A game with only two players, say player A and player B, is called a two-person zero sum game if the gain of the player A is equal to the loss of the player B, so that the total sum is zero.

**Definition
of two-person zero sum game**

A game with only two players, say
player A and player B, is called a two-person zero sum game if the gain of the
player A is equal to the loss of the player B, so that the total sum is zero.

**Payoff matrix**

When players select their
particular strategies, the payoffs (gains or losses) can be represented in the
form of a payoff matrix.

Since the game is zero sum, the
gain of one player is equal to the loss of other and vice-versa. Suppose A has
m strategies and B has n strategies. Consider the following payoff matrix.

Player A wishes to gain as large
a payoff *a*_{ij} as possible while player B will do his best to reach as small a value *a*_{ij} as possible where the gain to player B and loss to player A be (- *a*_{ij} ).

Tags : Operations Management - Game Theory, Goal Programming & Queuing Theory

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