How to find dominant strategies in a game matrix?

To find dominant strategies in a game matrix, we need to compare the payoffs of each player.

A dominant strategy is a strategy that is always the best choice for a player, regardless of the other player's strategy. To find a dominant strategy, we need to compare the payoffs of each player for each possible strategy combination.

For example, consider the following game matrix:

| | L | R |
|-------|-------|-------|
| T | 2, 1 | 0, 0 |
| B | 1, 2 | 3, 0 |

To find the dominant strategy for Player 1, we compare the payoffs for each row. If Player 2 chooses L, Player 1 gets 2 if they choose T and 1 if they choose B. If Player 2 chooses R, Player 1 gets 0 if they choose T and 3 if they choose B. Therefore, Player 1's dominant strategy is to choose B, as it gives them a higher payoff regardless of what Player 2 chooses.

To find the dominant strategy for Player 2, we compare the payoffs for each column. If Player 1 chooses T, Player 2 gets 2 if they choose L and 1 if they choose R. If Player 1 chooses B, Player 2 gets 0 if they choose L and 3 if they choose R. Therefore, Player 2's dominant strategy is to choose R, as it gives them a higher payoff regardless of what Player 1 chooses.

In some cases, there may not be a dominant strategy for either player. In these cases, players may need to use other strategies, such as mixed strategies, to maximize their payoffs.