# MACROeconomics - Game Theory

posted by on .

Consider the following game matrix:

....................................................Player B............
............................................Left............Right.......
Player A.........Top..............(a, b)...........(c, d).......
.......................Bottom........(e, f)............(g, h).......

a) If (top, left) is a dominant strategy equilibrium, then we know that “a” is greater than ____, “b” is greater than _____, “c” is greater than _______ and “f” is greater than _______.
a > c , b > e , c > f , f > c

b) If (top, left) is a Nash equilibrium, then which of the inequalities from your answer in part (a) must be satisfied?
a > b and b > f

c) If (top, left) is a dominant strategy equilibrium, must it be a Nash equilibrium?
No

• MACROeconomics - Game Theory - ,

I'm having some trouble with your notation. Let me asssume that (x,y) means that x is the outcome going to player A, y is the outcome going to player B.

If top left is a dominant strategy equilibrium, it implies A perfers outcome Top and B prefers outcome Left. Ergo, I think a>e, b>d, c>g, f>h

Under a Nash equilibrium, a player cannot do better by switching. So if starting in Top-Left, The choice for player A is to move to Bottom-Left. If he does not move, it must be that a>e. Similarly, for B not to move, b>d.
We cant say if A would perfer c over g or vice-versa. Ditto, we cant tell if B would prefer f over h.

c) I think yes. A dominant strategy equilibrium must also be a Nash equilibrium.