9781118041581

Negotiation Strategy 651

clearly how optimal bargaining behavior can result in a failure to attain cer-

tain beneficial agreements.

A TENDER OFFER Firm A (the acquirer) is about to make a first-and-final

price offer for the outright purchase of family-owned firm T (the target). Firm

A is confident the target will be worth $1.6 million under A’s own management.

It has only a vague idea of firm T’s reservation price, that is, the minimum

price current management will accept. Its best guess is that this value (denoted

by v) is uniformly distributed between $1 million and $2 million; that is, all pos-

sible values in this range are equally likely. What is the firm’s best offer? How

often will a sale be concluded?

Clearly the acquirer can confine its attention to offers in the $1 million to $1.6

million range. Firm A faces an obvious trade-off between the probability and prof-

itability of agreements. The higher its offer, the greater the chance of acceptance,

but the lower the transaction profit. The firm’s expected profit from offer P is

[15.3]

Here, we have used the fact that Pr(P is accepted) P 1. For instance, as pre-

dicted by this expression, the offer, P $1.5 million, is accepted half the time

(by a target with a value anywhere between $1 million and $1.5 million). The

higher offer, P $1.8 million, is accepted with probability .8, and so on. To

maximize expected profit, we set

Thus, the optimal offer is P* $1.3 million. The probability that this price will

be accepted is .3, implying that the acquirer’s maximum expected profit is

$90,000. The point to underscore is this: The acquirer maximizes its expected

profit by taking a calculated risk; it shades its offer well below its true value,

even though this tactic poses the risk of missing possible agreements (whenever

the target’s reservation price is between $1.3 million and $1.6 million).

The lesson of this example carries over to the case of multiple offers and

counteroffers. In equilibrium, a self-interested bargainer always should hold

out for terms that are strictly better than its true reservation price, thereby

incurring the risk that some possible agreements are missed. Put another way,

suppose one side always is willing to concede up to its true value, if necessary,

to reach an agreement. Clearly, the other side could take advantage of this

purely cooperative behavior by “waiting the player out”—agreeing to terms

only after the player has made full concessions. To protect itself against this

“waiting” strategy, a player must be willing to risk disagreement. As movie pro-

ducer Sam Goldwyn once said, “The most important thing in acting is honesty.

Once you’ve learned to fake that, you’ve got it made.” To a degree, the same

MdE()/dP2.62P0.

(1.6P)(P1)1.62.6PP^2.

E()[1.6P]Pr(P is accepted)

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