Question

This problem refers to the following game:

	A	B
A	(2, 4)	(0, 2)
B	(1, 1)	(3, 4)

a.       What are the pure-strategy Nash equilibria?

b.       Is there a mixed strategy Nash equilibrium where both players mix A and B? If so, find the equilibrium. If not, explain why not.

Answer 1

A There are two pure strategy Nash equilibria. First is A and A. The reason is if player 1 chooses A, player 2 will also choose A because returns are higher(4 compared to 2).Similarly if 2 chooses A, 1 will choose A because returns of 4 are higher than otherwise (1).

Similarly BB is Nash equilibria since whatever 1 does it is always better for 2 to choose B if A chooses B and it is always better for 1 to choose B if 2 chooses B.

No there is not any mixed strategy as they are satisfied with AA or BB depending on which player choose What initially.