In the Battle of the Sexes game, Man likes to go to 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:

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Quizplus · Accepted Answer

There is no dominant strategy for either player, as it depends on the other player's choice. Therefore, we need to look for a Nash equilibrium in mixed strategies, where each player chooses their strategy with a certain probability. In this case, Man could choose to go to football with a probability of p and choose to go to the mall with a probability of (1-p). Similarly, Woman could choose to go to the mall with a probability of q and choose to go to football with a probability of (1-q). The Nash equilibrium would be where neither player has an incentive to change their strategy given the other player's choice. Solving for the Nash equilibrium in mixed strategies, we get p=q=0.5, which means that both players should randomly choose between football and the mall with equal probability.

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