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