We.will illustrate the basic concepts of game theory by analyzing a duopoly price game. This is a situation where the market is supplied by two firms that are deciding whether to engage in economic warfare of low prices. For simplicity, we assume that each firm has the same cost and demand structure. Further, each firm can choose whether to charge its normal price or lower its price below marginal ‘costs and try to drive its rival into bankruptcy and then capture the entire market. The novel element in the duopoly game is that the firm’s profits will depend on its rival’s strategy as well as on its own.

A useful tool for representing the interaction between two firms or people is a two-way payoff table. A payoff table is a means of showing the strategies and the payoffs of a game between two players. Figure 11-4 shows the payoffs in the duopoly price game for our two companies. In the payoff table, a firm can choose between the strategies listed in its rows
or columns. For example, nEwBooks can choose between its two columns and Amazing can choose-between its two rows.

In this example, each firm decides whether to charge its normal price or to start a price war by choosing a lower price. Combining the two decisions of each duopolist gives four possible outcomes, which are shown in the four cells of the table. Cell A, at the upper left, shows the outcome when both firms choose the normal price; D is the outcome when both choose to conduct a price war; and B and C result when one firm bas a normal price and one a war price. The numbers inside the cells show the payoffs of the two firms, that is, the profits earned by each firm for each of the four outcomes, The blue number in the lower left shows the payoff to the player on the left (Amazing); the black entry in the upper right shows the payoff to the player at the top (nEwBooks). Because. the firms are identical, the payoffs are mirror images.

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