BDM mechanism design choice impact on valuation elicitation

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 exogenously changed each round to $3, $6, and $9 in random order. The distribution of possible offers is fixed across rounds and ranges from $0 to $12.

2026-02-23

2026-02-25

Individual willingness-to-accept values in each treatment

We use the elicited values to test whether moving the relative placement of the induced value within the support set results in changes to the distribution of willingness-to-accept values. Please see the Analysis Plan for more details.

N/A

Our survey maintains the same risk preference elicitation tasks from the initial experiment to minimize changes to the procedure; however, we omit the measures as secondary outcomes in this follow-up because our Analysis Plan does not include the corresponding heterogeneity analyses.

Our experiment is divided in two parts. In the first part, subjects are asked to submit offers to sell a card to the experimenter in three repeated rounds that vary within-subjects the value of the card at $3, $6 or $9 in random order. We fix the support set with lower and upper bounds of $0 and $12, respectively. 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 & 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

75 individuals

75 individuals

225 observations (75 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. As additional reference points, we conduct the same analysis using the results from our first experiment (AEARCTR-0016635). With an induced value of $3.00, mean willingness to accept increased from $3.413 in the $6.00 support range treatment to $5.451 with a pooled standard deviation of 2.069 and a between-treatment correlation of 0.42, yielding an effect size of 0.823 and sample size requirement of 15. Comparing the $6 treatment against the $4 treatment, we observe a mean shift of $0.737, a pooled standard deviation of 0.917, and correlation of 0.52, resulting in an effect size of 0.792 and sample size requirement of 16. Reducing the correlation to a hypothetical 0.25 increases the minimum sample size range to 17-22 subjects. In the interest of conservatism, we adopt the larger threshold of 53 subjects determined for the Phase 1 study. Accordingly, we target a sample size of 75 participants, representing the minimum threshold grossed up for incomplete or otherwise unusable responses.

BDM Design Elements Pre-Analysis Plan