Welcome-Instructions
- This is an experiment in economic decision-making.
- If you make good decisions, you may be able to earn a considerable amount of money, which will be paid to you privately at the end of the experiment.
- The experiment consists of {{ num_rounds }} rounds of decision-making.
- At the end of the experiment, the computer will randomly select one round that you played as the decision-that-counts, and you will be privately paid what you earned in the decision-that-counts.
- Note that, since all decisions are equally likely to be chosen, you should make each decision as if it will be a decision-that-counts.
- In addition, you will receive a participation fee of {{ session.participation_fee|to0 }}.
Overview of a round
- Each round of the experiment will consist of three stages.
- Your task is to infer an unknown state X in the second stage.
- The following is the overview of a round.
- In the first stage, Mother urns will be formed with numbers and shapes. The compositions of those numbers and shapes will be informed to you.
- In the second stage, Baby urns will be randomly formed from Mother urns. The compositions of those numbers and shapes in the Baby urns will NOT be informed to you.
- Your task is to infer a composition of a Baby urn, which will be referred to as state X.
- To help your inference, Signal urns will be randomly formed from Baby urns in the third stage. You will be given 15 seconds to observe the compositions of the Signal urns and make a decision about the unknown state X.
Stage 1: Mother urns
-
There are two urns, Mother Orange, and Mother Blue each of which has 100 balls.
Those 100 balls are represented by two characteristics: shape (e.g.,
)
or three-digit number (e.g., 
).
-
The number of shapes and three-digit numbers may vary across rounds.
At the beginning of each round, you will be informed of the compositions of the two Mother urns. -
For instance, the figure below shows the composition of each urn in a round.
In the Mother Orange urn, 52 balls are represented by shapes and 48 balls by numbers.
In the Mother Blue urn, 80 balls are represented by shapes and 20 balls by numbers.
Stage 2: Baby urns
-
The experimental program will create the Baby Orange and the Baby blue urns from each of the Mother urns.
25 balls are randomly drawn from each of the Mother Orange and the Mother Blue with Replacement: That is, after a ball is randomly selected from a Mother urn, the ball is put back into the Mother urn.
The following is an example of how Baby urns can be formed.
-
Draw of the first ball:
-
Draw of the second ball:
- ...
-
Draw of the last ball:
- The above shows how Baby urns can be created. Let's look into how a Baby Orange urn is formed.
-
First, a number ball (“
”) is randomly selected from the Mother Orange urn.
The Baby Orange urn has one “” ball.
After a draw, the “” ball is put back into the Mother Orange urn.
-
Second, now a shape ball (“
”) is randomly selected from the Mother Orange urn.
The Baby Orange urn has one “” ball and one “” ball.
After a draw, the "" ball is put back into the Mother Orange urn.
- The same procedure is repeated 25 times. In the end, the Baby Orange urn has 25 balls that consist of shapes and numbers.
- The same procedure will be done for the Baby Orange and the Baby Blue urns.
Decision of inferring X
- Your task is to infer the true composition of a Baby urn, which refers to the state X.
-
The state X can vary across rounds: the proportion of
(1) the Orange shape in the Orange Baby urn,
(2) the Orange number in the Orange Baby urn,
(3) the Blue shape in the Blue Baby urn,
(4) the Blue number in the Blue Baby urn, - Since you will not be informed of the true composition of the Baby urn (i.e., the state X), you will receive some clues as shown on the next page.
Stage 3: Signal urns
-
Now 25 balls will be randomly drawn from each of the two Baby urns with replacement.
We call these two urns the “Signal” urns. That is, 25 balls in the Signal Orange urn will be randomly drawn from the Baby Orange urn with replacement.
The same procedure applies to the Signal Blue urn.
The following is an example of how Signal urns can be formed.
-
Draw of the first ball:
-
Draw of the second ball:
- ...
-
Draw of the last ball:
- The above is an example of how Signal urns are created. Let's look into how a Signal Orange urn is formed.
-
First, a number ball (“
”) is randomly selected from the Baby Orange urn.
The Signal Orange urn has one “” ball.
After a draw, the "” ball is put back into the Baby Orange urn.
-
Second, now another number ball (“
”) is randomly selected from the Baby Orange urn.
The Signal Orange urn has one “” ball and one “” ball.
After a draw, the "" ball is put back into the Baby Orange urn.
- The same procedure is repeated 25 times. In the end, the Signal Orange urn has 25 balls that consist of shapes and numbers.
- You will receive 15 seconds to observe the composition of the Signal Orange and the Signal Blue urns. Once the two Signal urns disappear, you will be asked to make a decision about inferring the state X.
Summary of urns and random draws
Payment
- For the round that will be randomly selected that accounts for your payment, you will get paid more if your conjecture about the state X is closer to the true state of X.
-
Namely, the exact formula to compute your payment is as follows:
- Your payment = {{ incentive }} - {{ penalty }} ( X - your conjecture )².
- If your conjecture coincides with the state X, then you will receive "{{ incentive }}" points.
- Once your conjecture is further away from the state X, you will receive fewer points than "{{ incentive }}" points. Therefore, it is your interest to conjecture the state X as precisely as possible.
-
Each point that you will earn from each round is worth 10원.
- That is, 1 point = 10원.
- At the end of the experiment, you will receive feedback about the outcomes of each round and the total earnings from the experiment.