Question

Consider the following battle of sexes.

	Y1	Y2
X1	3,2	1,1
X2	0,0	2,3

(a) Find Minmax payoff values and plot the set of feasible payoffs.

(b) Which is the highest symmetric average payoff that can be sustained in the infinitely repeated game?

Answer 1

A) for row player

Maximum he can get when column player plays Y1 is 3

When he plays Y2, then maximum , row player can get is2

So minmax payoff = minimum of the maximum

= 2

for column player

when row player plays X1 , maximum he can get = 2

when X2 is played, then maximum column player can get = 3

so minmax = 2

so for both, minmax payoff = 2

sketch

k indfviduai Rational payo that can bo SuStained 23) SPNGe (213) a 3 2. (3,2) (010)

B)

Highest symmetric payoff

(2,2) bcoz it lies in the shaded region