Game theory is a study of mathematical models of conflict and cooperation between intelligent rational decision-makers. It is a branch of applied mathematics that is used to study strategic interactions among agents who have conflicting objectives. The most common way to solve a game is by finding its equilibria, which is a set of strategies that no player can improve upon unilaterally. One of the important concepts in game theory is dominant strategy, which is a strategy that is the best response to all possible moves of the opponent.
What is a Dominant Strategy?
A dominant strategy is a strategy that is the best response to all possible moves of the opponent. In other words, it is a strategy that is optimal regardless of what the opponent does. In game theory, a dominant strategy is one that yields the highest payoff for a player, regardless of what the other players do. Dominant strategies are important because they simplify the analysis of games, making it easier to predict outcomes and understand the behavior of players.
How Does Dominant Strategy Work?
When there are two players in a game, each player has two strategies to choose from. If player A chooses strategy 1, player B can choose either strategy 1 or strategy 2. If player A chooses strategy 2, player B can again choose either strategy 1 or strategy 2. If player A's best response is strategy 1 no matter what player B does, then strategy 1 is said to be a dominant strategy for player A. Similarly, if player B's best response is strategy 1 no matter what player A does, then strategy 1 is said to be a dominant strategy for player B.
Examples of Dominant Strategy
A classic example of a game with dominant strategies is the Prisoner's Dilemma. In this game, two criminals are arrested and held in separate cells. The police offer each criminal a deal: if one confesses and the other does not, the one who confesses will receive a reduced sentence, while the other will receive a harsher sentence. If both confess, both will receive a reduced sentence, but not as much as the one who confesses alone. If neither confesses, both will receive a moderate sentence. The dominant strategy for both criminals is to confess, even though both would be better off if they both remained silent.
Why is Dominant Strategy Important?
Dominant strategy is important in game theory because it simplifies the analysis of games. If a game has a dominant strategy for each player, then the outcome of the game can be predicted with certainty. In addition, the existence of a dominant strategy can help explain why certain behaviors are observed in real-life situations. For example, the dominant strategy of confessing in the Prisoner's Dilemma might explain why some criminals are willing to turn on their accomplices even though it may not be in their best interest.
Limitations of Dominant Strategy
While dominant strategy is a powerful tool in game theory, it has some limitations. One of the main limitations is that it assumes that players have complete information about the game and their opponents. In real-life situations, players may not have complete information, and their opponents may not behave as predicted. In addition, dominant strategy assumes that players are rational and always act in their best interest. In reality, players may not always be rational and may be influenced by emotions, social norms, and other factors.
Conclusion
Dominant strategy is an important concept in game theory that helps simplify the analysis of games. It is a strategy that is the best response to all possible moves of the opponent. While dominant strategy has some limitations, it is a useful tool for predicting outcomes and understanding the behavior of players in games. By understanding dominant strategy, we can better understand the decisions people make in real-life situations and how they might respond to different incentives.
