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In the payoff matrix what is the Nash equilibrium (dominant strategy)?

User Fuzes
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Final answer:

The Nash equilibrium in a game theory setting, such as a prisoner's dilemma or a duopoly in an oligopoly, is often where all participants choose the dominant strategy, which leads to a stable outcome where no individual can benefit by changing strategy unilaterally. The dominant strategy, often being to confess or increase output, leads to a less optimal collective outcome than possible with cooperation.

Step-by-step explanation:

The concept in question relates to game theory, specifically the Nash equilibrium, and dominant strategy in the context of a payoff matrix. In game theory, a Nash equilibrium refers to a situation where no player can benefit by changing their strategy while the other players keep theirs unchanged. The dominant strategy is an action that yields the best payoff for a player, no matter what the other players do.

In the classic prisoner's dilemma, the Nash equilibrium occurs when both prisoners choose to confess because confessing is the dominant strategy for both. Each prisoner's best response is to confess, regardless of the other's decision, as it minimises their own potential loss. This demonstrates the paradox where individual rational choices lead to a worse outcome than possible by mutual cooperation.

In a duopoly, an oligopoly with only two firms, the firms face a similar situation. If both firms cooperate and hold down output, they can earn higher monopoly-like profits. However, because their dominant strategy is to increase output, the Nash equilibrium is where both firms increase output, resulting in each earning lower profits.

User Aminul
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