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To confirm this result, let’s start with an extreme example of an inefficientout-

come: the no-agreement outcome (corresponding to Q R 0) shown as

point 0. Note that the parties’ contours through point 0 form a kind of “cat’s

eye.” Any agreement within the cat’s eye is better for each side (i.e., lies on a

higher profit contour) than the disagreement outcome. Point A (correspon-

ding to Q 12 and R 21.6) is an example. Although point A is an improve-

ment over point 0, it still is not efficient. Note that the buyer and seller contours

cross each other at point A, leading to a new (smaller) cat’s eye. Both sides can

earn higher profits by moving within this cat’s eye. As a general rule, as long as

the parties’ profit contours cross, the current agreement is inefficient; that is,

both sides can profit by moving to a new agreement within the cat’s eye.

When are all mutually beneficial improvements exhausted? This occurs at

any point in Figure 15.2 where the profit contours are tangent (i.e., no longer

cross). At points of tangency, such as B, C, D, and E, any movement to the

northeast or southwest is counterproductive, that is, lowers both sides’ profits.

Any other movement raises one side’s profit at the expense of the other’s.

Consequently, points of tangencies represent efficient agreements. In the fig-

ure, we observe that the set of tangencies lies along the vertical line at an out-

put of 20 units. This confirms what we already showed algebraically: 20 units is

the optimal (i.e., value-maximizing) output. By varying R (the vertical position

in the figure), we redistribute this maximum total profit between the parties.

We can sum up our discussion in this section with the following proposition:

When there are available monetary transfers that redistribute bargainers’ payoffs

dollar for dollar, an efficient agreement is one that maximizes the parties’ total

value from the transaction.

NEGOTIATION STRATEGY

Negotiations inevitably produce tension between the forces of competition and

cooperation. To reach a mutually beneficial agreement, both sides must coop-

erate. More than that, they must strive to uncover better agreements. Yet each

side’s ultimate objective is to secure the most favorable agreement for itself.

Of course, along the payoff frontier securing better terms for oneself implies

less favorable terms for the other side. Thus far, our discussion has focused on

identifying efficient agreements, that is, outlining the best the parties can do

together. However, for a variety of reasons, bargaining as actually practiced

often falls far short of optimal outcomes. In his seminal work on bargaining,

The Strategy of Conflict,Thomas Schelling puts the problem this way:

Most bargaining situations ultimately involve some range of possible

outcomes within which each party would rather make a concession than

fail to reach agreement at all. In such a situation any potential outcome

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