Voluntary Information Disclosure with Bounded Rational Agents: Experimental Evidence from the Housing Rental Market

The experiments are carried out with an online survey with participants recruited via Prolific. There are two distinct surveys: one for senders (proxy for owners) and one for receivers (proxy for renters). Both sides play the rental game, which is the voluntary disclosure game adapted from Jin et al. (2021): the owner must decide whether to disclose or not the quality of the house, and the renter must guess its value. The payoffs of the game are designed such that full unraveling (quality is always disclosed unless it takes the lowest value) is expected under perfect rationality.

Our goal is to test the role of bounded rationality in preventing full unraveling. We manipulate two features of the game. First, we manipulate (within-subject) the number of distinct values for quality. Each subject, must play the game with a large number of values (5), and a lower number (3 and 2) of values quality can take. As we reduce the number of values, the quality score becomes coarser and this is easier for players to understand the equilibrium outcome: i.e., no news is bad news. Second, we also manipulate (between-subject) the distribution of values, which is common knowledge. Under perfect rationality, the type of distribution should not matter, as long it is common knowledge.

The experimental design is inspired from Jin et al. (2021). We first simplify the game such that senders play against a computer, and receivers also play against a computer.

Our goal is to test the rationality of the participants, i.e., their ability to think strategically. We first manipulate the complexity of the game by varying the number of values the hidden dimension of quality can take. The game is designed such that under perfect rationality, senders should always disclose all values except for the lowest one (indifference). For instance, if quality can take five values, with a certain probability assigned to each value being realized, the sender should disclose with the same probability all values, except for the lowest one. The probability distribution of the quality should also not matter. Our second intervention consists of varying this distribution.

2024-05-23

2024-06-28

Sender/owner experiment:
For the sender/owner game, the probability of disclosure for each quality level is the main outcome. This probability is expected to be independent of the quality level for all values above the lowest one. The experiment is structured to induce the sender's action (disclose/not disclose) for each possible value.

At the end of each within-subject variation, we also collect the sender's first-order beliefs: specifically, the sender's prediction of the receiver's guess in the absence of disclosure. This probability of disclosure, matched with the beliefs, allows us to categorize each sender in terms of their strategic thinking. We anticipate identifying fully rational players, Min+k strategic naives, and others.

Receiver/renter experiment:
The guess for quality in the absence of disclosure forms the first part of the primary outcome and is the initial question answered in each within-subject variation.

For each possible value, we then ask about the receiver's estimate of the sender's likelihood of disclosing a quality of the given value. Furthermore, we gather answers regarding higher-order beliefs: specifically, the receiver's estimation of what the sender believes the receiver will guess, given a particular value.
Similar to the sender/owner experiment, we plan to use the guesses and higher-order beliefs to classify receivers in terms of "strategic type": including fully rationals, Min+k strategic naives, and others.

We aim to compare the proportion of each type between treatment arms and the probability of disclosures.

An additional significant outcome of the study is the trajectory of the rate of disclosure by senders across different within-subject scenarios (i.e., as the number of potential quality values shifts from 5 to 3 to 2 in a random order). We anticipate that, as the range of quality's scores increases, senders will be less likely to disclose lower values. A larger number of alternatives complicates the receivers' guessing ability, thus inducing more strategic thinking from senders.

Furthermore, we also expect the nature of the distribution (uniform, bell-shaped, fat-tailed) to significantly impact the players' strategic thinking. While rational players theoretically should not be influenced by the knowledge of a specific distribution, under bounded rationality, we expect that knowledge of a specific distribution will affect perceptions of probability and thus influence players' strategic decisions.

For Senders:
-The fully rational senders: correctly disclose all quality values (indifference with the low type) and guess that the receiver will guess the lowest value if there is no disclosure.
-The Min+1 strategic naives: they do not disclose the min and min +1 values and guess that the receivers will guess (min + min +1)÷2.
-The Min+2 strategic naives: they do not disclose the min, min +1, and min+2,values and guess that the receivers will guess (min + min+1 + min +2)÷3.
etc... until Min+k =Max -1.
-The others: they disclose values and have higher-order beliefs that do not follow any specific patterns that allow us to classify their strategic thinking.


For Receivers:
We follow a similar approach to classify into those types.

Regarding secondary outcomes that are still very relevant for our analysis, we begin by exploring the heterogeneity in the probability of being a specific type, using the results from the CRT-2 test.

Additionally, consistent with previous theoretical findings (Milgrom, 1981), we expect that senders will more frequently disclose more favorable values, which, given the structure of their payoffs, are higher quality scores (i.e., 3, 4, 5). Moreover, considering the payoff scheme, both players will benefit more from higher rates of disclosure than from no disclosure.

Next, we aim to analyze in greater detail the outcomes under each specific distribution. Due to bounded rationality, senders are more likely to disclose the score when they know that receivers are aware of a uniform distribution compared to a bell-shaped distribution. Since a bell-shaped distribution leads senders to believe that receivers expect values clustered around the mean are more probable, they are more likely to withhold information when assigned very low values, which are perceived as less likely.

However, senders will tend to disclose the quality score more frequently when they know that receivers are informed of a fat-tailed distribution than a bell-shaped or uniform distribution. We expect that a higher probability of lower values in a fat-tailed distribution increases the likelihood of senders disclosing these values, since they anticipate that receivers will guess lower values more frequently than higher ones.

These hypotheses are adapted to coherently motivate the receivers' guesses and beliefs.

At the end of the survey we included 4 open-ended questions which are part of the CRT-2 proposed by Thomson and Oppenheimer (2016), an alternative version to the well known CRT by Frederick (2005). The four questions (If you’re running a race and you pass the person in second place, what place are you in?; A farmer had 15 sheep and all but 8 died. How many are left?; Emily’s father has three daughters. The first two are named April and May. What is the third daughter’s name?; How many cubic feet of dirt are there in a hole that is 3’ deep x 3’ wide x 3’ long?) will be combined to create a unique rationality score for each participant. We will then explore the correlation between the strategic type and the CRT score.

The experimental design involves two parallel sessions to assess the elicitation of beliefs of both senders and receivers. The two sessions are performed as separate online experiments, one with the senders (Experiment 1) and one with the receivers (Experiment 2). The samples are recruited using the Prolific platform.
The experiments have a symmetric structure. First we ask for actions and then we measure beliefs. There are two treatments variations directions. The between-subjects treatment variation is designed to control for potential behavioral distortions due to the knowledge of a specific distribution of potential rating scores. The second scenario presents a within-subjects treatment variation whose objective is to check, independently of the distribution, whether the magnitude of B, the set containing all the possible values, affects the voluntary disclosure of the player. Participants will earn an additional amount according to their performance in each round. They will play a total of 10 rounds. The order of within-subjects vatiations is fairly randomised.

To provide more details, in the sender/owner experiment, participants are initially assigned to one of three between-subject treatments, each corresponding to a different probability distribution. They complete all three within-subject treatment variations, with the order being randomized. In each within- scenario, the sender is asked to decide whether to disclose or not disclose the information for each possible value; next the sender is asked to communicate his expectation about the renter's guess in case of not disclosure.
In the receiver/renter scenario, the general structure is the same. In each within- subject variation, the receiver is asked first to guess the quality score in case of non disclosure by the sender. Then, for each possible value, he has to communicate (i) whether he expects that the sender is going to disclose or not the value and (ii) the renter's guess of the sender's expectation of the renter's guess in case the sender decides not to disclose the value.
At the end of both experiments we ask four questions of a CRT, labelled as CRT-2 by Thomson and Oppenheimer (2016) who proposed an alternative version to the well known CRT by Frederick (2005).

The between-subjects treatment variation is designed to control for potential behavioral distortions due to the knowledge of a specific distribution of potential rating scores. Along this line we create three independent cohorts. The first one, which represents the control unit, is told that b,that is the quality score, follows a uniform distribution (C); the group representing the first treatment (T1), is acknowledged of a bell-shaped distribution of b; in the end, the last group represents the second treatment (T2), and it is associated with the knowledge of a fat-tailed distribution of b.
The second scenario presents a within-subjects treatment variation. The objective of this scenario is to check, independently of the distribution, whether the magnitude of B, the set containing all the possible values of b, affects the voluntary disclosure of the player.
At first, the participants play 5 rounds of the one shot game knowing that b ∈ B = 1,2,3,4,5, this represents the first treatment (T A); then
they are asked to play 3 rounds with b ∈ B = 1,2,3, that is the second treatment framework (TB ); in the end they are asked to play 2 additional rounds, this time knowing that b ∈ B = 1,2, which represents the control (T C) along the within-subjects variation framework. By considering both variation designs, we end up with nine distinct treatments.

Participants are recruited via Prolific and will be linked to a Qualtrics file, which is designed to ensure exhaustive randomization in both between and within scenarios.

Each individual is both randomly assigned to one of the three bewteen-subjects variation groups (to a specific distribution) and to a random order of within-subject scenario (i.e. he/she can either start with B=1,2,3,4,5, or B=1,2,3, or B=1,2 and randomly continue with the others). All the participants are exposed to all the within-subject variations in a random order and to only one between-subject variation.

No

No clustering needed.

We plan to have 300 participants in the sender's experiment and 300 participants in the receiver's experiment.

For both experimental scenarios we expect to get around 100 observations per between-subjects variations (100 C, 100 T1, 100 T2).

With the between-subject variation, we will compare the distribution of the probability of disclosure. This experiment is a pilot. Therefore, we have chosen the sample size based on out budget.