How do you read the two numbers in each cell of a payoff matrix?
In a normal-form payoff matrix, each cell contains an ordered pair of payoffs. The first number represents the payoff for Player 1 (the row player), and the second number represents the payoff for Player 2 (the column player).
Conditions
- The game is represented in normal form (a payoff matrix).
- Player 1 is assigned to the rows and Player 2 is assigned to the columns.
- The payoff convention is explicitly stated as (Player 1, Player 2).
Reasoning, step by step
- Identify the row player (Player 1) and the column player (Player 2).
- Locate the specific cell corresponding to the chosen actions of both players.
- Read the first number in the cell as the payoff for Player 1.
- Read the second number in the cell as the payoff for Player 2.
Example
In the displayed matrix, the cell for (UP, UP) contains (10,10), meaning Mary gets 10 and Harley gets 10. The cell for (UP, DOWN) contains (8,4), meaning Mary gets 8 and Harley gets 4.
Common misconceptions
- Assuming the first number always belongs to the player listed at the top of the matrix.
- Confusing the order of payoffs, which can lead to analyzing the wrong player's incentives.
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