Best-response table
A best-response table marks the actions that maximize each player’s payoff against each fixed action of the opponent. Mutual best responses are pure Nash equilibria.
Definition
A best-response table marks the actions that maximize each player’s payoff against each fixed action of the opponent. Mutual best responses are pure Nash equilibria.
Intuition
Check one player at a time while holding the other action fixed. Ties mean there may be several best responses.
Worked example
For payoffs (3,3), (0,2) in the top row and (2,0), (1,1) in the bottom row, both (top,left) and (bottom,right) are mutual best responses.
The math
A profile is Nash when no unilateral deviation strictly improves the deviator’s payoff. This test does not compare total welfare.
Where it is used
Use this method to check a two-player payoff table by hand. The bot explains the method; it does not parse arbitrary uploaded payoff matrices.
Go deeper
Sources
More in Game theory
Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.