9781118041581

Bargaining

One of the most fertile domains for applying game theory is in the realm of bar-

gaining and negotiation. The following example is intended to suggest some

of the strategic issues that arise in bargaining settings.

BARGAINING OVER THE TERMS OF A TRANSACTION Two firms, a buyer and

a seller, are in negotiations concerning the sale price of a good. Both sides

know that the seller’s cost to produce the good is $80,000 and that the buyer’s

value for the good (the maximum amount the firm can pay) is $120,000. Sup-

pose that, before negotiations begin, each side has formulated its final and best

offer, a price beyond which it will not concede in the negotiations. In particu-

lar, each is considering one of three possible final offers: $90,000, $100,000, or

$110,000.

The firms’ offers determine the final price as follows. First, if the firms’

price offers are incompatible—that is, the seller insists on a price greater than

the buyer is willing to pay—there is no agreement, and each side earns a zero

profit. Second, if the players’ final offers match, then this is the final price.

Third, if the buyer’s offer exceeds the seller’s demand, the final price is mid-

way between the two offers—as if the players conceded at equal rates toward

this final price.

Table 10.6 lists the payoffs that result from different combinations of final

offers in this stylized bargaining game. For instance, the three zero-profit out-

comes in the upper-left portion of the table are the result of incompatible

offers. Alternatively, if the buyer’s offer is $100,000 and the seller’s offer is

$90,000, the final price is $95,000. Therefore, the buyer’s profit is 120,000 

95,000 $25,000, and the seller’s profit is 95,000 80,000 $15,000. These

profits are shown in the middle-right entry. The other profit entries are com-

puted in analogous fashion.

Table 10.6 displays three distinct equilibria. In the middle equilibrium,

each side makes a price offer of $100,000, and this is the final agreement.

Facing this offer, the best the player can do is match it. Asking for less dimin-

ishes one’s profit, and asking for more results in a disagreement and a zero

416 Chapter 10 Game Theory and Competitive Strategy

TABLE 10.6

A Stylized Bargaining

Game

Even the simplest bar-

gaining situations

involve multiple

equilibria.

Seller Final Offers ($000s)

110 100 90

Buyer Final 90 0, 0 0, 0 30, 10

Offers (^100) 0, 0 20, 20 25, 15
($000s) (^110) 10, 30 15, 25 20, 20
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