Which of the following conditions correctly describes a Nash equilibrium when two firms are in the market? A) π₁(s₁^*, s₂^*) ≥ π₁(s₁, s₂^*) for all s₁. B) π₁(s₁^*, s₂^*) ≥ π₁(s₁, s₂^*) for all s₁ and π₂(s₁^*, s₂^*) ≥ π₂(s₁^*, s₂) for all s₂. C) π₁(s₁^*, s₂^*) ≥ π₂(s₁, s₂^*) for all s₁ and π₂(s₁^*, s₂^*) ≥ π₁(s₁^*, s₂) for all s₂. D) π₁(s₁, s₂^*) ≥ π₂(s₁^*, s₂^*) for all s₁ and π₂(s₁^*, s₂) ≥ π₁(s₁^*, s₂^*) for all s₂.

Question

Quizplus · Accepted Answer

In a two-firm market, a Nash equilibrium is achieved when neither firm can improve its profit by unilaterally changing its production strategy while the other firm keeps its production strategy unchanged. In this case, choice B correctly describes a Nash equilibrium because it states that firm 1's profit under the joint strategy of (s₁^*, s₂^*) is at least as high as its profit under any other strategy, and similarly, firm 2's profit under the joint strategy is at least as high as its profit under any other strategy. This means that neither firm can improve its profit by changing its strategy while the other firm keeps its strategy unchanged, which is the key characteristic of a Nash equilibrium.

Which of the Following Conditions Correctly Describes a Nash Equilibrium