Payoff variance in preference elicitation with the BDM mechanism

We implement the BDM mechanism in three repeated rounds to elicit willingness-to-accept for an induced value item. The value of the item is held constant at $3. The distribution of possible offers ranges from $0 to an upper bound that is exogenously changed each round to $4, $6, and $12 in random order. Shifting the upper bound changes the variance of the payoff, and we hypothesize it impacts subject behavior to explain overbidding (in $12), underbidding (in $4) and more symmetrical bidding (in $6) around the induced value.

2025-12-01

2025-12-05

Individual willingness-to-accept values in each treatment

We use the elicited values to test whether moving the upper bound of the support set results in changes to the distribution of WTA values. Please see the Analysis Plan for more details.

Individual risk preference measures elicited via the Bomb Risk Elicitation Task (BRET) from Crosetto and Filippin (2013) and self-evaluation.

We utilize the secondary outcomes to conduct robustness checks of the primary hypothesis and explore heterogeneous effects by risk preferences. Please see the Analysis Plan for more details.

Our experiment is divided in two parts. In the first part, subjects are asked to submit offers to sell a card worth $3 to the experimenter. We vary on a within-subjects basis the upper bound of the support set at $4, $6, and $12 in three repeated rounds in random order with the lower bound remaining at $0. At the end of the experiment, one of the three rounds is selected for realization. Following the BDM mechanism task, we ask respondents about their strategy selection process and give them the opportunity to explain a rationale in an open response format.

The second part of the experiment elicits subjects' risk preferences. We implement the static version of the BRET (Crosetto and Filippin, 2013). Subjects complete the task once with no practice rounds. The task presents participants with 100 boxes arranged in a 10x10 grid. One randomly selected box holds a bomb while the other 99 contain a reward of $0.10. Each subject then chooses how many boxes to collect. If the bomb is among the selected quantity of boxes, the participant receives no additional earnings from the task; otherwise, we add the amount of money inside the collected boxes to the subject's total payoff.

As a secondary measure of risk preferences, we also employ the self-reported risk question from the German Socio-Economic Panel survey (Dohmen et al., 2011).

Computer; all randomizations are performed within Qualtrics.

Treatment order is randomized at the individual level.

No

300 individuals

300 individuals

900 observations (300 individuals and 3 rounds)

We utilize the data from similarly parameterized treatments in Drichoutis et al. (2025) to estimate the inputs to our power calculations. With an induced value of $3.00, the average offer shifted from $2.701 with a support set upper bound of $4.00 to $3.158 with a support set upper bound of $6.00. Each subject participated in both treatments. The pooled standard deviation of the two offer distributions was 0.895. In our power analysis presented below, we conservatively assume a between-treatment correlation of 0.3, compared to the actual observed correlation of 0.501. We employ the asymptotic relative efficiency (ARE) method in our power calculation which estimates the sample size required under a parametric t-test at a given power level and converts the result to the sample size required by the nonparametric Wilcoxon signed-rank test that we use to test our primary hypothesis (Faul et al., 2009). The sample size required under a t-test is then 51. The ARE of the Wilcoxon test is approximately 0.955, implying a sample size of 53 (Faul et al., 2009). Utilizing the actual observed correlation value of 0.509 yields a sample size of 39. In order to ensure our tests analyzing the subpopulation of risk-tolerant subjects are adequately powered, we reviewed three BRET studies reporting the proportions of risk-averse, risk-tolerant, and risk-neutral responses and found that, on average, 24.3% of participants exhibited risk-tolerant behavior (Crosetto & Filippin, 2013; Gioia, 2017; Soetevent and Romensen, 2017). Our analysis, therefore, indicates a total sample size of 218 individuals provides adequate power to test our secondary hypotheses regarding heterogeneity by risk preferences. To account for attrition and unusable responses, we plan to target 300 total respondents which would yield approximately 199 risk-averse subjects, 73 risk-tolerant subjects, and 29 risk-neutral subjects. In the event that our initial sample does not reach the required threshold of 53 risk-tolerant subjects, we intend to extend our data collection to additional subjects until the quota is met. Please see the Analysis Plan for more detail and supporting calculations.

BDM Variance Pre-Analysis Plan