Question

Below is a game between player A and player B. Each player has two possible strategies: 1 or 2. The payoffs for each combination of strategies between A and B are in the bracket. For example, if A plays 1 and B plays 1, the payoff for A is -3, and the payoff for B is -2.

		Player B
		Strategy 1	Strategy 2
Player A	Strategy 1	(-3,-2)	(10,0)
	Strategy 2	(0,8)	(0,0)

How many pure strategy Nash equilibria does this game have? Explain your answer.

Answer 1

The answer is: there are two pure strategies nash equilibrium.

Using the best resposnes:

For player A, the best response is to choose strategy 2 when player B chooses strategy 1 (0>-3) and to choose strategy 1 when player B chooses strategy 2 (10>0)

For player B, the best response is to choose strategy 2 when player A chooses strategy 1 (0>-2) and to choose strategy 1 when player A chooses strategy 2 (8>0)

Thus, from best responses, we have two pure strategy nash equilibrium:

(1) Player A chooses strategy 1 and player B chooses strategy 2

(2) Player A chooses strategy 2 and player B chooses strategy 1.