The rely-or-verify game works as follows.
Your partner is the BLUE player, you are the RED player. Your payment depends on the BLUE player's choice.
BLUE player will report whether the amount of money in the jar of coins below is ODD or EVEN:
Both you and the BLUE player know the payment structure.
The BLUE player will be asked to report whether the amount of money in this jar of coins is ODD or EVEN.
1. Before they do, the BLUE player will receive a message from you (the RED player).
You will be informed about the number of coins and thus know whether the amount of money in the jar is ODD or EVEN.
You will send one of the following two messages: "The amount of money in the jar is ODD." or "The amount of money in the jar is EVEN."
The message that you send could be accurate or inaccurate.
The BLUE player will not know whether or not the message is accurate or inaccurate when they make the choice to RELY on your message or VERIFY your message.
2. Once the BLUE player has received your message, they can choose to RELY on your message, or they can VERIFY the message.
3. If the BLUE player chooses RELY, they will be paid based on whether or not you gave them accurate or inaccurate information.
If you gave the BLUE player accurate information and they RELY on it, BLUE player will correctly report whether the amount of money in the jar is ODD or EVEN, and the BLUE player will earn $8. You will earn $4.
If you gave the BLUE player inaccurate information and they RELY on it, BLUE player will incorrectly report whether the amount of money in the jar is ODD or EVEN, and the BLUE player will earn $0. You will earn $12.
4. If the BLUE player chooses VERIFY, the BLUE player will learn the correct amount of money in the jar.
If you gave the BLUE player accurate information and they VERIFY it, the BLUE player will earn $0 and you will earn $2.
If you gave the BLUE player inaccurate information and they VERIFY it, the BLUE player will earn $6 and you will earn $0.
Your decisions are represented in the figure below.
In summary:
You are the RED player and will send the BLUE player accurate or inaccurate information.
If you think the BLUE player will verify your information, you are better off sending accurate information.
If you think the BLUE player will not verify your information, you are better off sending inaccurate information.