Definition
A Nash Equilibrium is a concept within game theory describing a state in a non-cooperative game where no player has an incentive to deviate from their chosen strategy after considering the strategies of the other players.
- How to read: “For all players i, the utility function for player i evaluated at the optimal strategy profile is greater than or equal to the utility function for player i evaluated at any other strategy for player i, given the optimal strategies of the other players.”
- Meaning: No player can improve their payoff by unilaterally deviating from equilibrium strategy while all others hold fixed.
Why It Matters
In a Nash Equilibrium, no player can improve their outcome by changing their strategy alone. This often leads to ‘deadlocks’ where everyone is worse off than they could be (e.g., the Prisoner’s Dilemma). Understanding this equilibrium is critical for identifying when a system is stuck and needs external intervention to change.
Core Concepts
- Non-Cooperative Games: Scenarios where players make decisions independently without binding agreements.
- Dominant Strategy: A strategy that yields the highest payoff for a player regardless of what others do.
- Prisoner’s Dilemma: A classic game showing how rational individuals might not cooperate, even when it’s in their best interest to do so.
- Pareto Optimality vs. Nash Equilibrium: An outcome can be a Nash equilibrium without being socially optimal (Pareto efficient).