Knapsack Auctions

Last registered on May 08, 2023

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Pre-Trial

Trial Information

General Information

Title

Knapsack Auctions

RCT ID

AEARCTR-0011146

Initial registration date

March 28, 2023

Initial registration date is when the trial was registered.

It corresponds to when the registration was submitted to the Registry to be reviewed for publication.

First published

March 30, 2023, 4:01 PM EDT

First published corresponds to when the trial was first made public on the Registry after being reviewed.

Last updated

May 08, 2023, 11:50 PM EDT

Last updated is the most recent time when changes to the trial's registration were published.

Locations

Country

Australia

Region

VIC

Primary Investigator

Name

Peyman Khezr

Affiliation

Contact Primary Investigator

Other Primary Investigator(s)

PI Name

Vijay Mohan

PI Affiliation

Contact Investigator

Additional Trial Information

Status

In development

Start date

2023-03-30

End date

2023-08-31

Keywords

Behavior

Additional Keywords

Auctions

JEL code(s)

Secondary IDs

Prior work

This trial does not extend or rely on any prior RCTs.

Abstract

A well-known problem in the scientific community is the 'Knapsack Problem', which essentially deals with how to fit objects of varying dimensions, and worth different values, into a space with a limited capacity (the knapsack). In general, this problem has been encountered in a number of applications ranging from filling cargo in an airplane, to selling advertisement slots on the internet or on television. Recently, there has been an expanding volume of research in the application of the Knapsack Problem in the context of blockchains; specifically, this research seeks to examine how transactions of varying data sizes can efficiently be allocated into a block with limited data capacity.

Our project focuses on developing 'Knapsack Auctions': a mechanism to allocate transactions to blocks that factors in asymmetric information between participants in a blockchain. This project has both a theoretical and an experimental component. While the theory provides broad guidelines on how to construct a Knapsack Auction, it has gaps relating to the behavioral responses of agents. To fill this gap, we conduct experiments on three different versions of the Knapsack Auction: the discriminatory-price auction, the generalized second-price (GSP) auction and the uniform-price auction. There are three central issues the experiments seek to address: first, which of the 3 auction versions yields the highest revenue for the seller; second, whether the uniform price auction outcomes conform to theoretical prediction of truthful bidding ; and third, the extent to which the discriminatory and GSP auctions result in under-bidding.

External Link(s)

Registration Citation

Citation

Khezr, Peyman and Vijay Mohan. 2023. "Knapsack Auctions." AEA RCT Registry. May 08. https://doi.org/10.1257/rct.11146-1.1

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Experimental Details

Interventions

Intervention(s)

The study involves lab experiments to evaluate 3 different candidates for a Knapsack Auction.

Intervention Start Date

2023-03-30

Intervention End Date

2023-05-31

Primary Outcomes

Primary Outcomes (end points)

(a) The revenue obtained from each variant of the Knapsack Auction
(b) Whether participants engage in truthful bidding or not
(c) Efficiency of each variant

Primary Outcomes (explanation)

Secondary Outcomes

Secondary Outcomes (end points)

Secondary Outcomes (explanation)

Experimental Design

The experiment will seek to compare three alternative candidates for Knapsack Auctions: the discriminatory-price (DP) auction; the generalized second-price (GSP) auction; and, the uniform-price (UP) auction. Each variation is a treatment. Each iteration of an auction treatment involves 7 participants, and there are 10 iterations per treatment; each iteration will have different participants. There are 20 rounds of bidding planned for each iteration of the treatment.

In order to conduct these experiments, participants will be provided a units of experimental currency. The will also be assigned hypothetical objects with randomly assigned sizes. The participants will be instructed to submit bids (of the experimental currency) so that their object can be selected to fit into a knapsack of limited capacity. Each participant will be assigned a random value of the benefit (measured in units of the experimental currency) received if the object is indeed selected to fill the knapsack. Their cost will be in experimental currency units and will depend on the nature of the auction, as described below:
(a) In a DP auction, the cost to a participant will be his or her bid.
(b) In a GSP auction, the participant will pay the amount of the next lower bid.
(c) in a UP auction, all participants will pay a uniform amount equal to the highest losing bid.

A participant's payoff from the auction is the benefit minus the cost, again measured in units of the experimental currency. The goal of the participants will be to maximize their payoffs.

The outcomes we wish to test are:
(1) Which of the 3 auction versions yields the highest revenue for the seller
(2) Whether the uniform price auction outcomes conform to theoretical prediction of truthful bidding
(3) The extent to which the discriminatory and GSP auctions result in under-bidding
(4) How each of the versions perform in terms of efficiently allocating the knapsack space to potential bidders

Experimental Design Details

Randomization Method

Participants are randomly assigned to each treatment. Moreover, each participant will be randomly assigned values and sizes for objects to fit into the knapsack in every round that will be generated by a random number generator.

Randomization Unit

There are 3 treatments and 10 iterations per treatment. Each individual is randomly selected into a treatment, and then randomly assigned to an iteration.

Was the treatment clustered?

Yes

Experiment Characteristics

Sample size: planned number of clusters

There are 3 variations (treatments) of the Knapsack Auction. Each treatment will have 10 iterations, each with a distinct set of participants. So there will be 30 distinct iterations of the auction.

Sample size: planned number of observations

Each iteration will have 7 participants. No participant can take part in more than one iteration. The total number of unique participants required is 210 participants. Each participant will take part in 20 rounds of bidding in their assigned iteration, so there will be (a maximum of) 4200 bids across all rounds of the auction. Also given that there are 10 iterations for each version of the the knapsack auction, we collect 10 independent observations for each version.

Sample size (or number of clusters) by treatment arms

The bids will placed across 600 rounds of auction bidding, with 200 rounds for each treatment.

Minimum detectable effect size for main outcomes (accounting for sample design and clustering)

Supporting Documents and Materials

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