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Game Theory
Scan a 2×2 payoff matrix and flag every mutual best-response cell.
visualization
B: Silent
B: Confess
A: Silent
33
05
A: Confess
50
11
Start: find each player's best response.
A best responseB best responseNash equilibrium
Speed60
space · ◀ ▶ · r1 / 7
⏱ O(n·mᵏ)▢ O(nm)
A cell is a Nash equilibrium when neither player can gain by unilaterally switching. We mark each player's best response, then look for cells both marked.
Real-life: Pricing wars: two shops each cut prices because undercutting is each one's best response — even though both staying high would be better.
How it works
- 1For each of B's choices, mark A's payoff-maximizing row.
- 2For each of A's choices, mark B's payoff-maximizing column.
- 3Any cell marked by BOTH is a pure-strategy Nash equilibrium.
- 4In the Prisoner's Dilemma the only NE is (Confess, Confess).