Question

Consider the game below: Left(player 2) Right(player2) Top(player1) 23, 20 20, 22 Bottom(player1) 22, 19 19,...

Consider the game below: Left(player 2) Right(player2) Top(player1) 23, 20 20, 22 Bottom(player1) 22, 19 19, 18 Does player 1 have a dominant strategy? If yes, which one is it?

A. None of the other answers is correct. B. Yes,Top. C. No. D. Yes, Bottom.

Math   Statistics-And-Probability   
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Answer #1

Answer : C. Yes, top player 1 have dominant strategy

Player 2
Left Right
Player 1 Top 23, 20 20, 22
Bottom 22, 19 19, 18

Strategy X strictly dominant Y means Xi > Yi
Strategy X weakly dominant Y means Xi ≥ Yi

For player 1
If we fix the opponent strategy as Left(Player 2),
Strategy top(player 1 ) = 23 > bottom (player 1) = 22
Also fix right(Player 2) ,
Strategy top(player 1 ) = 20 > bottom (player 1) = 19

So top(Player 1) strictly dominant bottom (Player 1)

For player 2
If we fix the opponent strategy as top(Player 1),
Strategy Left(player 2 ) = 20 < Right (player 2) = 22
Also fix bottom(Player 1) ,
Strategy Left(player 2 ) = 19 > Right (player 2) = 18

So player 2 is not dominant.

PL??

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