A Nash equilibrium is:[Fill in the blank]

Question

BlackTom AI · Accepted Answer

An outcome in which each player’s strategy is a best response to the other’s is the defining property of a Nash equilibrium.

Relevant concepts:
- Best response: a strategy that gives a player the highest payoff given the other players’ strategies.
- Nash equilibrium (NE): a profile of strategies (s1*, s2*, ...) such that no single player can increase her payoff by unilaterally deviating.
- Pareto efficiency and dominant strategies are related concepts but not equivalent to NE.

Step-by-step reasoning and formal statement:
1. Let s1* and s2* be the strategies chosen by players 1 and 2. NE requires
   u1(s1*, s2*) ≥ u1(s1, s2*) for every possible s1 (player 1 cannot do better by changing unilaterally),
   and u2(s1*, s2*) ≥ u2(s1*, s2) for every possible s2 (player 2 cannot do better by changing unilaterally).
2. These inequalities encapsulate “each player’s strategy is a best response to the other’s.” There is no incentive for any single player to deviate given the other’s choice.
3. Thus option b is exactly the definition of Nash equilibrium.

Why the other options are incorrect:
- a. “An outcome where both players earn the same payoff” is false: NE does not require equal payoffs. Players can have very different payoffs at equilibrium.
- c. “Any outcome with a dominant strategy” is false: a dominant-strategy equilibrium (where every player has a strategy that is best regardless of others) is a special case of NE, but NE includes many outcomes where no dominant strategies exist. So dominance is sufficient but not necessary.
- d. “Always Pareto efficient” is false: many NE are Pareto-inferior. Example: the Prisoner’s Dilemma has the unique NE (Defect, Defect) that yields lower payoffs for both than (Cooperate, Cooperate), so the NE is not Pareto efficient.

Conclusion: The correct answer is b. This matches the provided answer: “an outcome where each player’s strategy is a best response to the other’s.”

A Nash equilibrium is:[Fill in the blank]Single choice

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