What is a Nash equilibrium in a noncooperative game?
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.
In game theory, a Nash equilibrium is an outcome in a noncooperative game involving two or more players where no player can improve their expected payoff by unilaterally changing their own strategy.1
A game is considered noncooperative when there is no mechanism for players to make binding agreements. In such scenarios, each player acts independently to maximize their own outcome, assuming the strategies of others remain fixed. The Nash equilibrium represents a state of stability: if every player has chosen a strategy and no one can benefit by switching, the current set of strategies is in equilibrium.1
Key characteristics include:
* Strategy Types: Equilibria can be "pure," where players consistently choose a single strategy, or "mixed," where players employ a specific probability distribution over multiple strategies.1
* Multiple Outcomes: A single game may possess more than one Nash equilibrium.1
* Collective vs. Individual: The equilibrium does not necessarily result in the best collective outcome for the players; it simply represents the point where individual incentives prevent further deviation.1
Named after the mathematician John Nash, this concept serves as a fundamental solution for analyzing interdependent decision-making in fields like economics and military strategy.1