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Can a game have more than one Nash equilibrium?

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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.

Yes, it is entirely possible for a game to have more than one Nash equilibrium.

In game theory, a Nash equilibrium represents a stable outcome where no player can improve their expected payoff by unilaterally changing their strategy. While some games result in a single equilibrium, others may feature multiple stable points depending on the players' interdependent decisions.1

A classic example of multiple equilibria is a coordination game where two friends want to see a movie together but disagree on the choice. If both individuals prefer seeing either movie together over seeing one alone, then both friends choosing the first movie is a Nash equilibrium, and both friends choosing the second movie is also a Nash equilibrium. In either scenario, neither person can switch their choice to the other film without resulting in a worse outcome for themselves.1

Furthermore, equilibria can be "pure," where a player consistently chooses one strategy, or "mixed," where a player employs a specific probability distribution across multiple strategies to prevent exploitation by opponents.1