Question-1: Consider a simultaneous game in which player A choose one of two actions (Up or Down), and B choose one of t

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Question-1: Consider a simultaneous game in
which player A choose one of two actions (Up or Down), and B choose
one of two actions (Left or Right). (25
points)
Player B
Left
Right
Up
3, 3
5, 1
Player A
Down
2, 2
4, 4
a. Find the Nash Equilibrium in this game. Explain. (5
points)
b. What are the dominant strategies of Player A and Player B
chooses Left or Right? (5+5 = 10 points)
c. Suppose the game in part (a) is changed to a new one in which
the payoff of Player A from playing Up is reduced by 2. The new
payoff matrix is shown below: Find the Nash Equilibrium in this
game. Explain. What are the dominant strategies of Player A and
Player B chooses Left or Right? Does any player experience a change
in his equilibrium payoff? Explain (5+5 = 10 points)
Player B
Left
Right
Up
1, 3
3, 1
Player A
Down
2, 2
4, 4