Game theory is a study of mathematical models that help in analyzing and understanding strategic interactions between different parties. It involves the study of decision-making, strategic behavior, and mathematical models to predict the outcomes of these interactions.

In game theory, a strategy refers to a set of actions taken by an individual or group to achieve their goals. A dominated strategy is a type of strategy that is never optimal, regardless of the choices made by other players.

A dominated strategy occurs when one player has another strategy that always gives them better outcomes regardless of what other players do. Therefore, it doesn’t make sense for the player to choose the dominated strategy. Instead, they should choose the alternative strategy that gives them better outcomes.

**Example:** Consider a simple two-player game where each player can either choose A or B. The outcome matrix for this game is as follows:

- If both players choose A, player 1 gets 3 and player 2 gets 3.
- If both players choose B, player 1 gets 2 and player 2 gets 2.
- If player 1 chooses A and player 2 chooses B, then player 1 gets 0 and player 2 gets 4.

In this example, choosing B is always better for both players than choosing A. If one player chooses A while the other chooses B, the one who chose B will always get a higher payout than the one who chose A.

### Dominant Strategy vs Dominated Strategy

It’s important to distinguish between dominant strategies and dominated strategies because they have opposite implications on game theory outcomes.

A dominant strategy refers to a situation where one strategy always provides better results than any other available option for any combination of strategies chosen by other players. In contrast, a dominated strategy provides worse results than any other available option for any combination of strategies chosen by other players.

A dominant strategy is always the optimal choice for a player in a game, whereas a dominated strategy is never the optimal choice. In fact, choosing a dominated strategy can often lead to disastrous outcomes for players.

### Why Dominated Strategies Matter in Game Theory

Dominated strategies are an essential concept in game theory because they help us identify strategies that are never optimal. This identification helps us eliminate these strategies from consideration and focus on the remaining options that provide better outcomes.

By eliminating dominated strategies, we can simplify complex games and identify the best possible outcomes for each player. This simplification not only makes it easier to analyze games but also helps us make better decisions in real-life situations where strategic interactions occur.

### Conclusion

Dominated strategies are a crucial concept in game theory that help us identify suboptimal strategies. By understanding this concept, we can eliminate these strategies and focus on the remaining options that provide better outcomes. This identification not only simplifies complex games but also helps us make better decisions in real-life situations where strategic interactions occur.