How do you find a Nash equilibrium using a payoff matrix?
To find a Nash equilibrium, identify the best response for each player to every possible action of their opponent. A Nash equilibrium occurs in the cell where both players' payoffs are best responses to each other, often marked by two underlines in the same cell.
Conditions
- Requires identifying best responses for all players.
- Applies to simultaneous move games represented by a payoff matrix.
Reasoning, step by step
- Underline the highest payoff for Player 1 in each column (responding to Player 2's actions).
- Underline the highest payoff for Player 2 in each row (responding to Player 1's actions).
- Locate the cell(s) that contain two underlined payoffs.
- The action profile corresponding to that cell is a Nash equilibrium.
Example
In the Mary-Harley game, both players' payoffs are underlined in the (UP, UP) cell, making (UP, UP) the Nash equilibrium.
Common misconceptions
- Looking for a cell with only one underline.
- Assuming there is always exactly one Nash equilibrium; some games have multiple or none.
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