Consider the following game. Player 1 has 2 actions (Top, Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1's payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x).
Player 2
Left Middle Right
Player 1 Top (2,-1) (-2,-1) (3,2)
Bottom (1,2) (-2,x) (2,3)
a) Determine the range of values for x such that Player 2 has a strictly dominant strategy.
b) Suppose that the value of x is such that player 2 has a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game?
c) Suppose that the value of x is such the player 2 does NOT have a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game?