Question

the graphical method in useful for the game where the payoff matrix is of the size?
a.m×n
b. m×3
c. 3×n
d.2×n​

Answer 1

Answer:

Reduce the size of the payoff matrix by applying dominance property, if it exists. This step is not compulsory. The size is being reduced to just simplify the problem. The game can be solved without reducing the size also.

After reducing the above game with the help of dominance property we get the following game.

Step 2: Let x be the probability of selection of alternative 1 by player A and (1 – x) be the probability of selection of alternative 2 by player A.

Derive the expected gain function of player A with respect to each of the alternatives of player B. To do this just multiply the column values of B’s alternative with its corresponding probability of selection of alternatives by player A. For example, the first alternative of player B is column number 1, so multiply -4 with x and 3 with (1 – x) and add them then the expression obtained is the A’s expected payoff function. Similarly, the second alternative of player B is column number 2, so multiply 2 with x and -9 with (1 – x) and add them. Similarly, the third alternative of player B is the column number 4, so multiply -6 with x and 4 with (1 – x) and add them. Please refer the shown table.

Step 3: Find the value of the gain when x = 0 and x = 1. See the table below: