Nash equilibrium (NE) is a game theory concept which illustrates the result of a particular game. Most fundamentally, NE is the result of a collection of decisions in which no player would like to change the result, holding all other decisions constant (because a player can only change his or her behavior).

Game Theory Series

Normal form gameExtensive form gameCooperative game

Equilibrium Concepts
Nash equilibriumSubgame perfect Nash equilibriumBackwards induction

Prisoner's dilemmaChicken gameHawk-Dove gameUltimatum gameCoordination gameDictator game

One way to find Nash equilibrium is to examine each possible outcome of a game (cells) and compare payoffs. If a player could get a higher payoff ceteris paribus, then that strategy is not Nash equilbrium.

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Also a NE is the outcome of a game where no player wants to unilaterally deviate. Which is another way to say, she can only control her own behavior not any other players. Also when working with Bayesian NE, remember to use the "INDIFFERENCE PRINCIPLE" which is to say at what point, given a probability P for action A, and probability 1-P for action B (assuming just 2 actions) would the player be indifferent between the 2 strategies. This is built off of expected utility from a strategy which COULD be a strategy from a set of strategy profiles.