2. In the original story of the Battle of the Sexes games the couple was reciprocally deeply in love and had different first choices for which activity to do together on a given evening, but each had preferences such that their first choice of the four cells in the 2 x 2 table was to attend together their preferred activity with their second choice being to attend together the preferred activity of the other person. A. Suppose that the Battle of the Sexes game is altered in the way depicted below: Table 1 Shawn likes Mary more than Mary likes Shawn Mary Movies 2.5, 0.5 Bowling 1.0, 1.0 Movies Shawn Bowling 0,0 1.5, 1.5 Find all Nash equilibria in pure strategies for this payoff matrix based on the changed assumptions of the Battle of the Sexes game. Explain why your choice(s) is(are) a Nash equilibrium? B. Suppose instead that the Battle of the Sexes game is altered in the way depicted below: Table 2 Mary and Shawn like each other a little Mary Movies 1.5, 0.5 Bowling 1.0, 1.0 Movies Shawn Bowling 0,0 0.5 1.5 Find all Nash equilibria in pure strategies for this payoff matrix based on the changed assumptions of the Battle of the Sexes game. Explain why your choice(s) is(are) a Nash equilibrium? C. Suppose now that the Battle of the Sexes game is altered in the way depicted below: Table 3 Mary and Shawn hate each other Mary Movies -0.5-1.5 Bowling 1.0 1.0 Movies Shawn Bowling 00 -1.5 -0.5 Find all Nash equilibria in pure strategies for this payoff matrix based on the changed assumptions of the Battle of the Sexes game. Explain why your choice(s) is(are) a Nash equilibrium? 2. In the original story of the Battle of the Sexes games the couple was reciprocally deeply in love and had different first choices for which activity to do together on a given evening, but each had preferences such that their first choice of the four cells in the 2 x 2 table was to attend together their preferred activity with their second choice being to attend together the preferred activity of the other person. A. Suppose that the Battle of the Sexes game is altered in the way depicted below: Table 1 Shawn likes Mary more than Mary likes Shawn Mary Movies 2.5, 0.5 Bowling 1.0, 1.0 Movies Shawn Bowling 0,0 1.5, 1.5 Find all Nash equilibria in pure strategies for this payoff matrix based on the changed assumptions of the Battle of the Sexes game. Explain why your choice(s) is(are) a Nash equilibrium? B. Suppose instead that the Battle of the Sexes game is altered in the way depicted below: Table 2 Mary and Shawn like each other a little Mary Movies 1.5, 0.5 Bowling 1.0, 1.0 Movies Shawn Bowling 0,0 0.5 1.5 Find all Nash equilibria in pure strategies for this payoff matrix based on the changed assumptions of the Battle of the Sexes game. Explain why your choice(s) is(are) a Nash equilibrium? C. Suppose now that the Battle of the Sexes game is altered in the way depicted below: Table 3 Mary and Shawn hate each other Mary Movies -0.5-1.5 Bowling 1.0 1.0 Movies Shawn Bowling 00 -1.5 -0.5 Find all Nash equilibria in pure strategies for this payoff matrix based on the changed assumptions of the Battle of the Sexes game. Explain why your choice(s) is(are) a Nash equilibrium