A Nash equilibrium is a condition
A. that results in the highest payoff to a player regardless of the opponent's action.
B. that guarantees the highest payoff given the worst possible scenario.
C. that describes a set of strategies in which no player can improve her payoff by changing strategy.
D. where a player randomizes over two or more available actions in order to keep rivals from being able to predict her act.
Answer (2)
A Nash equilibrium occurs when players in a game choose strategies such that no player can benefit by unilaterally changing their strategy. The correct answer is C, which indicates that it describes a situation where no player's payoff can improve by changing their strategy. This concept is essential in analyzing competitive interactions in economics and game theory.
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The question relates to game theory, specifically the concept of Nash equilibrium.
A Nash equilibrium is a fundamental concept in game theory that describes a situation in a strategic game where no player can benefit by unilaterally changing their strategy, given the strategies of all other players remain constant. To understand it better, let's first look at the given options and explain why one of them is correct:
A. 'A condition that results in the highest payoff to a player regardless of the opponent's action.'
This describes a dominant strategy rather than Nash equilibrium. A dominant strategy guarantees the highest payoff regardless of the other player's actions, but that is not what Nash equilibrium represents.
B. 'A condition that guarantees the highest payoff given the worst possible scenario.'
This is a description of maximin strategy , which focuses on maximizing the minimum payoff (considering the worst-case scenario). It is not specifically about Nash equilibrium.
C. 'A condition that describes a set of strategies in which no player can improve her payoff by changing strategy.'
This option correctly describes a Nash equilibrium. Here, each player’s strategy is optimal given the strategies chosen by other players. Hence, no player has anything to gain by changing only their own strategy unilaterally.
D. 'A condition where a player randomizes over two or more available actions in order to keep rivals from being able to predict her act.'
This option describes a concept related to mixed strategies , where players randomize their strategies to remain unpredictable. While Nash equilibrium can exist in such settings, this is not the specific definition of Nash equilibrium itself.
Based on these explanations, the correct choice is C: 'A condition that describes a set of strategies in which no player can improve her payoff by changing strategy.'
Nash equilibrium can exist in various games, including those involving multiple players, complex strategies, and even mixed strategies. It applies to many fields such as economics, politics, and business, where strategic interactions are analyzed to make optimal decisions.
