There is a fundamental assumption in the Neumann Morgenstern game theory which is worth mentioning. According to their game theory an oligopolists while choosing his strategy will assume which will be unfavorable to him. That is to say an oligopolists will adopt the policy of playing it safe given this assumption form among strategies which provide him various minimum gains an oligopolists will select that one which is maximum in those minimum gains.
In order to discuss the solute of oligopoly problem suggested by Neumann Morgenstern theory of game we suppose that oligopolists known the complete set of strategies open to him as well as those available to his rivaled in the industry. Further it is assumed that the straggle between the oligopolists is of the nature of strictly adversary game a strictly adversary game is one in which the out some which is favorable form the viewpoint of one is unfavorable to the other. Lastly two take a constant sum game in which the outcomes to the tow player’s oligopolists always add up to the same constant amount. Thus in a constant sum game one plays gain is always another player loss. Thus if the constant sum is profits of $ which is to be shared between the two sellers then if A receives $ 8 then B will be get $ 2 and if A gets $ 3 then B will obtain $ 7and so on. In our explanation of the game theory below we shall describe the behaviour of pair or duopolists A and B who compete for a given total profits of $ 10.when in a game aggregate of gain (+) and loss (-) is zero. The constant sum game becomes a zero sum game. In the oligopolistic market situation if advertising campaign launched by a firm for promoting the sales of its product merely causes a fixed number of consumers to swath from other brands of the product to his brand without adding to the total demand of the product it would be an example of a zero sum game.