3 mins read

Nash Equilibrium

Ankit0

A Nash equilibrium is a set of strategies, one for each player, where each player’s strategy is optimal given the strategies of the other players. In other words, it is a point where all players are satisfied with their chosen strategies, and there is no incentive for any player to change their strategy.

Key Concepts:

  • Players: Individuals or groups making decisions in a game.
  • Strategies: The choices available to each player.
  • Nash Equilibrium: A set of strategies, one for each player, where each strategy is optimal given the strategies of the other players.
  • Optimal Strategy: The strategy that maximizes a player’s payoff, given the strategies of the other players.
  • Payoff: The benefit or cost associated with each possible combination of strategies.

Examples:

  • Prisoner’s Dilemma: Two prisoners are interrogated separately and asked to testify against each other. If both prisoners testify, they each receive a penalty of 5 years. If one prisoner testifies and the other remains silent, the testifying prisoner receives a penalty of 2 years and the silent prisoner receives a penalty of 3 years. If both prisoners remain silent, they receive a penalty of 1 year. In this case, the Nash equilibrium is (T,T), where both prisoners testify.
  • Zero-Sum Game: Two players have two strategies each, and the sum of their payoffs is always zero. In a zero-sum game, there is always a Nash equilibrium, as each player can guarantee themselves a non-negative payoff by playing their best move.

Characteristics:

  • Non-cooperative: Players do not cooperate in choosing their strategies.
  • Strategic: Strategies are based on the expectations of other players’ actions.
  • Ex-ante: Strategies are chosen before the game begins.
  • Unique: In some games, there can be multiple Nash equilibria.

Applications:

Nash equilibrium is used in various fields, including:

Key Takeaways:

  • Nash equilibrium is a concept in game theory that describes a point where all players are satisfied with their chosen strategies.
  • The Nash equilibrium is a fundamental concept in game theory and has applications in various fields.
  • The existence of a Nash equilibrium depends on the specific game and the players’ strategies.

FAQs

  1. What is Nash equilibrium in simple words?

    Nash equilibrium is a situation in a game where no player can improve their outcome by changing their strategy, as long as the other players keep their strategies unchanged.

  2. Is Nash equilibrium a solution concept?

    Yes, Nash equilibrium is a key solution concept in game theory that predicts how rational players will behave in strategic situations.

  3. How do you identify a Nash equilibrium?

    A Nash equilibrium is identified when no player can benefit from changing their strategy while others stick to their current strategies.

  4. What is a real-life example of Nash equilibrium?

    A common real-life example is in traffic: if everyone chooses the fastest route, no one benefits from switching routes, leading to a Nash equilibrium in road choices.

  5. What is the Nash equilibrium in the Prisonerโ€™s Dilemma?

    In the Prisoner’s Dilemma, the Nash equilibrium occurs when both prisoners choose to betray each other, even though cooperation would have led to a better outcome.

Disclaimer

Related Posts