QUESTION 3
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.
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).
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