Approximation in Complex Pricing Mechanisms

Last registered on September 19, 2022


Trial Information

General Information

Approximation in Complex Pricing Mechanisms
Initial registration date
September 13, 2022

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
September 19, 2022, 4:07 PM EDT

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


Primary Investigator

University of Arizona

Other Primary Investigator(s)

PI Affiliation
University of Saskatchewan
PI Affiliation
University of Guelph
PI Affiliation
Purdue University

Additional Trial Information

In development
Start date
End date
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Recent research in mechanism design has shown that simpler pricing strategies can closely approximate the profits obtained by more complex profit maximizing pricing mechanisms. But these simpler strategies are highly sensitive to the firm’s knowledge of the distribution of demand for each good. This has restricted empirical research on the topic to case studies and limited the application of these pricing strategies. The question remains, how well do simpler pricing strategies approximate the profit maximizing mechanism? We propose to use a lab experiment to determine how simpler pricing strategies perform when gaps exist in firm knowledge regarding the demand for goods and the correlation between consumers’ reservation values for goods.
External Link(s)

Registration Citation

Michler, Jeffrey et al. 2022. "Approximation in Complex Pricing Mechanisms." AEA RCT Registry. September 19.
Experimental Details


Participants in the experiment act as multi-product monopolies selling goods or bundles of goods into a market of automated computer buyers (consumers). Our interest in the experiment is how less complex pricing mechanisms perform relative to the profit maximizing mechanism when firm knowledge of market demand is incomplete.

Our intervention randomizes what information a participant has regarding market demand. We have four different interventions/treatments:

1) Perfect information: Participants are provided with information regarding both the underlying distribution of consumer valuations and the correlation between consumers' valuation for the goods.

2) Unknown distribution: Participants are provided with no information regarding the underlying distribution of consumer valuations.

3) Unknown correlation: Participants are provided with no information regarding the correlation between consumers' valuation for the goods.

4) No information: Participants are provided with no information regarding both the distribution and the correlation.
Intervention Start Date
Intervention End Date

Primary Outcomes

Primary Outcomes (end points)
We have six primary outcomes:
1) Profitability: the strategy that attains the most money in the experiment.
2) Adaptability: the most profitable strategy across markets.
3) Effectiveness: the share of the maximum achievable profit obtained across all rounds and all markets.
4) Convergence: the most profitable strategy across rounds.
5) Maximin: the strategy that limits losses (has the largest minimum).
6) Variability: the strategy that minimizes the variance in profits.
Primary Outcomes (explanation)
The six primary outcomes are defined mathematically in the analysis plan document attached to this registration.

Secondary Outcomes

Secondary Outcomes (end points)
We have two sets of secondary outcomes. First is the decision-making process, measured as a) response time and b) number of values entered in a price field. Second is emotional response measured after each question using a slide bar and emojis.
Secondary Outcomes (explanation)
Details on construction of the secondary outcomes is in the analysis plan document attached to this registration.

Experimental Design

Experimental Design
A player in the lab experiment will act as a firm trying to decide the prices to set for the various goods that they sell. The marginal cost for all goods is zero. The "consumers" that the player is trying to sell to are a set of 10,000 computer buyers or bots that are pre-programmed to purchase goods or bundles of goods if the price is less than or equal to that bot's preset valuation. Firms are monopolistic, so each player is the sole seller in her market and does not compete against other players. We constrain the prices a player can set and the reservation values for the bots to be integers. The goal for the player is to set prices in order to maximize revenue (profit). Play takes place over 40 of rounds. Payouts will be calculated as a fixed percentage of average revenue earned across three randomly selected rounds.

There are four parameters which we will experimentally manipulate in order to induce random variation in the markets that a given play i will face.

1) Pricing Strategy. Through the course of the game, all players will play each of the four pricing strategies and be asked to make decisions about how to price their goods using that strategy. The game will take place in 4 sub-games with 10 rounds in each sub-game. In a sub-game the player is assigned, at random, one of the four pricing strategies. They then use that strategy for all 10 rounds in the sub-game. After the sub-game, the player is then assigned, at random, to a second of the pricing strategies. This continues until the player has played with all 4 pricing strategies.

2) Number of goods sold by the firm. In the experiment, there will be four possible goods that a firm could sell, denoted by color (blue, green, yellow, and red). Before the start of the game each player will be told the number of goods they are selling (2 through 4). For a given number of goods, all players selling that number of goods will be selling the same color goods.

3) Distribution of consumer valuations. At the start of the game, a player will be randomly assigned to a market in which consumer valuations are either uniformly distributed or follow a beta distribution. For the uniform distribution, valuations will follow U ~ (0,100), which has a mean of 50 and a standard deviation of 29. For the beta distribution, valuations will follow B ~ (5,5). Scaling the beta distribution by 100 gives the distribution a mean of 50 and a standard deviation of 15.

4) Correlation between consumer valuations. At the start of the game, a player will be randomly assigned to a market in which every consumer has the same correlation in their valuation for the goods on sale. Consumers will express either a negative correlation in their valuation for the goods or their valuations will be perfectly independent. Regardless of the distribution, the value for all goods will be drawn from distributions that have a correlation coefficient of -0.25.

With these four parameters, we can define four different markets which an individual player will be randomly assigned into: uniform-independent, uniform-negative, beta-independent, and beta-negative. We can also define three different production schedules which an individual player will be randomly assigned into: two goods, three goods, and four goods. This gives us 12 market-schedule combinations.

At the end of every round the participant will be asked to rate how they currently feel using a slide bar that displays different emojis.
Experimental Design Details
Randomization Method
Randomization of treatment is done by the oTree interface when participants log in to play the experiment.
Randomization Unit
Randomization is done at the participant (individual) level
Was the treatment clustered?

Experiment Characteristics

Sample size: planned number of clusters
1200 individuals.
Sample size: planned number of observations
1200 individuals.
Sample size (or number of clusters) by treatment arms
300 individuals for perfect information treatment, 300 individuals for the unknown distribution treatment, 300 individuals for the unknown correlation treatment, and 300 individuals for the unknown distribution and unknown correlation treatment.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
There is no prior literature to determine what a reasonable effect size is given our treatments and outcomes. Therefore we will maximize power by maximizing the number of individuals in the study. The Economic Science Lab (ESL) at University of Arizona currently has 2,225 students in the database. Given not all registered students activity participate in experiments, and given past experience with the share of active participants, we believe 1200 is the most students we can get to participate in the experiment.
Supporting Documents and Materials


Document Name
Experiment Instructions
Document Type
Document Description
Experiment Instructions

MD5: 91e4bf4497787794cf253d813a60f9c5

SHA1: 39f6cbfa1ccf4b5cfa56e848b6c4ad2589c4bafa

Uploaded At: September 12, 2022


Institutional Review Boards (IRBs)

IRB Name
University of Arizona Human Subjects Protection Program
IRB Approval Date
IRB Approval Number
IRB Name
University of Saskatchewan Behavioural Research Ethics Board
IRB Approval Date
IRB Approval Number
Analysis Plan

Analysis Plan Documents

Pre-Analysis Plan

MD5: 58670f26f431d3330978160695dbb861

SHA1: 09baa01d227dc915aa011e5d5507155ecd485354

Uploaded At: September 13, 2022


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