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D2 Game Theory Help

Hi can someone explain to me,
When you are converting a game theory pay off matrix into a simplex problem:
a) Why does the sum of the probabilities have to be less than or equal to 1?
b) Why does the pay off value (eg m) have to be less than or equal to all the expressions of the expected pay offs?
c) Why do you have to make all the elements of a pay off matrix non negative?

In exams, they sometimes ask these type of questions and I don't fully understand the reasoning in the mark scheme.
An example of such questions was 6iv and 6vi in this paper https://9dff9a1a8377623ff1fc81ae8c0aae81349351ba.googledrive.com/host/0B1ZiqBksUHNYaDZTTHhsTHBhY0E/January%20%202006%20QP%20-%20D2%20OCR.pdf

Thanks in advance.
Original post by Sahil_
Hi can someone explain to me,
When you are converting a game theory pay off matrix into a simplex problem:
a) Why does the sum of the probabilities have to be less than or equal to 1?
b) Why does the pay off value (eg m) have to be less than or equal to all the expressions of the expected pay offs?
c) Why do you have to make all the elements of a pay off matrix non negative?

In exams, they sometimes ask these type of questions and I don't fully understand the reasoning in the mark scheme.
An example of such questions was 6iv and 6vi in this paper https://9dff9a1a8377623ff1fc81ae8c0aae81349351ba.googledrive.com/host/0B1ZiqBksUHNYaDZTTHhsTHBhY0E/January%20%202006%20QP%20-%20D2%20OCR.pdf

Thanks in advance.


a) Due to the simplex algorithm requiring slack variables, the inequality acts as a kind of slack instead of adding another variable on
b) The pay off value or value of the game is the maximum worth of the game to the player so earnings must be less than or equal to it
c) The simplex algorithm simply requires positive values, a negative number can never be chosen as a pivot but I am unsure as to why

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