Zero-sum game

A game in which one participant’s gain is exactly balanced by another’s loss, so the participants’ payoffs sum to zero.

Minimax theorem: A theorem guaranteeing optimal strategies and a game value in finite two-player zero-sum games. It establishes that each player can secure the same value by maximizing or minimizing appropriately.
Strategic-form game: A representation of a game specifying players, available strategies, and payoffs for every strategy profile. Zero-sum games are commonly defined by restrictions on this representation's payoffs.
Matching pennies: A two-player game in which matching or differing coin choices determine opposite wins and losses. It is a simple example where randomization is necessary for optimal play.
Non-zero-sum game: A game in which participants’ payoffs do not always sum to a fixed zero total. It allows outcomes where players can gain or lose together.
Nash equilibrium: A strategy profile in which no player can benefit by changing strategy alone. In finite zero-sum games, equilibrium strategies coincide with minimax-optimal strategies.
Utility: A numerical representation of how much an outcome is valued by a decision-maker. Payoffs sum to zero only relative to the utilities specified for the players.
Rock paper scissors: A hand game in which each of three choices defeats one choice and loses to another. Its symmetric payoffs sum to zero, and uniform randomization is optimal.
Constant-sum game: A game in which the sum of all players’ payoffs is fixed, but not necessarily zero. Subtracting a constant from payoffs converts a constant-sum game into an equivalent zero-sum game.
Mixed strategy: A strategy that assigns probabilities to a player's available actions. Randomization can prevent an opponent from exploiting predictable choices.
Strategy: A complete plan specifying a player's action in each situation the game may reach. A zero-sum game's outcome depends on the strategies chosen by its participants.

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