Question

The following matrix gives the payoff for Player 1 and Player 2 with R and L strategies. Assume that they determine their strategies simultaneously and independently.

		Player 2
		R	L
	R	(5, 4)	(-1, -1)
Player 1	L	(-1, -1)	(2, 2)

(a) Does Player 1 have a dominant strategy? Why or why not? What is its dominant strategy, if existing?

(b) Does Player 2 have a dominant strategy? Why or why not? What is its dominant strategy, if existing?

(c) Identify the Nash equilibrium(s) in this game? State explicitly the respective strategy of Player 1 and Player 2 in each Nash Equilibrium.

Answer 1

(a) Given that player 2 choose R, player 1's best response is R(5).
Given that player 2 choose L, player 1's best response is L(2).
So, player 1 does not have a dominant strategy because there is no single strategy which is always chosen by player 1 irrespective of player 2's strategy which means player 1's decision changes based on player 2's decision.

(b) Given that player 1 choose R, player 2's best response is R(4).
Given that player 1 choose L, player 2's best response is L(2).
So, player 2 does not have a dominant strategy because there is no single strategy which is always chosen by player 2 irrespective of player 1's strategy which means player 2's decision changes based on player 1's decision.

(c) There are two Nash equilibrium(s) in the game as best response of both players occur simultaneously at two sets. They are:
(R, R) = (5, 4) where player 1 choose R and player 2 also choose R.
(L, L) = (2, 2) where player 1 choose 2 and player 2 also choose L.