Question

Consider the following game: Player2 U Player 1 M 100.99 0.0 99 100 0.0 1.1 0.0 99. 10000 100.99 a. Does player 1 have a strictly dominant strategy? If the answer is yes, write the dominant strategy in the specified area and if the answer is no just write no b. Does player 2 have a strictly dominant strategyIf the answer is yes, write the dominant strategy in the specified area and if the answer is no just write no c. Is this game dominance solvable? just answer yes or no d. In the Nash Equilibrium player 1 plays strategy strategy and player 2 plays e. Is the NE of the game Pareto efficient? just answer yes or no

Answer 1

(a) Player 1 does not have any dominant strategy.

(b) Player 2 does not have any dominant strategy.

(c)No as we can not eliminate any strategy using Iterated elimination of strictly dominated strategies

(d) Nash equilibrium of the game is where player 1 plays M and player 2 plays C.

• When player 1 plays U, the best strategy of player 2 is to play R, when player 2 plays R the best strategy of player 1 is to play D.
• When player 1 plays M, the best strategy of player 2 is to play C and when player 2 plays C the best strategy of player 1 is to play M. These, strategies are mutually reinforcing in a sense that both the players wouldnot want to deviate from this strategy as it is mutual best response to each others strategy. Hence, it is NASH EQUILIBRIUM OF THE GAME.
• When player 1 plays D, player, the best response of player 2 will be to play L, when player 2 plays L the best response of player 1 is to play R.