Introduction to Game Theory
Dominant strategies are a key concept in game theory, and refer to a strategy that is always the best choice for a player, regardless of the choices made by other players. In other words, a dominant strategy is a strategy that is optimal, no matter what.
To illustrate this concept, consider the classic example of the Prisoner's Dilemma. In this game, two prisoners are being held in separate cells and are given the option to either remain silent or confess. If both remain silent, they will each receive a light sentence. If both confess, they will each receive a harsh sentence. However, if one confesses and the other remains silent, the confessor will receive no sentence and the other will receive a harsh sentence. In this game, the dominant strategy for each prisoner is to confess, regardless of what the other person does. This is because confessing will always result in a better outcome than remaining silent, no matter what the other person chooses.
Dominant strategies can be identified through a process of elimination. Players can eliminate any strategy that is strictly dominated by another strategy. A strategy is strictly dominated if there is always another strategy that results in a better outcome, no matter what the other players do. Once all strictly dominated strategies have been eliminated, the remaining strategy (or strategies) is the dominant strategy.
It's important to note that not all games have dominant strategies. In some games, there may be multiple Nash equilibria, but no dominant strategy. In other games, there may be no Nash equilibria at all. However, when a dominant strategy does exist, it simplifies the decision-making process for players and can lead to more predictable outcomes.
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