Question

QUESTION 3

1. 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

When player A plays strategy 1, B will be better off by strategy 2 because 0 from choosing strategy 2 is greater than -2 from choosing strategy 1. Therefore, the outcome is (strategy 1, strategy 2).

When player A chooses 2, B will be better off by choosing strategy 1 because 8 > 0. Therefore, the strategy becomes (Strategy 2, strategy 1).

When player B chooses 1, player A will be better off by choosing strategy 2 because 0 > -3. Therefore, the strategy becomes (strategy 2, strategy 1).

When player B chooses 2, player A will be better off by choosing 1, because 10 > 0. Therefore, the strategy becomes (strategy 1, strategy 2).

Therefore, this game has two pure strategy nash equilibria : (strategy 1, strategy 2) with payoff (10, 0) and (strategy 2, strategy 1) with payoff (0,8).