In the Battle of the Sexes game,Man likes to go to watch football,while Woman likes to go to the mall.Both of them would rather go together than go alone.They decide to show up to one of these places without contacting each other.A game like this will have
A)a dominant strategy for Man and none for Women.
B)one dominant strategy for both the players.
C)no Nash equilibrium strategies.
D)a Nash equilibrium in mixed strategies.

Question

Quizplus · Accepted Answer

This scenario can be modeled as a Battle of the Sexes game. Both Man and Woman have two options: go to the football game or go to the mall. Both players want to spend time together, so the best outcome for both of them is to coordinate and end up at the same place.
There is no dominant strategy for either player in this scenario. If Man chooses to go to the football game, and Woman chooses to go to the mall, that is not a Nash equilibrium because both players would prefer to be together. Similarly, if Man chooses to go to the mall, and Woman chooses to go to the football game, both players would be unhappy.
The best strategy for both players is to randomize between the two options. This means that each player chooses each option with a certain probability. For example, if Man chooses to go to the football game with probability 0.6 and go to the mall with probability 0.4, and Woman chooses to go to the mall with probability 0.6 and go to the football game with probability 0.4, then there is a Nash equilibrium in mixed strategies. This is because neither player can improve their outcome by unilaterally changing their strategy. 
Therefore, the best answer is D.

In the Battle of the Sexes Game,Man Likes to Go