What is a Nash equilibrium?

What is a Nash equilibrium?

• A. A situation in which no player can improve their payoff by unilaterally changing their strategy.
• B. A strategy that maximizes the total payoff for all players.
• C. A stable outcome where players always choose the same strategy.
• D. An outcome in which one player can always influence the others.

Answer: (A)

The main idea being tested is that a Nash equilibrium is a stable situation where each player’s choice is the best response to the others’ choices. In other words, once everyone has chosen their strategies, no player can improve their own payoff by changing only their own strategy while the others keep theirs fixed. That definition is exactly what the correct option expresses: given what the other players are doing, no one can increase their payoff by unilaterally changing their strategy. It captures the stability against unilateral deviation, which is the heart of a Nash equilibrium. It’s helpful to distinguish this from maximizing the total payoff for everyone—that describes a social optimum, which is not guaranteed to be stable if someone can gain by changing their own action. It’s also not about everyone always picking the same action, since equilibria can involve different actions or even randomized (mixed) strategies. And it isn’t about one player always having influence; Nash equilibria can occur in balanced situations where influence isn’t one-sided.

The main idea being tested is that a Nash equilibrium is a stable situation where each player’s choice is the best response to the others’ choices. In other words, once everyone has chosen their strategies, no player can improve their own payoff by changing only their own strategy while the others keep theirs fixed.

That definition is exactly what the correct option expresses: given what the other players are doing, no one can increase their payoff by unilaterally changing their strategy. It captures the stability against unilateral deviation, which is the heart of a Nash equilibrium.

It’s helpful to distinguish this from maximizing the total payoff for everyone—that describes a social optimum, which is not guaranteed to be stable if someone can gain by changing their own action. It’s also not about everyone always picking the same action, since equilibria can involve different actions or even randomized (mixed) strategies. And it isn’t about one player always having influence; Nash equilibria can occur in balanced situations where influence isn’t one-sided.