Editing Game theory (section)

===Battle of the sexes ===
{{main|Battle of the sexes (game theory)}}

The "battle of the sexes" is a term used to describe the perceived conflict between men and women in various areas of life, such as relationships, careers, and social roles. This conflict is often portrayed in popular culture, such as movies and television shows, as a humorous or dramatic competition between the genders. This conflict can be depicted in a game theory framework. This is an example of non-cooperative games.

An example of the "battle of the sexes" can be seen in the portrayal of relationships in popular media, where men and women are often depicted as being fundamentally different and in conflict with each other. For instance, in some romantic comedies, the male and female protagonists are shown as having opposing views on love and relationships, and they have to overcome these differences in order to be together.<ref>{{Cite web |title=Battle of the Sexes {{!}} History, Participants, & Facts {{!}} Britannica |url=https://www.britannica.com/topic/Battle-of-the-Sexes-tennis |access-date=2023-04-23 |website=www.britannica.com |archive-date=23 April 2023 |archive-url=https://web.archive.org/web/20230423131644/https://www.britannica.com/topic/Battle-of-the-Sexes-tennis |url-status=live }}</ref>

In this game, there are two pure strategy Nash equilibria: one where both the players choose the same strategy and the other where the players choose different options. If the game is played in mixed strategies, where each player chooses their strategy randomly, then there is an infinite number of Nash equilibria. However, in the context of the "battle of the sexes" game, the assumption is usually made that the game is played in pure strategies.<ref>{{Cite web |last=Athenarium |date=2020-08-12 |title=Battle of the Sexes – Nash equilibrium in mixed strategies for coordination |url=https://athenarium.com/battle-of-the-sexes-mixed-strategies/ |access-date=2023-04-23 |website=Athenarium |archive-date=23 April 2023 |archive-url=https://web.archive.org/web/20230423144200/https://athenarium.com/battle-of-the-sexes-mixed-strategies/ |url-status=live }}</ref>