## What is a dominant strategy?

Dominant strategy is a situation in which one particular strategy is the best option for a player regardless of what strategies the opponents choose. A dominant strategy is a term used in game theory to describe a strategy that is optimal for a player, regardless of the strategies employed by the other players.

It is dominant because it guarantees the best possible outcome for the player. A strictly dominant strategy is a strategy that is always better than any other strategy, no matter what the other player does.

In other words, a dominant strategy is one that gives a player the best possible outcome, no matter what the other players do.

There may be more than one dominant strategy for a given game, but there can only be one dominant strategy per player. In some cases, there may be no dominant strategy. Dominant strategies are very powerful because they allow a player to always come out ahead, no matter what their opponent does.

That player has an advantage when all things are equal in the game. It implies that, whatever methods the opponent uses, the dominant player will always dominate the end result.

## How dominant strategy is used in game theory?

In game theory, the dominant strategy is used as a way to predict the outcome of a game. It is often used in conjunction with Nash equilibrium, which is a situation in which no player can improve their position by changing their strategy.

A dominant strategy is not always the same as a Nash equilibrium, but it can be used to find one. If there is a dominant strategy for each player in a game, then the game has what is called a dominant strategy equilibrium.

There are some games where it is impossible to have a dominant strategy equilibrium. These are called games of incomplete information.

## An example of dominant strategy

One example of a dominant strategy is in the game of chicken. In this game, two players each have a car and drive toward each other. The first player to swerve out of the way loses.

If both players know that the other is going to swerve, then the best strategy for both players is to swerve at the same time. However, if both players think that the other is going to stay on course, then the best strategy is to stay on course as well.

In this game, there is no dominant strategy equilibrium because each player has a different best strategy depending on what they think the other player will do.

## Dominant Strategy Outcomes

### 1. Strictly Dominant Outcome

A strictly dominant outcome is an outcome that is better than all other outcomes for a player, regardless of the strategies employed by the other players.

### 2. Weakly Dominant Outcome

A weakly dominant outcome is an outcome that is better than all other outcomes for a player, except for one.

### 3. Equivalent Outcome

An equivalent outcome is an outcome that is just as good as another outcome for a player, regardless of the strategies employed by the other players.

### 4. Intransitive Outcome

An intransitive outcome is an outcome in which one player may have two different dominant strategies, depending on the strategy of the other player.

## Types of Dominant Strategy

There are two types of dominant strategy: dominant strategy equilibrium and dominant strategy incentive compatible.

### 1. Dominant Strategy Equilibrium

A dominant strategy equilibrium is a situation in which there is a dominant strategy for each player in a game.

### 2. Dominant Strategy Incentive Compatible

A dominant strategy incentive compatible is a situation in which a player has an incentive to truthfully reveal their preferences.

## The Nash Equilibrium

The Nash equilibrium is a dominant strategy equilibrium in which each player has chosen the best possible strategy, given the strategies of the other players.

To find the Nash equilibrium, each player must first find their dominant strategy. They then choose the strategy that gives them the best outcome, given the dominant strategies of the other players.

The Nash equilibrium is the only dominant strategy equilibrium in which each player has chosen the best possible strategy.

There are two dominant strategies in the game of chicken. The first player can either swerve or stay on course. The second player can either swerve or stay on course.

The Nash equilibrium is for both players to stay on course. This is because it is the only outcome in which each player has chosen the best possible strategy.

## Dominant Strategy Solution vs. Nash Equilibrium Solution

The dominant strategy solution is the outcome of a game in which each player has chosen their dominant strategy. The Nash equilibrium solution is the outcome of a game in which each player has chosen the best possible strategy, given the dominant strategies of the other players.

The dominant strategy solution is not always the same as the Nash equilibrium solution. This is because the Nash equilibrium is the only dominant strategy equilibrium in which each player has chosen the best possible strategy.

## Dominant vs Dominated strategies

A dominated strategy is a strategy that is never the best possible choice, no matter what the other player does. A player has a dominated strategy if they have a strategy that is never the best possible choice, no matter what the other player does.

A dominant strategy is one that strictly dominates all other strategies. This means that it is always the better choice, no matter what the other player does. While strictly dominated strategies should be eliminated, sometimes a strategy is only weakly dominated. This means that it is not always the best choice, but it is still worth considering. If a dominant strategy exists, it is the only one worth considering. All other strategies can be safely ignored.

When looking at possible strategies, it is important to consider whether any of them are strictly dominated. If so, they can be eliminated from consideration immediately. It is also worth considering whether any of them are only weakly dominated. While these strategies are not always the best choice, they may still be worth considering.

### Strictly dominated strategies vs Weakly dominated strategies

A strictly dominated strategy is one where there is another strategy that strictly outperforms it, regardless of the other player’s choices. A weakly dominated strategy is one where there is another strategy that outperforms it, but only when the other player takes a specific action.

## Tips for Eliminating Dominated Strategies

One of the most important things to remember when playing any game is that there are always strategies that are strictly dominated by others. This means that there is always a strategy that is better than another in every possible scenario. So, if you’re trying to figure out the best way to win, it’s important to eliminate all of the strictly dominated strategies.

Here are some tips for eliminating strictly dominated strategies:

- Understand what it means for a strategy to be strictly dominated.
- Consider all of the possible scenarios in which you could use each strategy.
- Determine which strategy is better in each scenario.
- Eliminate the strictly dominated strategy.
- Repeat steps 2-4 until you’re left with only one strategy.
- Use that strategy to win the game!

When it comes to eliminating strictly dominated strategies, one of the most important things to understand is the concept of the best response. The best response is the strategy that gives you the highest payoff given the strategy of your opponents. So, if you want to win, you need to figure out what your best response is to the strategies of your opponents.

Once you know what your best response is, you can then eliminate all of the other strategies that are strictly dominated by it. To do this, you just need to consider all of the possible scenarios in which you could use each strategy and determine which one is better in each scenario. If there is always a better strategy, then that strategy is strictly dominated and you can eliminate it.

Once you’ve eliminated all of the strictly dominated strategies, you’re left with strictly dominant strategies. The dominant strategy is the strategy that is always better than any other strategy, no matter what your opponents do. So, if you want to win, you need to find the dominant strategy and use it.

Eliminating weakly dominated strategies is a fundamental concept in game theory and economics. The elimination of these strategies simplifies the analysis of a game and often results in a strategic dominance.

## Examples of Dominant Strategies

Finding the dominant strategy can be tricky, but once you’ve found it, you’re guaranteed to win! To help you find the dominant strategy, we’ve included a few examples below.

### Example 1: The Prisoner’s Dilemma

The Prisoner’s Dilemma is a classic example of a game in which there is a dominant strategy. In this game, two prisoners are interrogated separately and each has the option to confess or remain silent. If they both confess, they each receive a 3-year prison sentence. If one confesses and the other remains silent, the confessor goes free while the silent prisoner receives a 5-year sentence. If they both remain silent, they each receive a 1-year sentence.

The dominant strategy in this game is to confess regardless of what the other player does. This is because no matter what the other player does, you are better off confessing than remaining silent. If the other player confesses, you receive a 3-year sentence instead of a 5-year sentence. If the other player remains silent, you go free instead of receiving a 1-year sentence.

### Example 2: The Battle of the sexes

The Battle of the sexes is another example of a game with a dominant strategy. In this game, two spouses are trying to decide what to do on their weekends. One spouse wants to go to the football game while the other spouse wants to go to the ballet. If they both go to their preferred activity, they each receive a payoff of 2. If they both go to the other activity, they each receive a payoff of 1. If they go to different activities, they each receive a payoff of 0.

The dominant strategy in this game is for each spouse to go to their preferred activity. This is because no matter what the other spouse does, you are better off going to your preferred activity than going to the other activity. If the other spouse goes to their preferred activity, you still receive a payoff of 2. If the other spouse goes to your preferred activity, you receive a payoff of 1.

### Example 3: The chicken game

The chicken game is another example of a game with a dominant strategy. In this game, two drivers are racing towards a cliff. If they both drive off the cliff, they each die. If one driver drives off the cliff and the other doesn’t, the driver who didn’t drive off the cliff is declared the winner. If they both don’t drive off the cliff, they each receive a payoff of 0.

The dominant strategy in this game is for each driver to drive off the cliff. This is because no matter what the other driver does, you are better off driving off the cliff than not driving off the cliff. If the other driver drives off the cliff, you die anyway. If the other driver doesn’t drive off the cliff, you are declared the winner.

Hopefully, these examples have helped you understand what a dominant strategy is and how to find one. Remember, once you’ve found the dominant strategy, you’re guaranteed to win!

### Conclusion!

A dominant strategy is a choice that gives the best possible outcome for an individual, regardless of what others may do.

Dominant strategies often arise in game theory situations, where players are trying to maximize their own benefits while minimizing losses.

In some cases, a dominant strategy may be to cooperate with others, while in other cases it may be to compete. Dominant strategies are not always easy to identify, but they can be a powerful tool for making decisions in difficult situations.

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