Here is an example of the Battle of the Sexes game discussed in the text. Two people,

Question:

Here is an example of the €œBattle of the Sexes€ game discussed in the text. Two people, let us call them Michelle and Roger, although they greatly enjoy each other€™s company, have very different tastes in entertainment. Roger€™s tastes run to ladies€™ mud wrestling, while Michelle prefers Italian opera. They are planning their entertainment activities for next Saturday night. For each of them, there are two possible actions, go to the wrestling match or go to the opera. Roger would be happiest if both of them went to see mud wrestling. His second choice would befor both of them to go to the opera. Michelle would prefer if both went to the opera. Her second choice would be that they both went to see the mud wrestling. They both think that the worst outcome would be that they didn€™t agree on where to go. If this happened, they would both stay home and sulk.

(a) Is the sum of the payoffs to Michelle and Roger constant over all outcomes? _________ Does this game have a dominant strategy equilibrium? __________
(b) Find two Nash equilibria in pure strategies for this game.
(c) Find a Nash equilibrium in mixed strategies.