Fixed-Equity Auctions with Common Values

The experiment involves a mixed within- and between-subject treatment design.

The within-subject treatment will vary the fixed-equity rate that participants of auctions must pay. The rate is redrawn randomly at the beginning of each round for each group from the uniform distribution over 0%, 20%, 40%, and 60%.

The between-subject treatment changes the way in which earnings from the auction are converted into currency payments for subjects. In all auctions, payoffs are denominated in terms of points. In the baseline treatment, 100 points are worth one dollar. In the risk aversion treatment, 100 points are worth one dollar until 3000 points, at which point the conversion rate becomes 250 points to one dollar.

2025-09-24

2025-10-31

The primary outcome variables will be bids and auction revenue.

Bids and auction revenue will be directly observed, so no construction needs to take place.

N/A

N/A

Subjects will participate in a lab experiment using common-value auctions.

We develop a controlled environment to examine how security-bid instruments shape behavior in common value auctions. Participants face a first-price auction over a project whose value equals the sum of independent and identically distributed signals. As part of each auction, there is a fixed equity share ranging from 0% to 60%. The winner of the auction must pay their bid plus this equity share of the final value of winning. Some sessions will include a treatment to induce (apparent) risk aversion, described further below. All experimental sessions will be carried out in-person in the CUBES Laboratory at the University of Queensland.

Subjects begin the experiment by reviewing instructions that describe the structure of the auctions they will participate in. They are presented with three examples that demonstrate how the auctions work as well as how payoffs can be computed. After reviewing the examples, subjects complete a quiz and receive feedback about the correct answers for the quiz. They then move on to complete 30 rounds auctions.

In the auctions, all valuations and bids are described in terms of points. Each buyer in an auction receives a signal that is drawn from the uniform-discrete distribution between 0 and 1000 (in 20 point increments). Buyers’ signals are drawn independently of each other. They are told that the value of winning is the sum of the three buyers’ signals. Buyers make bids in points using a slider (see Figure 1) that is restricted to be between 0 and 3000 and takes values in 20 point increments. Buyers that lose receive their budget of 3000 points. Buyers that win receive (1) their budget, (2) minus their bid, (3) plus the product of the value of winning and one minus the fixed equity rate.

Our design combines between- and within-treatment variation.

Our within subject treatment varies the fixed equity rate which applies to the auction. We randomly select between 0%, 20%, 40%, and 60% for each group within each round. Each rate is drawn with an equal chance.

In our between-subject treatment, we vary the way in which subjects are paid. Specifically, we change the rule by which the point payoff from a single round of the auction is converted into dollars. In our baseline treatment, 100 points are always worth $1. In our “risk aversion” treatment, each 100 points up to 3000 is worth $1. Each additional 100 points above 3000 is only worth $0.40.

We provide subjects with a figure that helps them compute payoffs. The figure includes two graphs, and changes as the subject activates and moves the slider. On the left-hand side, the graph computes the buyers’ payoff in points. Before the slider is activated, the graph demonstrates the possible values of winning given their signal, and indicates that the payoffs for losing are constant at 3000 for all possible values of winning. Once the slider has been activated, the figure shows the payoffs that the subject would receive for all possible values of winning conditional on their current bid. The right-hand-side graph shows subjects how their payoff in points maps to their payoff in dollars. When the slider has not yet been activated, the single point of their payoffs conditional on losing the auction is marked on the graph. Once the slider has been activated, the range of potential payoffs conditional on winning the auction at the current bid is marked on the graph.

The experimental software will randomize automatically. Groups, signals, and fixed-equity rates are re-randomized each round.

Randomization will occur in each round.

No

Our final sample size is expected to be 150-170 subjects.

With 160 subjects participating in 30 rounds, the total number of observations is expected to be 4800.

We expect to have 80 subjects in the two between-treatments.

Pre-Analysis Plan