Competitive Strategy 423a low price is each firm’s dominant strategy. As a result, firms find themselves in
a low-profit prisoner’s dilemma. But what if the game is played indefinitely? One
possibility is for the players to charge low prices every period (that is, simply to
repeat the single-stage equilibrium). Charging low prices indefinitely is one equi-
librium of repeated competition, albeit a very unattractive one. After all, who
wants to be trapped in a prisoner’s dilemma forever?
Are there other more favorable possibilities? Common sense would sug-
gest that players would strive to coordinate on a cooperative, high-price strat-
egy. The question is how firms can keep this kind of implicit agreement from
breaking down. One way is to exploit the power of contingent strategies.
Consider the following punitive (or grim) strategy:The firm (1) sets a high price in the first period, (2) sets a high price in every suc-
ceeding period, provided the other firm does likewise, and (3) sets low prices for-
ever after, if the other firm ever charges a low price.In short, any defection from the cooperative high-price outcome is penalized
by immediate and perpetual defections to low prices.
Let’s check that the firms’ mutual play of this punitive strategy constitutes
an equilibrium in the repeated competition. If each firm adheres to this strat-
egy, each charges a high price in the first and all other periods. Each earns a
profit of 10 each period forever. Alternatively, could a firm benefit by unilater-
ally deviating from the punitive strategy? What if the firm deviated by charging
a low price, say in the first period (as good a time as any)? In this period, it
increases its profits from 10 to 12. However, this triggers low prices from the
other firm forever. Thus, the best it can do is to continue with low prices as well,
earning a profit of 7 each period henceforth. Clearly, a one-time 2-unit profit
increase is not worth a 3-unit profit reduction into perpetuity.^9 Accordingly, the
firm’s interest is to maintain its reputation for cooperative play throughout the
repeated competition. To sum up, the play of punitive strategies, by holding out
the threat of retribution, supports a cooperative, high-price equilibrium.
The general lesson is that, in infinitely repeated competition, the threat
of punishment can be sufficient to enforce a cooperative equilibrium. Indeed,
swift but limited penalties may be sufficient to support cooperation. For
instance, the strategy “tit-for-tat” is much less drastic than the punitive strategy
just described. Under tit-for-tat,The firm (1) sets a high price in the first period, and (2) in each succeeding period,
echoes (i.e., imitates) the competitor’s previous price.(^9) The astute reader will recognize that this conclusion depends on how the firm weighs future ver-
sus present profits. Firms discount future profits. For discount rates of any reasonable magnitude,
neither firm has an incentive to cut price. (However, in the extreme case of an extraordinarily
high discount rate, future profits would carry almost no weight and the firm would opt for the
immediate price cut.)
c10GameTheoryandCompetitiveStrategy.qxd 9/29/11 1:33 PM Page 423