# Dominant Strategy

Last Updated :

21 Aug, 2024

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Dheeraj Vaidya

Table Of Contents

## What Is A Dominant Strategy in Game Theory?

A dominant strategy is a decision-making strategy in game theory where a player chooses an action that guarantees the highest payoff for them, regardless of what the other players do. The purpose is to simplify the decision-making process for players and to identify a stable and predictable outcome where no player has the incentive to deviate from their chosen strategy.

Dominant strategies are important because they simplify the decision-making process for players, as they do not need to consider the actions of their opponents in determining their optimal strategy. Additionally, suppose all players in a game have a dominant strategy; in that case, it can lead to a predictable outcome, known as a Nash equilibrium.

##### Table of contents

- A dominant strategy is a decision-making strategy in game theory where a player chooses an action that guarantees the highest payoff for them, regardless of what the other players do.
- Dominant strategies simplify decision-making by allowing players to choose an action that guarantees the highest payoff for them.
- If all players in a game have a dominant strategy, it can lead to a stable and predictable outcome, known as a Nash equilibrium.
- However, dominant strategies are not always present in games, and when they are, they may not always lead to the best overall outcome for all players.

### Dominant Strategy Explained

Dominant strategies are often considered in game theory to simplify the analysis of a given game. By identifying it, a player can decide without needing to consider the actions of their opponents. This is especially useful in games with multiple players and complex decision trees, as it can reduce the amount of information that needs to be processed to make a decision.

However, it's important to note that dominant strategies may not always lead to the best overall outcome for all players. Players may sometimes need to consider other strategies, such as cooperative or non-dominant strategies, to achieve the best outcome for all parties involved. Therefore, while dominant strategies can be useful, it's important to consider the full range of strategies available in a given game and to evaluate their potential outcomes carefully.

In game theory, a dominant strategy is a choice that is optimal for a player, regardless of what the other players do. In other words, it is a strategy that yields the best outcome for a player, regardless of the actions taken by their opponents.

### Examples

Let us look at the examples for a better understanding of the concept.

#### Example #1

Consider that two traders, Alice and Bob, are trying to decide whether to buy or sell a particular stock. Each trader can choose between two options: buy or sell. If both traders buy, the stock price will rise, and they will both earn a profit of $100. If both traders sell, the stock price will fall, and they will both earn a profit of $50. Thus, if one trader buys while the other sells, the trader who buys will earn a profit of $150, while the trader who sells will lose $50.

In this scenario, buying the stock is the dominant strategy for both traders since it yields a higher profit regardless of the other trader's choice. Thus, this game is for both traders to buy the stock. However, both would have earned more if they had both sold. This illustrates how dominant strategies can sometimes lead to a suboptimal outcome in financial markets.

#### Example #2

Suppose two competing companies, A and B, are trying to set product prices. Each company can choose between a high price or a low price. If both companies choose the high price, they profit $10 million. If both companies choose the low price, they profit $5 million. Hence, if one company chooses the high price while the other chooses the low price, the one that chooses the high price earns a profit of $12 million, while the one that chooses the low price earns a profit of $2 million.

In this scenario, choosing the high price is the dominant strategy for both companies since it yields a higher profit regardless of what the other company chooses. Thus, the Nash equilibrium in this game is for both companies to choose the high price, even though both would have earned more if they had both chosen the low price. This illustrates how dominant strategies can sometimes lead to a suboptimal outcome in business.

### Benefits** **

Let us look at the major benefits of dominant strategy:

**Simplifies decision-making**: Identifying this strategy can help to simplify the decision-making process for players, as they can choose an action that guarantees the highest payoff for them, regardless of what their opponents do. This can be especially useful in games with multiple players and complex decision trees.**Predictable outcomes**: If all players in a game have this strategy, it can lead to a stable and predictable outcome, known as a Nash equilibrium. In this equilibrium, no player has the incentive to deviate from their chosen strategy, which can help to reduce uncertainty and create a more predictable environment for decision-making.**Saves time and resources**: By identifying it, players can save time and resources that would otherwise be spent considering all possible strategies and their potential outcomes. This can be particularly valuable in situations where time and resources are limited.**Provides insights into strategic behavior**: The presence or absence of these strategies can provide insights into the strategic behavior of players in a given game. For example, the absence of dominant strategies may suggest that players must coordinate or cooperate to achieve the best outcome.

**Dominant Strategy vs Nash **Equilibrium

Here is a comparison between the two:

Basis | Dominant Strategy | Nash Equilibrium |
---|---|---|

Definition | A strategy that guarantees the highest payoff for a player, regardless of what the other players do | A state in which each player is making the best decision they can, given the decisions of the other players |

Decision-making | It simplifies decision-making by allowing players to choose an action that guarantees the highest payoff for them. | Requires players to consider the decisions of the other players and make their best decision accordingly |

Stability | Depending on the number of players and the game's complexity, it may or may not result in a stable outcome. | Generally results in a stable outcome, where no player is incentivized to change their decision. |

Optimization | It may not lead to the best overall outcome for all players | Generally leads to the best overall outcome for all players |

Applicability | Applicable only in games where a player has a dominant strategy | Applicable in games where there is no dominant strategy |

### Dominant Strategy vs Dominated Strategy

Here is a comparison between the two:

Basis | Dominant Strategy | Dominated Strategy |
---|---|---|

Definition | A strategy that guarantees the highest payoff for a player, regardless of what the other players do | A strategy that yields a lower payoff for a player, regardless of what the other players do |

Decision-making | It simplifies decision-making by allowing players to choose the best action for them. | Should be avoided in decision-making, as it will always result in a worse outcome |

Strategic considerations | Assumes that all other players will be rational and play their dominant strategies | Assumes that other players will not play dodominanttrategies |

Optimization | This leads to the best outcome for a player | This leads to a suboptimal outcome for a player |

Applicability | Applicable in games where a player has a dominant strategy | Applicable in games where a player has a dodominanttrategy |

### Frequently Asked Questions (FAQs)

**1.**

**How to find a dominant strategy**?To find it, a player needs to compare the outcomes of all possible actions they could take, given the actions of their opponents, and choose the action that yields the highest payoff for them regardless of their opponent's actions. This involves considering all possible actions and outcomes to identify the best decision for the player.

**2.**

**What is the dominant strategy in the prisoner's dilemma**?In the Prisoner's Dilemma, each prisoner's dominant strategy is to confess, regardless of what the other prisoner does, which leads to a suboptimal outcome for both players. This means that each player will choose to confess, even though both would have earned a better outcome if they had chosen not to confess.

**3.**

**Can both firms have a dominant strategy?**Yes, in certain situations, both firms can have a dominant strategy. This can lead to a stable outcome, known as a Nash equilibrium, where neither firm has the incentive to deviate from its chosen Strategy.

### Recommended Articles

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