{{ block title }} Description of the game {{ endblock }} {{ block content }}

Duration

This experiment will last for one period.

Roles

You will be randomly matched with another participant to form a group of two. You can have one of two roles as a participant: Player 1 or Player 2. The roles are randomly assigned, and each participant has an equal chance of being assigned either role.

Types:

Player 2 has a type that affects how earnings are determined. Hence, Player 2’s earnings are affected by their type, their decision and the decision of Player 1. 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 chance of being Type I is 30%, and the chance of being Type II is 70%.
Player 2 is assigned one of two possible types: Type I or Type II. The chance of being Type I is 70%, and the chance of being Type II is 30%.
Player 1 has no type i.e. their earnings are only determined by their choice and that of Player 2.

Sequence

1) Decision of Player 1

First, Player 1 chooses a number X between 0 and 10. Then, one of two things will happen: the world will be RED with a probability X/10, or the world will be BLUE with (1-X/10) probability.

So for example, if Player 1 chooses 2, then the world is RED with a probability 2/10 and with a probability 8/10 (i.e. 1-2/10) the world is BLUE.

Player 1 sees whether the world is RED or BLUE. After seeing this, Player 1 decides whether to disclose the world's colour to Player 2.

If Player 1 chooses to disclose, Player 2 will see whether the world is RED or BLUE.
If Player 1 chooses not to disclose, Player 2 will not see whether the world is RED or BLUE. Player 2 only knows that the world is RED with chance X/10, and the world is BLUE with chance 1-X/10.

2) Decision of Player 2

Player 2 sees Player 1’s choice (X) and whether Player 1 chooses to disclose the world's colour. Player 2 then chooses between two choices, A and B.

Earnings:

If Player 2 is Type I, the earnings for the different possible outcomes are as follows. All earnings are given in points.

If the world is RED, and Player 2 chooses A, then Player 1 receives 30-X points, and Player 2 receives 23 points.
If the world is RED, and Player 2 chooses B, then Player 1 receives 40-X points, and Player 2 receives 30 points.
If the world is BLUE, and Player 2 chooses A, then Player 1 receives 10-X points, and Player 2 receives 43 points.
If the world is BLUE, and Player 2 chooses B, then Player 1 receives 40-X points, and Player 2 receives 40 points.

This is also illustrated using the table below

	A	B
RED	30-X, 23	40-X, 30
BLUE	10-X, 43	40-X, 40

Table 1: Payoffs if Player 2 is type I

If Player 2 is Type I, the earnings for the different possible outcomes are as follows. All earnings are given in points.

If the world is RED, and Player 2 chooses A, then Player 1 receives 30-X points, and Player 2 receives 28 points.
If the world is RED, and Player 2 chooses B, then Player 1 receives 40-X points, and Player 2 receives 30 points.
If the world is BLUE, and Player 2 chooses A, then Player 1 receives 10-X points, and Player 2 receives 48 points.
If the world is BLUE, and Player 2 chooses B, then Player 1 receives 40-X points, and Player 2 receives 40 points.

This is also illustrated using the table below

	A	B
RED	30-X, 28	40-X, 30
BLUE	10-X, 48	40-X, 40

Table 1: Payoffs if Player 2 is type I

If Player 2 is Type II, the payoffs for the different possible outcomes are as follows.

If the world is RED, and Player 2 chooses A, then Player 1 receives 30-X points, and Player 2 receives 14 points.
If the world is RED, and Player 2 chooses B, then Player 1 receives 40-X points, and Player 2 receives 10 points.
If the world is BLUE, and Player 2 chooses A, then Player 1 receives 10-X points, and Player 2 receives 34 points.
If the world is BLUE, and Player 2 chooses B, then Player 1 receives 40-X points, and Player 2 receives 40 points.

This is also illustrated using the table below

	A	B
RED	30-X, 14	40-X, 10
BLUE	10-X, 34	40-X, 40

Table 2: Payoffs if Player 2 is type II