Bidder Power in a Multi-Unit Auction

2023-10-31

2023-11-30

Subjects' decisions and market outcomes:
- two bids per round and subject (40 per subject; 40 per cluster in treatment B1, 80 per cluster in treatment B2),
- one market price per round (20 per cluster).

In the following, we list our hypotheses and the related statistical tests.

With Hypothesis 1, we examine if two large human bidders are able to lower the price in comparison to the situation with only one large human bidder.

Hypothesis 1: The price of the good in B2 is lower than the price in B1.

Test: We calculate the average price across all rounds for each individual (B1) and each pair of individuals (B2). Then we use the Wilcoxon-Mann-Whitney test to compare the average prices between the two treatments.

With Hypothesis 2, we examine if the presence of an additional large human bidder in B2 reinforces or weakens play according to the predicted strategy (i.e. bidding truthful for the (first) higher bid, and bidding lower than their valuation on the second (lower) bid) compared to B1.

Hypothesis 2a: Truthful bidding is not different between the two treatments.

Test: We calculate the average of the higher of the two bids for each individual (B1) and each pair of individuals (B2) across all rounds. We then use the Wilcoxon-Mann-Whitney test to compare these numbers between the two treatments. To account for the different valuations of each bidder in each round, we also use (i) the percentage deviation of each bid from the bidder's valuation, and (ii) the absolute deviation of each bid from the bidder's valuation.

Hypothesis 2b: Strategic bidding is not different between the two treatments.

Test: We calculate the average of the lower of the two bids for each individual (B1) and each pair of individuals (B2) across all rounds. We then use the Wilcoxon-Mann-Whitney test to compare these numbers between the two treatments. To account for the different valuations of each bidder in each round, we also use (i) the percentage deviation of each bid from the bidder's valuation, and (ii) the absolute deviation of each bid from the bidder's valuation.

We will also use regressions on individual-level data as an additional test for Hypotheses 1, 2a, and 2b.

Questionnaire items: subjects' gender, student of management or economics (1=yes,0=no), student of game theory (1=yes,0=no), high school math grade, individual decision times (in seconds).

Here is the pipeline of planned exploratory analyses/questions:
- How do revenue and efficiency differ between treatments?
- Do subjects learn over time (the number of auctions)? Do subjects in B1 learn to bid truthfully on their (first) higher unit and to underbid on their (second) lower unit? Do subjects in B2 learn to coordinate (and underbid on their second unit) or do they compete stronger as time passes?
- Can past periods' bids and outcomes explain current periods' behavior?
- Do questionnaire characteristics explain observed behavior?

We conduct a lab experiment with two treatments.

In treatment B1, one subject with demand for two units of a good participates in an auction. Two units of the good are auctioned. Three computer-simulated bidders (each with demand for one unit of the good) bid their valuation.

In treatment B2, two subjects with demand for two units of a good participate in an auction. Two units of the good are auctioned. One computer-simulated bidder (with demand for one unit of the good) bids its valuation.

In each auction, the highest two bids receive a unit of the good. The price is determined by the highest rejected bid. The bidders of the successful bids pay their private valuation minus the price. All other bids do receive nothing.

Each individual (B1) or each pair of individuals (B2) goes through 20 rounds (auctions). In B2, the matching of pairs is fixed throughout the experiment.

Not available

A random subset of potential subjects in a database will receive an invitation to one or more of the sessions at a time. The randomization is computer-based. The potential subjects do not know the content of the experiment, and they also do not know the treatment for which they sign up at the time they register. Each subject only takes part in one experimental session.

Randomization is by experimental session. All participants of a session participate either in treatment B1 or treatment B2.

No

40 independent observations per treatment: treatment B1 with 40 individual subjects, treatment B2 with 40 pairs of two subjects.

120 subjects.

40 subjects in B1, 80 subjects in B2.