Scaling and Equity Auctions: The Types-as-Quantities Case

The experiment primarily involves a between-subject treatment design. Each session will involve either scaling auctions or equity auctions.

2025-10-23

2025-11-14

The focus of our study will be the outcomes of the auctions, both in terms of the expected amount the auctioneer would need to pay the winning bidder and the expected costs that would need to be spent on the project.

This study compares two procurement auction formats, scaling (unit-price) and equity-bid auctions, under uncertainty about input quantities. In each round, participants bid for the right to complete a project that requires two costly inputs and a fixed setup cost. In the scaling treatment, bidders specify per-unit prices for each input, and the bidder with the lowest weighted score wins. In the equity treatment, bidders request a percentage reimbursement of their variable costs, and the lowest requested share wins. After winning, payoffs depend on realized input quantities, which vary randomly to capture cost uncertainty. The design allows us to compare how the two mechanisms allocate risk and select efficient providers when project requirements are uncertain.

This experiment studies how different procurement auction formats perform when there is uncertainty about the amount of inputs a contractor will need to complete a project. We compare two mechanisms: scaling (unit-price) auctions and equity-bid auctions. In both settings, participants compete in a reverse auction to win the right to carry out a project that requires two costly inputs in addition to a fixed setup cost. Each participant has private information about their likely input needs, which are drawn randomly each round to represent uncertainty about real-world project requirements.

In the scaling treatment, participants submit a bid for each input, representing the price per unit they wish to be paid. These two bids are combined using fixed weights to form a score, and the bidder with the lowest score wins the auction. The winner then pays the fixed cost and earns or loses points depending on the difference between their bid prices and the true input costs once quantities are realized. In the equity treatment, participants instead submit a single bid indicating the percentage of their variable costs they want reimbursed. The lowest percentage bid wins. The winner receives a fixed upfront payment and reimbursement equal to their chosen share of realized variable costs. In both treatments, only one randomly selected round is used to determine final payment in cash.

The experiment consists of 30 rounds, each with random rematching between bidders. Subjects first complete detailed instructions, examples, and a comprehension quiz with feedback to ensure understanding. Each round’s screen shows the participant’s personal input requirements, potential payoffs under different outcomes, and a slider interface to enter bids. After each round, participants see both bids (or scores) and the corresponding payoffs. At the end, participants complete a short demographic questionnaire, a cognitive reflection test, and an exit survey on their understanding and decision process. This design allows us to compare how the scaling and equity formats affect bidding behavior, cost efficiency, and implicit risk sharing in a controlled environment.

The experimental software will randomize automatically. Groups and types are re-randomized each round.

Groups and types are re-randomized each round.

No

Our final sample is expected to be 90-110 subjects.

With 100 subjects participating in 30 rounds, the total number of observations is expected to be 3000.

We expect to have 50 subjects in the two between-treatments.