How do you find the best response for a player in a payoff matrix?

Conditions

• Requires knowing the opponent's action.
• Requires comparing payoffs across available actions.
• Applies to a specific cell column (for the row player) or row (for the column player).

Reasoning, step by step

1. Identify the opponent's chosen action.
2. Look at the corresponding column (if finding the row player's best response) or row (if finding the column player's best response).
3. Compare the payoffs for the player in question across all their available actions in that column or row.
4. Select the action with the maximum payoff.

Example

When Harley plays UP, Mary compares her payoffs of 10 (for UP) and 4 (for DOWN). Since $10 > 4$, Mary's best response to Harley playing UP is to play UP.

Common misconceptions

• Comparing payoffs across the wrong axis (e.g., looking at rows when you should be looking at columns).
• Assuming the best response is always the same regardless of the opponent's action (which is only true for dominant strategies).

Watch the explanation

Explore next

• What is the definition of a dominant strategy in game theory?
• How do you find a Nash equilibrium using a payoff matrix?