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payoff matrix
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A diagram showing a variable-sum payoff matrix from game theory, with player A in red and player B in blue, displaying four outcome boxes with different numerical payoffs for each player based on their choices. A colorful payoff matrix for a normal form game in game theory, showing strategy options-support, oppose, evade-for both party A and party B. Each cell contains cartoon figures representing each party's action and lists percentage payoffs for A and B. The bottom-right cell is labeled saddlepoint, highlighting the equilibrium. A payoff matrix diagram for game theory shows a safe-cracker choosing between robbing two safes and a guard choosing to protect one; each cell illustrates who gets the money depending on their choices, with outcomes ranging from nothing stolen to $100,000 stolen, and no single optimal strategy for either player.
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A diagram showing a variable-sum payoff matrix from game theory, with player A in red and player B in blue, displaying four outcome boxes with different numerical payoffs for each player based on their choices.
variable-sum payoff matrix Table 3

In variable-sum games each payoff depends on both players' actions. Therefore, each matrix entry lists two payoffs, one for each player.

In game theory, a payoff matrix is a tool used to determine the optimal strategy for players in a noncooperative game. It visually represents the potential outcomes for each player based on the strategies they choose. Each row typically corresponds to a strategy for one player, and each column represents a strategy for another. The intersection of a row and column shows the payoff (e.g., points, money, or years in prison) for each player given their chosen strategies. This helps players analyze interdependent decisions and identify the best course of action, aiming to maximize their own gains or minimize losses, even when facing an opponent with opposing interests. The concept of a "saddlepoint" in a payoff matrix indicates a stable outcome, known as a Nash equilibrium, where no player can improve their situation by unilaterally changing their strategy.123

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3 Britannica Sources
  1. Nash equilibrium
  2. game theory - Classification of games
  3. game theory - Games of imperfect information

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