Duration
This experiment will last for one period.
Roles
You will be randomly matched with another participant to form a group of two. In the game, there are two possible roles: Player 1 or Player 2. Roles are assigned randomly, and each participant has an equal chance of being assigned to either role.
Types
Player 1 has no type.
Player 2 has a type that affects how payoffs are determined. This type is private information. Player 2 will know their own type, while Player 1 will not know Player 2’s type.
- Player 2 is assigned one of two possible types: Type I or Type II. The probability of being Type I is 60%, and the probability of being Type II is 40%.
Sequence:
At the start of the game, each player receives an initial endowment of 800 points.
1) Decision of Player 1
Player 1 chooses an integer X between 0 and 400 (inclusive), which affects the likelihood of the two states. After X is chosen, one of two possible states is realised.
- The game proceeds to state RED with probability X/400.
- The game proceeds to state BLUE with probability 1 − X/400.
Player 1 observes which state has been realised (RED or BLUE).
After observing the state, Player 1 decides whether to disclose this information to Player 2:
- If Player 1 chooses to disclose, Player 2 will see whether the state is RED or BLUE.
- If Player 1 chooses not to disclose, Player 2 will not observe which state occurred.
2) Decision of Player 2
After Player 1 makes the choices, Player 2 observes Player 1's choice (X) and whether Player 1 has chosen to disclose the realized state.
- If Player 1 chooses to disclose, Player 2 will see whether the state is RED or BLUE.
- If Player 1 chooses not to disclose, Player 2 will not observe which state occurred. Player 2 only knows that state RED occurs with probability X/400 and state BLUE occurs with probability 1 − X/400.
Player 2 then chooses between two actions: A and B.
Payoffs:
The payoff of each player depends on Player 2’s type, the realised state, and the choices made in the game. We describe the decision process and resulting earnings separately for each type of Player 2.
If Player 2 is Type I, the sequence of decisions is shown in the game tree below. You can understand the figure in the following way. First, Player 1 chooses an integer X between 0 and 400. After observing the realised state, Player 1 decides whether to disclose this information to Player 2.
If Player 1 discloses, Player 2 will see whether the state is RED or BLUE. Otherwise, Player 2 will only see the value of X.
Then Player 2 chooses between A and B.
The numbers shown at the end of each branch indicate the earnings for both players. The first number in each bracket corresponds to Player 1’s earnings, and the second number in each bracket corresponds to Player 2’s earnings.
As you can incur losses, any losses you incur will be deducted from your initial endowment.
All the earnings in the figure are given in points.
Below is an example showing how to read the payoffs when Player 2 is Type I. When Player 1 chooses a value of X, the payoffs depend on which state is realised and on Player 2’s action:
- If the state is RED (with probability X/400):
- Player 2 chooses A, then Player 1 receives -10-X points, and Player 2 receives -200 points.
- Player 2 chooses B, then Player 1 receives 400-X points, and Player 2 receives -50 points.
- If the state is BLUE (with probability 1- X/400):
- Player 2 chooses A, then Player 1 receives -300-X points, and Player 2 receives 200 points.
- Player 2 chooses B, then Player 1 receives 300-X points, and Player 2 receives 50 points.
If Player 2 is Type II, the sequence of decisions is the same, but the earnings differ. The payoffs for each combination of choices are shown in Figure 2.
Below is an example showing how to read the payoffs when Player 2 is Type II. When Player 1 chooses a value of X, the payoffs depend on which state is realised and on Player 2’s action:
- If the state is RED (with probability X/400):
- Player 2 chooses A, then Player 1 receives -10-X points, and Player 2 receives -200 points.
- Player 2 chooses B, then Player 1 receives 400-X points, and Player 2 receives -350 points.
- If the state is BLUE (with probability 1- X/400):
- Player 2 chooses A, then Player 1 receives -300-X points, and Player 2 receives 200 points.
- Player 2 chooses B, then Player 1 receives 300-X points, and Player 2 receives 550 points.