(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 528

CHAPTER 13 • Game Theory and Competitive Strategy 503 by one firm and the response by its competitor; entry-deterring investment by an incumbent firm and the decision whether to enter the market by a potential competitor; or a new government regulatory policy and the investment and output response of the regulated firms We will look at a variety of sequential games in the remainder of this chapter As we will see, they are often easier to analyze than games in which the players move at the same time In a sequential game, the key is to think through the possible actions and rational reactions of each player As a simple example, let’s return to the product choice problem first discussed in Section 13.3 This problem involves two companies facing a market in which two new variations of breakfast cereal can be successfully introduced as long as each firm introduces only one variation This time, let’s change the payoff matrix slightly As Table 13.9 shows, the new sweet cereal will inevitably be a better seller than the new crispy cereal, earning a profit of 20 rather than 10 (perhaps because consumers prefer sweet things to crispy things) Both new cereals will still be profitable, however, as long as each is introduced by only one firm (Compare Table 13.9 with Table 13.3—page 493.) Suppose that both firms, in ignorance of each other’s intentions, must announce their decisions independently and simultaneously In that case, both will probably introduce the sweet cereal—and both will lose money Now suppose that Firm can gear up its production faster and introduce its new cereal first We now have a sequential game: Firm introduces a new cereal, and then Firm introduces one What will be the outcome of this game? When making its decision, Firm must consider the rational response of its competitor It knows that whichever cereal it introduces, Firm will introduce the other kind Thus it will introduce the sweet cereal, knowing that Firm will respond by introducing the crispy one The Extensive Form of a Game Although this outcome can be deduced from the payoff matrix in Table 13.9, sequential games are sometimes easier to visualize if we represent the possible moves in the form of a decision tree This representation is called the extensive form of a game and is shown in Figure 13.2 The figure shows the possible choices of Firm (introduce a crispy or a sweet cereal) and the possible responses of Firm to each of those choices The resulting payoffs are given at the end of each branch For example, if Firm produces a crispy cereal and Firm responds by also producing a crispy cereal, each firm will have a payoff of - To find the solution to the extensive form game, work backward from the end For Firm 1, the best sequence of moves is the one in which it earns 20 and Firm earns 10 Thus it can deduce that it should produce the sweet cereal because Firm 2’s best response is then to produce the crispy cereal TABLE 13.9 MODIFIED PRODUCT CHOICE PROBLEM Firm Firm Crispy Sweet Crispy −5, −5 10, 20 Sweet 20, 10 −5, −5 • extensive form of a game Representation of possible moves in a game in the form of a decision tree