A matrix showing the pay-offs to each player in a two-player game. Usually the strategies available to the ‘row player’ are shown to the left of the matrix and the strategies available to the ‘column player’ are shown above the matrix. A choice of strategy for the row player and for the column player uniquely identifies a cell in the matrix. Each cell in the pay-off matrix contains two numbers. The number to the left is the pay-off of the row player and the number to the right is the pay-off to the colunm player. A pay-oflf matrix conforming to this description is shown below.
In the special case of a zero-sum game the pay-offs to one player are equal and opposite to those of the other, so only one set needs to be shown explicitly.
Reference: Oxford Press Dictonary of Economics, 5th edt.