{{ block title }} Different Cabinets for each Participant {{ endblock }} {{ block content }}
Every round, you and another participant (Participant 2) bet on the probability that Yellow box was selected to generate the observed number of marbles from each color. You and Participant 2 observe the same number of marbles.
Every round, the computer selects one box at random from cabinet 1 for you and one box from cabinet 2 for Participant 2. This box will be placed again in the cabinet at the end of each round. Each cabinet has a different number of boxes of each color. Cabinet 1 has nine Yellow boxes and one Green box, while Cabinet 2 has nine Green boxes and one Yellow box.
Cabinet 1: Your Cabinet | ||||
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Cabinet 2: Participant 2's Cabinet | ||||
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Therefore, the Yellow box is selected for you with a 90% probability and the Green box with a 10% probability. However, you will be matched with the answers from Participant 2, for whom the computer selects the Yellow box with a 20% probability and the Green box with an 80% probability. Your payoffs will be affected by the accuracy of your prediction of the bet of Participant 2, who observes the same information but has different beliefs. The box selected for Participant 2 is neither affecting the box selected for you nor your payoffs.
In each round, you and Participant 2 make a bet with the probability that the sequence observed came from a Yellow box. Also, you must estimate Participant 2’s bet for the Yellow box.
Notice that you and Participant 2 have different probabilities that the computer selects the Yellow box. However, both observe the same sequence. The next table summarizes the associated probabilities for each participant:
Box | Probability that the computer selects each box | Participant 2's believed probability that the computer selects each box |
---|---|---|
90 | 20 | |
10 | 80 |