nash equilibrium

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Thân thiện
Definition
  1. Noun:
    • (Game Theory) A stable state of a system involving several interacting participants in which no participant can gain by a change of strategy as long as all the other participants remain unchanged. It is a fundamental concept in game theory describing a solution where, given the strategies of all other players, no single player can benefit by unilaterally changing their own strategy.
Usage Examples
  • Noun:
    • In the classic Prisoner's Dilemma, both prisoners confessing represents a Nash equilibrium.
    • The economist explained that a Nash equilibrium does not necessarily mean the best overall outcome for the group, only that no individual has an incentive to deviate.
    • Finding the Nash equilibrium is crucial for analyzing strategic interactions in economics and political science.
Advanced Usage
  • "To be in a Nash equilibrium": Describes a situation where the conditions of a Nash equilibrium are currently met.
    • The market prices are in a Nash equilibrium; no single firm can increase profits by changing its price alone.
  • "To reach a Nash equilibrium": Describes the process or outcome of arriving at this stable state.
    • After several rounds of bidding, the auction reached a Nash equilibrium.
Variants and Related Words
  • Nash equilibrium point (n): Another term for Nash equilibrium, emphasizing it as a specific solution point within a game.
  • Equilibrium (n): A state of balance. In game theory, it specifically refers to a solution concept like Nash equilibrium.
  • Game Theory (n): The study of mathematical models of strategic interaction among rational decision-makers, which is the field where Nash equilibrium is defined.
Synonyms
  • Strategic equilibrium: A general term for a stable state in a strategic game.
  • Non-cooperative equilibrium: Highlights that the concept applies to situations where binding agreements are not possible.
Related Concepts (Not Phrasal Verbs)
  • Dominant strategy: A strategy that is best for a player regardless of what the other players do. A Nash equilibrium may involve dominant strategies.
  • Pareto efficiency: A state where no individual can be made better off without making someone else worse off. A Nash equilibrium is not always Pareto efficient.
  • Mixed-strategy Nash equilibrium: A Nash equilibrium where at least one player randomizes over (mixes) several pure strategies.
Noun
  1. (game theory) a stable state of a system that involves several interacting participants in which no participant can gain by a change of strategy as long as all the other participants remain unchanged

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