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Your chances to make the extra $8 are maximized if you report your true believe of the Yellow box being selected, and your true expectation of participant 2's beliefs on the same event. Only one round will randomly be selected to determine your final payment. So, please make your best decision each round.
A detailed explanation of how you increase your chances of making $8 by reporting your true beliefs is described next. You can continue with the experiment by clicking the 'Next' button, but feel free to read the details if you have any doubt.
In every round, you will indicate a number p between 0 and 100 that states the probability you believe the Yellow box was selected. This determines the probabilities in the next bet:
Bet on box selected by the computer:
If the computer selected box Yellow, you will make $8 with probability (p2) If the computer selected box Green, you will make $8 with probability (1- p2)
Notice that if you are confident that the Yellow box was selected, you should choose p=1 since this guarantees you $8.
Bet on Participant 2’s bet:
Participant 2 will also bet on which box was selected for them by reporting the number x. You will indicate a number q between 0 and 100 that tries to capture the bet made participant 2 (x).
You will make $8 with probability (1- (x-p)2).
Notice that if you are confident that participant 2 bet on the Yellow box (x=1), you should choose q=1 since this guarantees you $8.
These bets were designed such that, if you are accurate about the probability of each outcome, your chances of getting an $8 prize are maximized. Be as accurate as possible, and carefully consider the probability of each outcome. Every round is independent of every other, and only one will be selected randomly to determine your final payment. So, please make your best decision in each round.
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