Payoff matrix

In two-player games both decision-makers choose an action simultaneously and the result depends on the pair of choices: this is the domain of game theory (von Neumann, Nash). The first tool for representing them is the payoff matrix.

Definition — Payoff matrix

A finite two-player game is represented by an $m\times n$ payoff matrix: the rows are Player 1’s pure strategies, the columns Player 2’s. Each cell contains the pair $(v_1; v_2)$ of the winnings for the two players corresponding to that profile of choices.

If $v_1(s)+v_2(s)=0$ for every profile $s$, the game is zero-sum (what one gains the other loses).

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Topics: Probability
Concepts: Zero-sum game · Payoff matrix · Game theory
Methods: Zero-sum game
Skills: Modelling
People: Von Neumann