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 1, and the payoff for B is 0.

		Player B
		Strategy 1	Strategy 2
Player A	Strategy 1	(1,0)	(0,1)
	Strategy 2	(0,1)	(1,0)

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

Answer 1

		PLAYER B
		STRATEGY 1	STRATEGY 2
PLAYER A	STRATEGY 1	(1,0)	(0,1)
STRATEGY 2	(0,1)	(1,0)

Considering,

Player A as the row player and the first mover.

Player B is the column player and the second mover.

If player A chooses strategy 1 , player B chooses strategy 2 comparing the pay off on B's part.(i,e comparing (1,0) and (0,1), here 1>0, so player B chooses strategy 2)

similarly,

If player A chooses strategy 2 player B chooses strategy 1.

If player B chooses strategy 1 player A chooses strategy 1.

If player B chooses strategy 2 player A chooses strategy 2.

So we can conclude that there is no pure strategy Nash Equilibrium.