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game theory
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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. 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 diagram illustrating the prisoners' dilemma in game theory, showing two prisoners, A and B, with four possible outcomes based on whether each confesses or remains silent. Years of prison time are indicated for each scenario, with visual icons showing happy or sad prisoners in cells or free.
prisoner's dilemma in game theory
A biological payoff matrix for game theory showing outcomes when hawk, dove, and bourgeois strategies compete, with colored bird icons and cells listing offspring gains or losses for each interaction. Diagram illustrating game theory concepts in voting, showing a grid of possible voting strategies for two voters, Y and Z, each with different candidate preferences, and indicating outcomes such as which candidate wins and which strategies are dominated. Diagram illustrating a game theory scenario in voting, showing two voters with different candidate preferences and a matrix of voting outcomes. Voter Y prefers y over z over x, and voter Z prefers z over x over y. The matrix displays possible votes, with outcomes labeled as x wins, z wins, and dominated strategy.
See how game theory applies to the peacock's tail evolution
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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.
payoff matrix with saddlepoint Table 1

The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.

game theory

mathematics
Written by
Morton D. Davis
Professor of Mathematics, City College, City University of New York. Author of Game Theory: A Nontechnical Introduction.
Morton D. DavisAll
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Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree....
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game theory, branch of applied mathematics that provides tools for analyzing situations in which parties, called players, make decisions that are interdependent. This interdependence causes each player to consider the other player’s possible decisions, or strategies, in formulating strategy. A solution to a game describes the optimal decisions of the players, who may have similar, opposed, or mixed interests, and the outcomes that may result from these decisions. Although game theory can be and has...

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