Nash equilibrium. Here each side’s action is a best response against the other’s.
As long as each competitor is smart enough to recognize the Nash equilibrium
and expect the other to do likewise, this is how each should play.
But what if one player is not so smart? Consider the market-share battle
once again. Suppose the manager of firm 2 is convinced that firm 1 plans to use
strategy R3. This might not seem to be a very smart move by firm 1. (Perhaps
it is lured to R3 by the mistaken hope of a 7 payoff.) But let’s say that there is
ample evidence that this is how firm 1 will play. (It already has begun launching
the R3 advertising campaign.) Then, surely, firm 2 should choose C3, gaining
a 5 percent share increase at firm 1’s expense. By changing from C2 to C3,
firm 2 can profit from firm 1’s mistake. The point is this: In a Nash equilib-
rium (unlike a dominant-strategy equilibrium), there exist some circumstances
where it might pay to use a nonequilibrium strategy. If one player deviates from
equilibrium (by mistake or for any other reason), the other player may be able
to improve its payoff by deviating also.
Are we recommending nonequilibrium play in Table 10.2 for either firm?
Certainly not. Equilibrium play is quite transparent and should be grasped
readily by both sides. But in a different setting where there is reason to antici-
pate one player deviating from equilibrium play, the other player may be able
to profit from that action by deviating (optimally) as well.408 Chapter 10 Game Theory and Competitive StrategyCHECK
STATION 3In Chapter 9’s example of dueling suppliers, each firm had constant unit costs AC MC
$6, and market demand was described by P 30 (Q 1 Q 2 ), where output is meas-
ured in thousands of units. The following payoff table lists the firm’s profits for three lev-
els of output. Choose one entry and check that the payoffs are correct. Does either firm
have a dominant strategy? From the table, the firms appear to prefer outputs of 6,000
units each. Explain why this is not an equilibrium outcome. Find the firms’ equilibrium
quantities. (Confirm that this matches the answer derived algebraically in Chapter 9.)Firm 2’s Quantity (000s)
6810
6 72, 72 60, 80 48, 80
Firm 1’s Quantity 8 80, 60 64, 64 48, 60
(000s)
10 80, 48 60, 48 40, 40THE PRISONER’S DILEMMA ONCE AGAIN Before concluding this section, we
take a brief second look at the paradigm of the prisoner’s dilemma (PD) intro-
duced in Chapter 9. The top portion of Table 10.3 reproduces the price-war pay-
offs of Table 9.2. The middle portion of the table portrays a different sort of PD:
an arms race between a pair of superpowers. Finally, the bottom portion uses
symbolic payoffs to represent the general features of the prisoner’s dilemma.c10GameTheoryandCompetitiveStrategy.qxd 9/29/11 1:33 PM Page 408