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How can two friends choosing between two movies produce multiple Nash equilibria?

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A colorful payoff matrix for a normal form game in game theory, showing strategy options-support, oppose, evade-for both party A and party B. Each cell contains cartoon figures representing each party's action and lists percentage payoffs for A and B. The bottom-right cell is labeled saddlepoint, highlighting the equilibrium. — game theory Table 1
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.

In game theory, a Nash equilibrium occurs when no player can improve their expected outcome by unilaterally changing their strategy. When two friends choose between two movies, multiple Nash equilibria can arise if both individuals prioritize seeing a movie together over seeing a specific film alone.

In this scenario, if both friends prefer to be together, the two possible outcomes where they both attend the same movie—either Movie A or Movie B—each constitute a Nash equilibrium. This is because, in either case, if one friend were to switch to the other movie, they would end up watching a film alone, which is a worse outcome for them. Since neither friend can improve their situation by changing their choice while the other remains constant, both joint-attendance scenarios are stable.1

This situation highlights how interdependent decisions can lead to multiple solutions where coordination is key to achieving a preferred outcome, even without formal communication.12