Game theory is a branch of mathematics that deals with decision-making in situations where two or more individuals have conflicting interests. It is used extensively in economics, political science, psychology, and other fields. One of the key concepts in game theory is the dominant strategy. A dominant strategy is a strategy that is always the best choice for a player, no matter what the other players do.
What is a Strategy?
A strategy is a plan of action that a player chooses to follow in a game. In game theory, a player is an individual or group of individuals who make decisions that affect the outcome of the game. Each player has a set of possible strategies that they can choose from. The strategy that a player chooses depends on the choices that the other players make.
What is a Dominant Strategy?
A dominant strategy is a strategy that is always the best choice for a player, no matter what the other players do. In other words, if a player has a dominant strategy, it does not matter what the other players choose to do, the player will always be better off following their dominant strategy.
Examples of Dominant Strategy
One of the most well-known examples of a dominant strategy is in the game of rock-paper-scissors. In this game, each player chooses one of three options: rock, paper, or scissors. Rock beats scissors, scissors beats paper, and paper beats rock. If both players choose the same option, the game is a tie.
In this game, there is no dominant strategy. However, if one player knows that the other player is going to choose rock, then the best strategy for that player is to choose paper. This is because paper beats rock, and the player will win the game. In this case, choosing paper is a dominant strategy for the player.
Another example of a dominant strategy is in the game of prisoner's dilemma. In this game, two suspects are arrested and put in separate cells. The police offer each suspect the opportunity to confess and betray the other suspect, or to remain silent.
If both suspects remain silent, they will both receive a light sentence. If one suspect confesses and the other remains silent, the confessing suspect will receive a reduced sentence, and the silent suspect will receive a harsh sentence. If both suspects confess, they will both receive a harsh sentence.
In this game, the dominant strategy for each suspect is to confess, regardless of what the other suspect does. This is because if one suspect confesses, and the other remains silent, the confessing suspect will receive a reduced sentence. If both suspects confess, they will both receive a harsh sentence, but the individual's sentence will still be less than if they remained silent.
Conclusion
Dominant strategies are an important concept in game theory. They are strategies that are always the best choice for a player, no matter what the other players do. Examples of dominant strategies include choosing paper in rock-paper-scissors when the other player is going to choose rock, and confessing in the prisoner's dilemma game.
