MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

## Two - Person Matrix games

My English is not good so i wanna ask my question as follow(with implication operator):

X = (The matrix game is Two-Person game) -> (The matrix game is Two-Person Zero-Sum game)

Is X equal to TRUE ?

-
Elvin, have you thought about this question? If you describe a game in normal form as a matrix, is it at all possible to have a zero-sum game? In that same situation, is it at all possible to have a game which is not zero-sum? That should help you figure out the answer. Is this question from homework? If so, you should ask at a different website; see the FAQ above. If it's not homework, please describe how you came to this question and what kind of work you've done to understand the answer so far. – sleepless in beantown Dec 19 2010 at 7:31
So you are asking if every two person matrix game is in fact a two person, zero-sum matrix game? It will boil down to how much you restrict your pay-off matrix. For a two person game that isn't zero sum, see the Prisoner's Dilemma. – Mikael Vejdemo-Johansson Dec 19 2010 at 7:34
@Mikael, I also didn't leave an explicit answer because I suspect this is homework because of its simplicity and the fact that the underlying assumptions are not stated. It looks like a direct rewrite of a problem set type of question. – sleepless in beantown Dec 19 2010 at 7:44
I am new at this theory... i couldn't imagine the game with nonZero-sum past bu now i can. thank you very much! I came to this question from my course work, its name is The matrix game of Two-Person but we have learnt only Two - Person Zero-Sum Matrix games in University. Now i learned that Two-Person nonZero-sum games exist and is more complicated subject. – Elvin Dec 20 2010 at 5:10