Price Informativeness, belief updating, and information aggregation

This study investigates how individuals update beliefs and engage in trading when presented with varying types of information, with a particular focus on the influence of consensus price signals. Rooted in the tradition of experimental economics and building on the framework of Plott and Sunder (1988), the study introduces novel features such as randomized information treatments and pairwise trading interactions. Participants engage in repeated rounds of simplified trading, where they are required to submit threshold prices reflecting their willingness to buy or sell a risky asset with an unknown payoff. The core objective is to understand how pre-trade information—especially in the form of an aggregated consensus price from previous trading activity—affects individual decision-making and belief formation.

Increasing attention has been devoted to the problem of aggregating the diffuse opinions of a large number of agents into a unique prediction. This general idea goes by the name of “Wisdom of Crowds” (WOC) and it has been applied to many contexts, from guiding investment decisions, generating new business ideas, predicting political or financial events, to forming a consensus about climate change. Various models have been proposed to capture the WOC, and empirical evidence shows that crowd consensus can potentially deliver accurate predictions. However, these predictions can be unreliable because their accuracy depends on strong assumptions on the distribution of agents’ opinions and these procedures are not robust to agents’ strategic manipulation. The goal of the MALERP project is to propose a new aggregation mechanism called "Generalized Market Predictions” (GMP) that improves upon alternative ways to harness the WOC. GMP is inspired by the literature on Financial Economics, General Equilibrium, Computer Science, and Experimental Economics. It is a flexible theory for aggregating agents’ opinions in a consensus which is reliable and efficient. These two properties are not guaranteed by other aggregators of public opinions. GMP is guaranteed to be reliable and efficient because of two innovations. First, GMP recommends informing agents about a tentative crowd consensus before they express their final opinion. Second, the consensus is calculated by weighting the opinions of different agents taking into account their past performance. To test the effectiveness of our design, we will conduct an experimental study involving real subjects.

This study investigates how individuals update beliefs and engage in trading when presented with varying types of information, with a particular focus on the influence of consensus price signals. Rooted in the tradition of experimental economics and building on the framework of Plott and Sunder (1988), the study introduces novel features such as randomized information treatments and pairwise trading interactions. Participants engage in repeated rounds of simplified trading, where they are required to submit threshold prices reflecting their willingness to buy or sell a risky asset with an unknown payoff. The core objective is to understand how pre-trade information—especially in the form of an aggregated consensus price from previous trading activity—affects individual decision-making and belief formation.

The experiment is conducted online using the oTree platform and involves around 200 adult participants recruited through Prolific or Amazon Mechanical Turk. Each session includes eight rounds of trading, with each round consisting of two trading tasks. Depending on random assignment, participants are placed into either a treatment group that receives the consensus price signal or a control group that does not. In later rounds, participants are also exposed to private asymmetric information about the potential payoffs of the asset, such that belief heterogeneity naturally emerges. Participant earnings are determined based on trade outcomes and are converted into real monetary compensation at the end of the experiment.

Through this design, the study aims to isolate the effect of informational cues on market behavior and belief accuracy, while controlling for strategic behavior typically induced by more complex market mechanisms. The findings are expected to contribute to a deeper understanding of how individuals process aggregated information and revise their expectations in economic environments characterized by uncertainty.

2025-12-21

2026-06-30

1) trading behavior
2) accuracy and convergence of beliefs

These outcomes capture the core mechanisms of interest: trading behavior reveals how participants act on information, while the accuracy and convergence of beliefs measure the extent to which information—especially the consensus price signal—is effectively processed and aggregated.

We will be testing the hypothesis of naive behavior of subjects. According to this hypothesis, which serves as a benchmark, given the difficulty of the experimental task, we expect subject not to place their prices strategically, but rather place them based on the expected value of the asset. Importantly, under this assumptoin, we should expect fully revealing behavior from subjects.

influence of price signals on belief updating

This outcome isolates the causal effect of exposure to consensus price signals on participants’ belief revision, providing direct evidence on how aggregated market information shapes individual expectations.

Additionally, we will study whether subjects give more importance to the price of their partner or to the consensus price.

The experiment follows a randomized controlled design with between-subject treatment assignment. Participants engage in repeated rounds of pairwise trading of a risky asset with uncertain payoffs. In each session, individuals are randomly assigned to a treatment group that receives a consensus price signal—computed from prior trading outcomes—or to a control group without such information. This design allows identification of the causal effect of exposure to aggregated price information on trading behavior and belief updating.

This research project is designed to investigate how individuals revise beliefs and engage in trading when exposed to varying types of information. The study is grounded in the tradition of experimental economics and is inspired by the work of Plott and Sunder (1988), with novel additions including randomized price signals and pairwise trading. The study’s goal is to understand the mechanisms by which information, particularly in the form of consensus price signals, influences belief updating dynamics and the accuracy of the resulting (aggregate) final beliefs. The methodology by which such information is elicited is by means of trading choices under different informational sets. The challenging part is disentangling the process of belief updating that we want to measure from the strategic considerations and the default price revelation that standard continuous double auction markets generate (see, e.g., Plott and Sunder, 1988). The idea is that, through different rounds of simple pairwise trades, in which participants can only submit a threshold price that divides the range of prices at which they would like to buy from those at which they would like to sell, one can understand how the information provided before the trade influences the choices of the traders and, thus, their beliefs. We will provide treated participants with some aggregation of the realized exchange prices in the previous trading task (a consensus price signal). The theory suggests that such a piece of information should influence how participants make their choices and, therefore, the price emerging from trade. Thus, if traders process the information as we expect, on average the price consensus under its disclosure should be closer to the rational value than the same quantity computed when it is not disclosed. In what follows we describe the randomized control-trial experimental study that we propose to measure such an informative effect of consensus price signal on people's beliefs.

Participants will be adults aged 18 or older, proficient in English, and recruited online through trusted platforms such as Prolific or Amazon Mechanical Turk. Each experiment
will involve between six and twelve participants and will be conducted entirely online using the oTree platform. A total of approximately twenty such experiments are planned, leading to a projected sample size of around two hundred individuals. The experiments will be hosted on a secure server, with all data stored in anonymized form and managed in compliance with institutional data protection standards.

Each experiment will last around sixty minutes. At the beginning, participants will be directed to a webpage containing the information sheet and consent form. Participation is voluntary, and only those who provide explicit consent will proceed. Those who do not consent will automatically be excluded from the study. Following consent, participants complete a brief demographic questionnaire collecting basic background data such as age, gender, education, and employment status. Moreover, we will include a simple test to measure subjects’ risk aversion (e.g. Gneezy and Potters, 1997; Filippin and Mantovani, 2023). This information will help ensure a balanced treatment assignment and support later analysis.

Once the demographic section is completed, participants will be presented with detailed instructions explaining the structure and purpose of the experiment. They will be informed that they will engage in repeated rounds of pairwise trading. Each round is composed of two trading tasks. In each session they are endowed with an amount of experimental currency units (ECU) and one unit of a financial asset. Such an asset can yield a randomly determined payoff of given amounts of ECUs, with each outcome equally likely. The random draw of the asset payoff occurs at the beginning of the round, it is kept fixed for the two trading tasks, and it is not (completely) disclosed. The trading mechanism involves pairwise interactions, where participants must choose whether they want to sell or buy 1 unit of the asset from the other participant. They interact through the platform submitting a price p. This p is such that they would like to buy the asset if the exchange price P is smaller than p and sell vice versa. They have around 3 minutes to submit the price p. The matching and trade resolution protocol specifies that if one participant submits a lower price than the other, a trade occurs at the average of the two prices, with the lower-price submitter selling and the higher-price submitter buying. Final participants’ payoffs in each trading task are computed according to the trades that occurred and the random draw of the asset payoff.

After reading the instructions, participants must complete a short comprehension quiz designed to ensure they understand the experimental rules. They cannot proceed unless all answers are correct. This step helps maintain the quality and reliability of the data. Once the quiz is passed, participants engage in a short training session, where they participate in mock trading to practice the decision-making process and become familiar with the interface and feedback system.

Each experiment session is initially randomly assigned to either the “control” or the “treatment” group. Each experiment session consists of eight rounds, with two trading tasks in each round. In each trading task, participants receive a fresh endowment and are randomly paired with another participant. They submit a price reflecting their willingness to buy or sell the asset, and trades are resolved according to the established rules. In experiment sessions assigned to the “treatment” group participants receive the consensus price signal after the first trading task. In experiment sessions assigned to the “control” group participants do not receive the signal. The signal is computed as a weighted average of the exchange prices from the first trading task of the round, with weights determined by each participant’s accumulated earnings. The signal is meant to simulate a belief revision that shall result in a modification of trading actions in the second trading task.

In the first two rounds, information is symmetric, that is, the only relevant piece of information they have is the distribution of the asset payoff. The third round introduces private asymmetric information. Each participant is placed into one of two groups of equal size. One group is informed of one of the asset payoffs that will not occur, while the other group is informed of the other (this setting closely follows the one of Plott and Sunder, 1988). In the trading couple formation of each trading task, here we take care that each member of the first group is randomly matched to one member of the second group. Rounds four through eight repeat the structure of the third round, with new asset payoff draws random and reassignments of group membership. Participants continue to receive the price consensus signal depending on the treatment assignment carried out earlier in the experiment session.

At the end of the experiment session, each participant’s total earnings in ECUs are computed and converted to real monetary compensation using a fixed exchange rate, which is communicated to participants in the instructions. Compensation is processed through the same platform used for recruitment. Participants are also shown a debriefing page that explains the purpose of the study, the nature of the information treatments, and contact information for follow-up questions.

All data collected are anonymous, and no personally identifiable information is stored. The only identifiers used are platform-specific IDs necessary for payment processing. Data are stored securely and access is restricted to the research team. The data will be retained for the time necessary to allow for academic analysis. Risks to participants are non-existent. The experimental tasks involve standard economic decision-making without deception, coercion, or sensitive subject matter. Participants are informed that they may withdraw from the experiment at any time before completion of the session.

in office by a computer

Session

Yes

20

3200 trading decisions

200 participants

Assuming 20 clusters (sessions) randomized 1:1, ≈10 participants per session (≈200 participants total), α=0.05, and 80% power, the minimum detectable standardized effect (Cohen’s d) is approximately 0.34 assuming an intracluster correlation of 0.05 (range 0.29–0.47 for ICC = 0.01–0.20). The analysis will account for clustering at the session level.