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Competitive Strategy 417

profit. Thus, this is an equilibrium. In the lower-left equilibrium, the final price

favors the seller, whereas in the upper-right equilibrium, the final price favors

the buyer. Each of these is a legitimate, though not necessarily fair, equilib-

rium. For instance, against a seller who “plays hardball” and sets $110,000 as her

final price, the best the buyer can do is concede by offering $110,000 as well.

Twenty-five percent of something is better than 50 percent of nothing.

To keep things simple, we have limited the buyer and seller to three offers.

Of course, in actual bargaining, each side’s final offer could lie anywhere in the

range from $80,000 to $120,000. In general, all matching offers in this range

constitute equilibria. The problem is that there are too manyequilibria. The

equilibrium concept does rule out certain outcomes. For instance, the bar-

gaining game should never end in a disagreement. Nevertheless, there are

matching equilibrium offers that have the bargainers splitting the total gains

from an agreement in any proportion (10–90, 40–60, 70–30, and so on). In

Chapter 15, we will say much more about how bargaining tactics can influence

which equilibrium is reached.

Sequential Competition

In the competitive settings analyzed thus far, players have taken one-shot

actions. Of course, many realistic competitive settings involve a series of actions

over time. One firm may make a move, its rival a countermove, and so on. In

a sequential game,players take turns moving. To portray the sequence of

moves, we use a game tree.As we shall see, when one party makes its current

decision, it must look ahead and try to anticipate the actions and reactions of

its competitors at their turns in the game tree. To illustrate the method, we

start with a compact example.

A multinational firm (MNF) is pondering whether to accept a developing coun-

try’s (DC) invitation to invest in the development of a copper mine on its soil.

Management of MNF is contemplating an agreement in which MNF and DC

split the profits from the mine equally. By its estimates, each side’s profit is

worth about $50 million (in net present value). Both sides are aware that any

agreement, being unenforceable, is not really binding. For instance, after MNF

has sunk a large investment in the project, DC’s leaders could decide to break

the agreement and expropriate the mine. Given DC’s desperate economic con-

dition, this is a real possibility. In such a case, MNF would suffer a loss of $20

million. The value of the nationalized mine—run less efficiently by DC—would

be $80 million. Finally, each side must look to the other to launch the mineral

project. MNF sees no other countries in which to invest, and DC has found no

other companies capable of launching the mine.

Given this description, we can use the game tree in Figure 10.1 to portray

the sequence of actions by MNF and DC. (Such a depiction is commonly called

An

International

Mineral Lease

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