Question

In: Economics

Below is a game between player A and player B. Each player has two possible strategies:...

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.

Solutions

Expert Solution

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.


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