, you reduce the amount you would gain by $0.10. Likewise, each time you increase the amount you can gain by $1, you reduce the chance of you winning it by 10 percentage points (that is 1 divided by 10). You are simply required to position the slider in the position that you like the most for each of the nine decision screens. Just as before, only one of your nine decisions will be selected at random. Because you do not know which decision will be selected it would be reasonable to make each decision as if it were the decision that contributed to you final payment.

AH choice pairs
Supplementary Table 5 includes the 9 pairs of budgets µ and price in the two rounds of our experiment. The price reflects the cost of getting 1% extra of a winning probability, and µ the amount that can be won with a corresponding probability of zero, or the budget. To win with any positive probability, participants have to buy additional winning probability. For example, in round 1, a participant could chose to win 27.3 − 10 · 0.28 = 24.5 with a probability of 10%, 27.3 − 20 · 0.28 = 21.7 with a probability of 20%, and so on.