9781118041581

some circumstances, incumbent firms actually may welcome costly government

regulations if these policies have the effect of limiting entry.

BACKWARD INDUCTION Moving beyond these compact examples, one can

construct game trees to model more complicated competitive settings, for

instance, those that involve multiple sequential moves by more than two play-

ers. As long as the number of moves is finite (so the game cannot go on

forever) and all players have perfect information about previous moves, the

optimal moves of the players can be found by backward induction, that is, by

solving the game tree from right to left. In other words, to determine a player’s

optimal action at any point of decision, one must first pin down the optimal

plays for all future moves. The resulting sequences of optimal moves constitute

the players’ equilibrium strategies. Thus, we note an important result in

game theory:

Any sequential game with perfect information can be solved backward to obtain a

complete solution.

Thinking ahead is the watchword for sequential games. Or, in the words of the

philosopher Soren Kierkegaard, “Life can only be understood backwards, but

it must be lived forwards.”

Repeated Competition

Frequently, firms encounter one another in repeated competition. For

instance, duopolists may compete with respect to prices and/or quantities, not

just in a single period of time, but repeatedly. Similarly, an incumbent monop-

olist may encounter a number of would-be entrants over time. How does rep-

etition of this sort affect strategy and behavior?

Repeated competition introduces two important elements into the play-

ers’ strategic calculations. First, players can think in terms of contingentstrate-

gies. For instance, one firm’s pricing decision this month could depend on the

pricing behavior of its rival during prior months. (The firm might want to pun-

ish a rival’s price cuts with cuts of its own.) Second, in repeated play, the pres-

ent isn’t the only thing that counts; the future does as well. Accordingly, a player

may choose to take certain actions today in order to establish a reputationwith

its rivals in the future. As we shall see, the use of contingent strategies and the

formation of reputations serve to broaden the range of equilibrium behavior.

REPEATED PRICE COMPETITION As one example of a repeated game, sup-

pose the price competition shown in Table 10.3a is played not once, but repeat-

edly over time. Thus, when the firms independently set prices in January, they

know they will face new price decisions in February and in March and in each suc-

ceeding month into the indefinite future. Recall that in one-time play, charging

422 Chapter 10 Game Theory and Competitive Strategy

c10GameTheoryandCompetitiveStrategy.qxd 9/29/11 1:33 PM Page 422