Normal-Form Game

The normal form is the standard representation of a simultaneous-move game as a payoff matrix. Rows are Player 1's strategies, columns are Player 2's strategies, and each cell holds a pair (payoff to P1, payoff to P2) — the first number is always Player 1's payoff.

When to use

Use the normal form for any simultaneous game with a small finite number of strategies — Prisoner's Dilemma, coordination games, Battle of the Sexes, Rock-Paper-Scissors. The matrix is the input to the best-response method for finding Nash Equilibria, and to Iterated Dominance for eliminating dominated strategies. Sequential games are better drawn as extensive-form trees, not matrices.