(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 528
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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 1 can gear up its production faster and introduce its
new cereal first. We now have a sequential game: Firm 1 introduces a new cereal,
and then Firm 2 introduces one. What will be the outcome of this game? When
making its decision, Firm 1 must consider the rational response of its competitor. It knows that whichever cereal it introduces, Firm 2 will introduce the other
kind. Thus it will introduce the sweet cereal, knowing that Firm 2 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 1 (introduce a crispy or a sweet cereal) and the possible responses of Firm 2 to each of those choices. The resulting payoffs are
given at the end of each branch. For example, if Firm 1 produces a crispy cereal
and Firm 2 responds by also producing a crispy cereal, each firm will have a
payoff of - 5.
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
2 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 2
Firm 1
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.
