Question

13. Consider the following game between two early settlers in the United States:
    

		Settler 2
		Move West	Move North
Settler 1	Move West	60, 110	100, 140
	Move North	70, 130	90, 100

1. Which player has dominant strategy?

What is (are) equilibrium outcome(s) of the game?                                                        

Answer 1

a-

If settler 1 moves west, it is optimal for settler 2 to move north.

If settler 1 moves north, it is optimal for settler 2 to move west.

So, there is no dominant strategy for settler 2.

If settler 2 moves west, it is optimal for settler 1 to move north.

If settler 2 moves north, it is optimal for settler 1 to move west.

So, there is no dominant strategy for settler 1.

Therefore, no player has any dominant strategy.

b-

There are 2 equilibrium outcomes:

Settler 1 moves north, settler 2 moves west.

Settler 1 moves west, settler 2 moves north.

At these strategies there is no incentive for any settler to switch to other strategy and hence they are nash equilibrium.