In this experiment you will be given with a 9 by 9 matrix. Each column represents a color and each row represents a shape. Each cell of the matrix can generate a payoff of 1 or 0. However, you will not be given any information about the payoff from any cell. For illustration, let us consider a 2 by 2 matrix:
| Red | Blue | Average | |
|---|---|---|---|
| Square | P1 | P2 | C1 |
| Triangle | P3 | P4 | C2 |
| Average | R1 | R2 |
You'll need to complete the following two tasks:
For the information task you need to find the payoff from various cells. There are two ways you can learn about the payoff for a shape, color pair. You can either open the corresponding cell. For example, if you want to learn about the payoff from a Blue-Square, then you need to open cell P2.
Alternatively, you can open an average as well. For example, if you open average C1 you will learn how many cells in the first row, i.e., for shape Square would generate payoff 1. If this value is 1, then you know that one of the two cells generate 1 but you would not be given any information about which cell contains payoff 1.
For each round a random number between {{Constants.low_limit}} and {{Constants.high_limit}} would be generated. This value would be called the cutoff value If you choose to open a cell you will get a problem of the following form,
Solve: 0.23141552+0.24661835-0.23638687.
The cutoff value is .2435673.
Since the result of this expression .241647 is lower than the cutoff value .2435673 the payoff from the cell is 0. Whereas if the cutoff value was .2409898, then the payoff from the chosen cell would be 1. However, during the experiment you WILL NOT be given any feedback about your solution, whether it is correct or not.
Note that, you will be provided with a calculator.
If you choose to open an average row or average column (in short, we will call it average ) then you will get a problem of the following form:
The fourth digit represents the number of ones in the row:
.51217116.
Since the fourth digit is 1, there exists exactly one cell in this row that gives payoff 1, all other cells give payoff 0. However, no further information would be given which cell generates payoff 1.
For any round you can open any number of cells and averages. Once you solve a problem for a given cell or average you will be able to observe your own solution before you decide whether to open another cell or average. You can also go back and reopen any cell or average.
You can open the cells and averages in any order. Also you can always choose to not solve the problem in any given cell or average. In case you open a cell or average and do not solve the problem you will see "None" in place of the solution on the next page. Once you are done with opening cells and averages you need to proceed to the choice stage.
At the beginning of each round you will be provided with possible number of cells with zero in the matrix. There may be more than one possibility given to you. For each possibility the percentage of chance would also be given to you.
For example, if there are only two possibilities, namely, exactly one cell contains payoff 1 or, exactly three cells contain payoff 1 in the 2 by 2 matrix with equal probability, then there is a 50% chance only one cell generates payoff 1 and each cell is equally likely to generate payoff 1 and with 50% chance only one cell generates 0 and again each cell is equally likely to generate payoff 0.
Similarly, there can be more than two possibilities. For example, in the 2 by 2 example you may be told that there are 3 cells with 0 with 25% chance, 1 cell with 0 with 25% chance and 2 cells with 0 with 50% chance.
In the choice stage you need to choose combination of color and shape. If you choose shape i and color j then you will get the payoff from cell (i, j). You will make the choices of row and column from a dropdown menu.
You are also allowed to choose the average row or column. For example, if you choose average column and second row, then one cell would be chosen randomly from second row and your payoff would be the payoff of the randomly chosen cell.
You need to make {{Constants.num_choices}} choices in the choice stage. You are allowed to choose the same option all {{Constants.num_choices}} times but you can always choose other options as well. Only one choice will be chosen at random for payoff. Each combination of color and shape chosen by you would be considered for final payoff with equal chances.
For example, consider our 2 by 2 example from before. Suppose the actual matrix is as follows:
| Red | Blue | Average | |
|---|---|---|---|
| Square | 1 | 0 | 1 |
| Triangle | 0 | 0 | 0 |
| Average | 1 | 0 |
Then with 50% chance Red Square will be selected and you will get 1 but with 50% chance Blue Square will be selected and you will get 0.
After each choice you will be shown a list of choices where the choices would be recorded by the row and column number instead of name of color and shape. For example, in the 2 by 2 matrix above if you choose Red and Triangle then the list will show that you have chosen row 1 and column 2.
In the following few pages we will ask you questions about the structure of the experiment to make sure you have understood how to find the value for a cell and an average. You can only start the actual experiment if you can answer at least four questions correctly. The instructions for the quiz will be provided in the following pages.
For the actual experiment you will have {{Constants.time_limit}} minutes to finish as many rounds as possible. Your total payoff will be the sum of all the payoffs from each round. Each payoff of 1 is equivalent to 1 dollar. If time runs in the middle of a round then no payoff would be added for that round.
Good Luck!
{% else %}Sorry you haven't correctly answered 4 questions. To go to the actual experiment you have to retake the quiz.
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