Consider the game of the battle of sexes. How would you modify the payoffs to (F,O) and (O,F) to reflect the following:

For the husband, the ranking of payoffs are as follows:

F with wife > F alone > O with wife > O alone;

and for wife

O with husband > O alone > F with husband > F alone.

Namely, the husband is unhappiest when he is at the opera by himself, he is a little happier when he is with his wife at the opera, he is happier still when he is at the football game by himself, and he is the happiest if they are both at the football game. The story of the wife is similar.

a. Put down a normal form game (strategic form game) to reflect the above rankings.

b. Write down the set of strategy combinations S.

c. Does H have a dominant strategy? Prove your answer.

d. Does the game have a dominant strategy solution? If yes, which one?