Belief Precision and Communication

Last registered on September 04, 2023


Trial Information

General Information

Belief Precision and Communication
Initial registration date
August 30, 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
September 04, 2023, 6:48 AM EDT

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



Primary Investigator

University of Potsdam

Other Primary Investigator(s)

PI Affiliation
University of Potsdam

Additional Trial Information

In development
Start date
End date
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
In this paper, we study one channel through which communication may facilitate cooperative behavior. In a prisoner’s dilemma experiment, we hypothesize that communication not only makes individuals more optimistic that their partner will cooperate but also increases the precision of this belief, thereby reducing strategic uncertainty. To disentangle the shift in mean beliefs from the increase in precision, we elicit beliefs and precision in an incentive-compatible two-stage procedure and in three situations: without communication, before communication, and after communication. Comparing mean beliefs without and before communication, we can estimate the mean shift. The comparison of the precision of this belief before and after communication provides our measure for a reduction of strategic uncertainty.
External Link(s)

Registration Citation

Bruttel, Lisa and Vasilisa Petrishcheva. 2023. "Belief Precision and Communication." AEA RCT Registry. September 04.
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Experimental Details


Intervention Start Date
Intervention End Date

Primary Outcomes

Primary Outcomes (end points)
(1) Belief precision without communication,
(2) Belief precision before communication,
(3) Belief precision after communication.
Primary Outcomes (explanation)
Details are provided in the “Experimental Design” section.

Secondary Outcomes

Secondary Outcomes (end points)
(1) Belief without communication,
(2) Belief before communication,
(3) Belief after communication,
(4) Cooperation without communication,
(5) Cooperation with communication.
Secondary Outcomes (explanation)
Details are provided in the “Experimental Design” section.

Experimental Design

Experimental Design

In this experiment, subjects interact in a prisoner’s dilemma. They play the game twice, each time with a different random partner. Feedback about the actions of the partner in both games is provided only after the second game. Each subject can choose between actions X and Y. We use the following calibration of the game :
(X,X): (50,50),
(Y,Y): (20,20),
(X,Y): (10,80),
(Y,X): (80,10).

This experiment contains two stages. In Stage 1, two subjects are randomly matched to play a prisoner’s dilemma without communication. In Stage 2, subjects are rematched to play a prisoner’s dilemma with communication with a new partner. In total, we elicit three point beliefs and three measures of belief precision per subject. The timeline of the experiment is as follows.


- General instructions and control questions.
Stage 1: No communication.
- Belief elicitation: belief without communication [beliefnocom, precisionnocom],
- Decision in the prisoner’s dilemma: decision 1 [cooperationnocom].
Stage 2: Communication.
- Rematching subjects,
- Instructions about upcoming communication,
- Belief elicitation: belief before communication [beliefbefore, precisionbefore],
- Communication: 5-minute open chat,
- Belief elicitation: belief after communication [beliefafter, precisionafter],
- Decision in the prisoner’s dilemma: decision 2 [cooperationcom].


This experimental design is before-after within-subject. We made this choice based on two key arguments.

Argument 1 (Within-subject advantage). In addition to aggregate comparisons of main outcomes without, before, and after communication, we observe individual effects too. We collect data on three point beliefs and three measures of belief precision per subject. Thus, we can observe a potential change in belief precision at the individual level.

Argument 2 (Not randomizing the order). In the context of our experiment, randomizing the order of Stages 1 and 2 (without and with communication) is not particularly useful. Placing Stage 2 (with communication) first would create, in expectation, strong spillover effects on the outcomes of Stage 1 (without communication). As the changes in the baseline belief about cooperativeness in the population without communication are not the main focus of our study, we aim to focus on the benchmark belief without *any* communication. Furthermore, randomizing the order of the belief elicitation before and after communication does not make sense for obvious reasons.


We elicit beliefs and their precision at three points in time: once for the decision without communication and twice for the decision with communication, namely before and after the chat takes place. This procedure has the advantage that we can disentangle the increase in mean beliefs with and without communication from the increase in precision we are mainly interested in. If subjects on average correctly anticipate the cooperation-enhancing effect of communication, this effect will be fully captured by the shift in mean beliefs without and *before* communication. The shift in precision before and after communication then provides a clean estimate for an increase in belief precision due to communication between the two subjects.

We elicit subjects’ beliefs by asking the question: “Do you think it is more likely that the other person you are about to interact with will choose X or Y, respectively?”. Subjects’ answer to this question is binary, i.e., X or Y.

Belief precision.
We elicit subjects’ belief precision by asking the question: “How confident are you in your assessment?”. They can answer on a continuous scale (slider) from “Blind guess” to “Absolutely sure”. The slider has no default value.

The elicitation of beliefs and belief precision is jointly incentivized using the binarized scoring rule, i.e., the closer the subjects’ guess is to the action of their partner, the higher the probability of receiving a fixed bonus is. Subjects can access detailed explanations of the incentive scheme by clicking the button “Information” on the belief elicitation screen.


Hypothesis 1 (Cooperation, replication). Communication increases cooperation rates.
We hypothesize that, on average, subjects’ cooperation rates with communication are higher than without communication, i.e., cooperationcom > cooperationnocom.

Hypothesis 2 (Average beliefs). Anticipation of communication increases subjects’ beliefs that their partner will cooperate.
We hypothesize that, on average, subjects’ belief before communication is higher than without communication, i.e., beliefbefore> beliefnocom.

In our setup, we consider two comparisons: without vs. before communication (Update 1) and before vs. after communication (Update 2).
Update 1 captures subjects’ belief updating in anticipation of communication. Importantly, in both cases, they do not receive any additional information or signal from their matched partner. However, subjects get to know that they will have a chance to deliver their arguments to their matched partner and try to convince them to cooperate. Hence, one can think of this shift as a measure of how convincing subjects expect *their argument* to be. Additionally, as there is no new information at this point, their belief precision would remain, in expectation, unchanged.

Hypothesis 3 (Belief precision). Communication increases subjects’ belief precision about their partners’ likelihood of cooperation.
We hypothesize that, on average, subjects’ belief precision after communication is higher than before communication, i.e., precisionafter > precisionbefore.

Update 2 contains a belief shift when communication is realized. Based on the law of iterated expectations, the belief, on average, does not shift anymore. At this point, subjects can judge how convincing they find their partners’ arguments and update their belief precision according to the new information.

We expect that communication reduces strategic uncertainty, i.e. it makes subjective beliefs about the partners’ likelihood of cooperation more precise. This effect can work in both directions: exchanging credible promises about cooperative choices can make subjects more certain about the likelihood that their partner will cooperate if they have already held a rather optimistic belief about the subject pool in general. Conversely, it can also turn such a general optimistic belief into a precise pessimistic belief about the cooperativeness of the partner. Based on the law of iterated expectations, these shifts should cancel out each other on average across the population of subjects making the mean belief before and after communication the same. However, the belief about the partner’s cooperation should be more precise after the communication.

Due to the matched data structure and the directed hypotheses, we will rely on one-sided matched-pairs signed-rank tests and regression analyses to test the hypotheses described above. For the non-parametric tests, we will use individual subjects as the unit of observation. We plan to use the regression analysis to account for the interdependence of individual observations after communication. Furthermore, we will analyze communication content to shed further light on communication effects on beliefs, belief precision, and cooperative behavior in humans. We plan to use (unsupervised) machine learning methods to analyze chat data in an attempt to discover not only whether but *how* communication affects these outcomes. The specific computation method depends on the characteristics of actual data (e.g., length of the messages, number of topics within the messages, variance across the messages, etc.).
Experimental Design Details
Randomization Method
Before-after within-subject design, hence, none is required.
Randomization Unit
Not applicable.
Was the treatment clustered?

Experiment Characteristics

Sample size: planned number of clusters
136 individuals.
Sample size: planned number of observations
136 individuals.
Sample size (or number of clusters) by treatment arms
136 individuals.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Power calculations for the one-tailed Wilcoxon signed-rank test (for belief precision, continuous) and one-tailed binomial tests (for beliefs and cooperation rates, binary) are based on the pilot data (N=36) with 80% power and 95% significance. We perform power calculations using G*Power (Faul et al., 2009). (1) Mean(belief precision before communication)= 3.63, Std. Dev.=1.36; (2) Mean(belief precision after communication)= 4.01, Std. Dev.=1.23; (3) Mean(belief without communication)= 0.64, Std. Dev.= 0.49; (4) Mean(belief before communication)=0.75, Std. Dev.= 0.44; (5) Mean(cooperation without communication)=0.50, Std. Dev.= 0.51; (6) Mean(cooperation with communication)=0.61, Std. Dev.= 0.49. Minimum Detectable Effect Size for (1) vs. (2): N=136; Minimum Detectable Effect Size for (3) vs. (4): N=114; Minimum Detectable Effect Size for (5) vs. (6): N=130. Therefore, as our main hypothesis focuses on belief precision and our sample size should be divisible by 4, we plan to collect 136 individual observations.
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