"In game theory, the Nash equilibrium, named after the mathematician John Nash..."
A concept in game theory that describes a stable state of a game in which no player can improve their payoff by unilaterally changing their strategy.
Game theory: A branch of mathematics that studies decision-making in situations where two or more individuals or groups have conflicting interests.
Strategic interactions: Situations where individuals or groups make decisions that affect the outcome of the game.
Decision-making process: The steps individuals or groups take when making a decision in a strategic interaction.
Non-cooperative games: Games in which players make decisions independently of one another and do not enter into binding agreements.
Cooperative games: Games in which players can enter into binding agreements that affect the outcome of the game.
Mixed strategy: A strategy in which a player selects more than one action with certain probabilities.
Dominant strategy: A strategy that is best for a player regardless of what the other players do.
Prisoner's dilemma: A classic example of a non-cooperative game in which two criminals face a decision to cooperate or defect.
Battle of the sexes: A classic example of a coordination game in which two individuals must choose between two options.
Game trees: A graphical representation of a game that shows the possible outcomes and decision points.
Nash equilibrium: A solution concept in which no player can improve their payoff by unilaterally changing their strategy.
Pareto efficiency: A state where no player can be made better off without making another player worse off.
Zero-sum games: Games in which one player's gain is another player's loss.
Positive-sum games: Games in which all players can gain from cooperation.
Sequential games: Games in which players make decisions in a specific order.
Simultaneous games: Games in which players make decisions simultaneously.
Continuous games: Games in which players make decisions over a continuous range of actions.
Coefficient matrix: A matrix that represents the outcomes of all possible strategies.
Nash bargaining solution: A solution concept for cooperative games.
Evolutionary game theory: A framework for studying the evolution of strategies in populations of players.
Pure strategy Nash equilibrium: Every player takes one particular action and no player can unilaterally change their strategy to gain an advantage.
Mixed strategy Nash equilibrium: Players choose actions randomly according to a probability distribution over potential actions.
Symmetric Nash equilibrium: All players have the same strategy.
Asymmetric Nash equilibrium: Players have different strategies.
Strong Nash equilibrium: Once an equilibrium is reached, no coalition of players can gain by deviating from their strategy.
Weak Nash equilibrium: No individual player can gain by switching to a different strategy, but a coalition of players can still gain by coordinating their actions.
Perfect Bayesian Nash equilibrium: Players have all the information they need to make optimal choices, and their strategies take into account the possibility of other players having different pieces of information.
Trembling hand perfect Nash equilibrium: Overtime, players may make small mistakes, so this equilibrium accounts for this phenomenon.
Correlated equilibrium: Players may coordinate without explicitly communicating through chance or shared randomness.
Evolutionarily stable strategy: This equilibrium predicts the strategy that will be most likely to survive in a population of players over time.
"The Nash equilibrium...is the most common way to define the solution of a non-cooperative game involving two or more players."
"Each player is assumed to know the equilibrium strategies of the other players."
"No one has anything to gain by changing only one's own strategy."
"The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs."
"In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy."
"(A, B, C, D) is a Nash equilibrium if A is Alice's best response to (B, C, D), B is Bob's best response to (A, C, D), and so forth."
"Nash showed that there is a Nash equilibrium, possibly in mixed strategies, for every finite game."
"Cournot...applied it to competing firms choosing outputs."
"(A, B, C, D) is a Nash equilibrium if A is Alice's best response to (B, C, D), B is Bob's best response to (A, C, D), and so forth."
"...to define the solution of a non-cooperative game involving two or more players."
"no one can increase one's own expected payoff by changing one's strategy while the other players keep theirs unchanged."
"Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob has no other strategy available that does better than B at maximizing his payoff in response to Alice choosing A."
"Nash showed that there is a Nash equilibrium, possibly in mixed strategies, for every finite game."
"...applied it to competing firms choosing outputs."
"...competing firms choosing outputs."
"Nash showed that there is a Nash equilibrium, possibly in mixed strategies, for every finite game."
"No one has anything to gain by changing only one's own strategy."
"Each player is assumed to know the equilibrium strategies of the other players."
"each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy."