Dominant Game Theory is a concept in game theory that helps to predict the outcome of a game by identifying the best strategy for each player. It is a widely used tool in economics, politics, and other fields where decision making is an essential part of the process.

## What Is Game Theory?

Game theory is the study of how people or entities make decisions when they are aware that their choices will affect others. It tries to explain how rational individuals would behave in strategic situations where the outcome depends on the actions of multiple players.

## What Is Dominant Strategy?

A dominant strategy is a strategy that is always better than any other strategy regardless of what other players do. In other words, it is a strategy that provides the highest payoff for a player regardless of what strategies other players choose.

### Example:

Suppose there are two players A and B, and they are playing a game where they have to choose between two options: Option 1 and Option 2. If A chooses Option 1 and B chooses Option 1, both get $5 as payoff.

If A chooses Option 1 and B chooses Option 2, A gets $10, and B gets $0 as payoff. Similarly, if A chooses Option 2 and B chooses Option 1, A gets $0, and B gets $10 as payoff. Finally, if both choose Option 2, both get $1 as payoff.

In this example, choosing Option 1 dominates over choosing Option 2 for both players because choosing Option 1 yields higher payoffs irrespective of what option the other player chooses.

## Dominant Strategy Equilibrium

Dominant strategy equilibrium occurs when all players in a game play their dominant strategies simultaneously. In this situation, no player has an incentive to change their strategy because any deviation from their dominant strategy will result in a lower payoff.

### Example:

Suppose there are two players A and B, and they are playing the same game as in the previous example. In this case, the dominant strategy equilibrium is for both players to choose Option 1 because it yields the highest payoffs for both players.

## Limits of Dominant Game Theory

Dominant game theory has some limitations. It assumes that all players have complete information about the game, including the strategies available to other players and their payoffs.

In reality, this is not always the case. Players may have incomplete or imperfect information about the game, which can affect their decision-making process.

Moreover, dominant strategy equilibrium may not exist in some games. In such situations, other concepts such as Nash equilibrium may be used to predict outcomes.

## Conclusion

Dominant Game Theory is a useful concept that helps to predict outcomes of strategic games by identifying the best strategies for each player. It assumes that all players have complete information about the game and that they always choose their dominant strategies. However, it has some limitations and may not be applicable to all situations.