gauravkumarjha427

Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right.

The payoffs are given in the following table

Player 2 Left Right Player 1Top 6 59 4 Bottom 7 45 3 where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.

A) Does player 1 have a dominant strategy, and if so what is it?

B) Does player 2 have a dominant strategy and if so what is it?

C) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:i) Top/Leftii) Top/Rightiii) Bottom/Leftiv) Bottom Right

D) What is Player 1’s maximin strategy?

E) What is player 2’s maximin strategy?

F) If the game were played with Player 1 moving first and player 2 moving second, using the backward induction method discussed in the class notes, what strategy will each player choose?

Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table:

Left of payoff is player A and Right of Payoff is Player B

A) Does player 1 have a dominant strategy, and if so what is it?

B) Does player 2 have a dominant strategy and if so what is it?

C) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:

i) Top/Left

ii) Top/Right

iii) Bottom/Left

iv) Bottom Right

D) If each player plays their maximin strategy, what payoff will each of them receive?

E) Now suppose the same game is played with the exception that Player 1 moves first and Player 2 moves second. Using the backward induction method, what will be the outcome of the game? (Hint: it will be helpful to sketch the game tree.)

Need to doublecheck my work and answers. Please Show Work.

Suppose that two players are playing the following game. Player A can choose either Top or Bottom, and Player B can choose either Left or Right. The payoffs are given in the following table:

left right

top 4 5 1 4

bottom 5 1 3 8

A) Does player A have a dominant strategy, and if so what is it?

B) Does player B have a dominant strategy and if so what is it?

C) For each of the following say True if the strategy combination is a Nash equilibrium, and False if it is not a Nash equilibrium:

i) Player A plays Top and Player B plays Left

ii) Player A plays Bottom and Player B plays Left

iii) Player A plays Top and Player B plays Right

iv) Player A plays Bottom and Player B plays Right

D) If each player plays her maximin strategy what will be the outcome of the game? (Give your answer in terms of the strategies each player chooses—for example, “Player A plays Bottom and Player B plays Rightâ€)

E) Now suppose the same game is played with the exception that Player A moves first and Player B moves second. Draw the game tree associated with this situation. Using the backward induction method discussed in the online class notes, what will be the outcome of the game?

3. (18 points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table:

where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.

A) Does player 1 have a dominant strategy, and if so what is it?

B) Does player 2 have a dominant strategy and if so what is it?

C) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:

i) Top/Left

ii) Top/Right

iii) Bottom/Left

iv) Bottom Right

D) For each of the following strategy combinations, write TRUE if it is Pareto Efficient, and FALSE if it is not:

i) Top/Left

ii) Top/Right

iii) Bottom/Left

iv) Bottom Right

I need help with the concept of pareto effiency in game theory.

What do you look for when you're determining if a strategy is pareto effient?

And please tell me which strategies are pareto efficient in this game

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