In this experiment you will be given with a {{Constants.num_rows}} by {{Constants.num_rows}} 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 particular 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 wanys 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 R1 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 second last digit represents the number of ones in the row:
.51217116.
Since the second last 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 avearges. 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 also open the cells and avearges in any order possible. You can always choose to not solve the problem in any given cell or avearge. 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 possibilities given to you. For each possibility the percentage of chance would also be given to you.
For example, if there are only two possibilites, 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 a color and a shape. If you choose shape i and color j then you will get the payoff from cell (i,j).
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 will be given {{Constants.num_choices}} choices in the choice stage. 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 . You can also choose the exact same cell or avearge more than once.
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.
Whereas if you select Red Square 3 out of 4 choices and Blue Square only once, then with 75% chance Red Square is selected and you will get 1 and with only 25% chance Blue Square is selected in which case you will get zero.
In the following few pages we will ask 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 clear the quiz. 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 would be the sum of all the payoffs from each round. If time runs in the middle of a round then no payoff would be added for that round.
Good Luck!
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