Payoff Matrix in Game Theory

Game theory summarizes in a tabular way the possible choices available to firms in oligopoly. Game theory applied to oligopoly uses a table that indicates the profit of each firm given the choice of strategy chosen by each. All possible strategies are represented in the table, and so all possible outcomes can be considered at once. This table is called a payoff matrix. The profits listed in the payoff matrix represent/exemplify underlying cost and demand information.

Suppose again that there are two firms. For simplicity, suppose that price and costs are all taken as given and that the only decision for these two firms is how much to send and advertising of both engage in high levels of advertising, neither will enjoy particularly high profits. If neither firm advertises at a high level, each will keep its respective market share, but both will make larger profits. However, if one advertises while the other does not then the firm that advertises will gain market share and get big increase in profits while the other incurs losses. Assume that advertising might increase on hold the firm’s share of the market but that it has little effect in expanding total industry sales. Finally, assume that firms reveal their strategies simultaneously and do not change them. Although it is quite simple, this model contains money of the features of the recognized interdependence of oligopolists.

The model is depicted in the payoff matrix in table.

Payoff Matrix

Firm A’s strategy
High Level of Advertising                                   Low Level of Advertising
High Level of Advertising   X gets Rs. 5,000      A gets Rs. 2,000
                                         Y gets Rs. 5,000      B gets Rs. 2,000

Low Level of Advertising   X gets Rs. 2,000     A gets Rs. 10,000
                                         Y gets Rs. 20,000   B gets Rs. 10,000

In both firms, choose high levels of advertising, they then earn profits Rs. 5,000 each. If both adopt low levels of advertising they each enjoy profits Rs. 10,000. But of one firm advertises much and the other little, the firm with the high level of advertising earns profits of Rs. 20,000 and the other firm losses Rs. 2,000.

Now put yourself in the place of the Manager of firm B. the choice of B firm will depend precisely on what you think from A will do. If you think firm A will try to do you in, then you will assume that if you try to get the Rs. 10,000 profit available by going for a low level of advertising, Firm A will choose a high level of advertising in self-protection. This strategy assumes you of at least Rs. 5, 000.

Firm A has exactly the same choices have, and so if the assumes that firm B is not be trusted, firm A also chooses a high level. If advertising for his self-preservation. Thus, the conservative maximum strategy leads both firms to high levels of advertising. As a result, each gets a Rs. 5,000 profit.

Only of the firms cooperated can they earn the Rs. 10,000. Profits that is available to each. If firm B assumes that firm A is a profit maximizing firm with managers who behave rationally, then firm B concludes that firm A will adopt a low level of advertising. If firm A makes the same assumption about firm B then each attains profits of Rs. 10,000.

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