How do I prove that optimal strategy exists for both players in matrix game 2x2?
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I am new to game theory and mathematical proofs generally and I read in my textbook that if in a 2x2 matrix game with two players the first player has optimal strategy then for sure the second one has also, sadly I can't find any proofs and frankly I am new to the field and I am not so sure where to look or start.
game-theory
asked Jan 24 at 16:18
kuskmenkuskmen
1014
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add a comment |
$begingroup$
I am new to game theory and mathematical proofs generally and I read in my textbook that if in a 2x2 matrix game with two players the first player has optimal strategy then for sure the second one has also, sadly I can't find any proofs and frankly I am new to the field and I am not so sure where to look or start.
game-theory
asked Jan 24 at 16:18
kuskmenkuskmen
1014
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Are you referring to zero sum games?
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– Kaind
Jan 26 at 16:29
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@Kaind its not said, it says only 2x2 matrix game
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– kuskmen
Jan 26 at 19:45
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How do you define an optimal strategy for non-zero sum games?
$endgroup$
– Kaind
Jan 26 at 20:03
add a comment |
$begingroup$
I am new to game theory and mathematical proofs generally and I read in my textbook that if in a 2x2 matrix game with two players the first player has optimal strategy then for sure the second one has also, sadly I can't find any proofs and frankly I am new to the field and I am not so sure where to look or start.
game-theory
asked Jan 24 at 16:18
kuskmenkuskmen
1014
$endgroup$
I am new to game theory and mathematical proofs generally and I read in my textbook that if in a 2x2 matrix game with two players the first player has optimal strategy then for sure the second one has also, sadly I can't find any proofs and frankly I am new to the field and I am not so sure where to look or start.
game-theory
game-theory
asked Jan 24 at 16:18
kuskmenkuskmen
1014
asked Jan 24 at 16:18
kuskmenkuskmen
1014
asked Jan 24 at 16:18
kuskmenkuskmen
1014
asked Jan 24 at 16:18
kuskmenkuskmen
1014
asked Jan 24 at 16:18
kuskmenkuskmen
1014
1014
$begingroup$
Are you referring to zero sum games?
$endgroup$
– Kaind
Jan 26 at 16:29
$begingroup$
@Kaind its not said, it says only 2x2 matrix game
$endgroup$
– kuskmen
Jan 26 at 19:45
$begingroup$
How do you define an optimal strategy for non-zero sum games?
$endgroup$
– Kaind
Jan 26 at 20:03
add a comment |
$begingroup$
Are you referring to zero sum games?
$endgroup$
– Kaind
Jan 26 at 16:29
$begingroup$
@Kaind its not said, it says only 2x2 matrix game
$endgroup$
– kuskmen
Jan 26 at 19:45
$begingroup$
How do you define an optimal strategy for non-zero sum games?
$endgroup$
– Kaind
Jan 26 at 20:03
$begingroup$
Are you referring to zero sum games?
$endgroup$
– Kaind
Jan 26 at 16:29
$begingroup$
Are you referring to zero sum games?
$endgroup$
– Kaind
Jan 26 at 16:29
$begingroup$
@Kaind its not said, it says only 2x2 matrix game
$endgroup$
– kuskmen
Jan 26 at 19:45
$begingroup$
@Kaind its not said, it says only 2x2 matrix game
$endgroup$
– kuskmen
Jan 26 at 19:45
$begingroup$
How do you define an optimal strategy for non-zero sum games?
$endgroup$
– Kaind
Jan 26 at 20:03
$begingroup$
How do you define an optimal strategy for non-zero sum games?
$endgroup$
– Kaind
Jan 26 at 20:03
add a comment |
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$begingroup$
Are you referring to zero sum games?
$endgroup$
– Kaind
Jan 26 at 16:29
$begingroup$
@Kaind its not said, it says only 2x2 matrix game
$endgroup$
– kuskmen
Jan 26 at 19:45
$begingroup$
How do you define an optimal strategy for non-zero sum games?
$endgroup$
– Kaind
Jan 26 at 20:03