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VI. Negotiation Exercises
Face-to-face negotiation is an excellent vehicle for engaging students and
promoting “learning by doing.” The following exercises are good examples. To
conduct the exercises, the instructor should distribute buyer and seller
information sheets and pair the students. An easy way to create pairings is to
hand out a “chit” to each student labeled Buyer 1, Buyer 2,... or Seller 1, ... and
so on, in random fashion. Then have a roll call asking Buyer 1 and Seller 1 to
raise hands and pair off, and so on. If negotiations are conducted in class, tell
student pairs to negotiate quietly (and amicably). Also tell students not to be
distracted by prices they might hear other pairs discussing. These are irrelevant
since different pairs may have different reservation prices. After completing
the exercise, students can hand in data sheets and the instructor can lead a class
discussion of what negotiation strategies were used and with what outcomes.
Typical in-class questions:
- What kind of negotiation was this? (A distributive bargain; a multi-issue
bargain; resolution of a dispute)
- What was the alternative to a negotiated agreement?
- How much information did each side have?
- Summarize the course of your partnership’s negotiations. Who made the
opening offer? What was it? What was the counter offer? Were concessions
fast or slow? What was the final price?
- What bargaining strategies seemed to work well? Is it advantageous to make
the opening offer?
- Did you “lay your cards on the table” or “play things very close to the vest?”
- How would things change if one side knew both reservation prices (and the
uninformed side didn’t know about the other’s information advantage?)
Discussion. This type of exercise has been run many times using student
subjects. At the risk of some oversimplification, a convenient way to present an
overview of typical results is to draw an analogy with the game of chess and
speak of strategies in the opening, middle game, and end play.
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As is universal in bargaining, students typically begin by making extreme
opening offers -- buyer offers in the 130-160 range, seller demands in the
190-220 range. Because they frame the range in which subsequent offers are
made, opening offers are an important determinant (in fact the most important
determinant) of final price. Moreover, opening offer strategy is crucial in the
following sense. An opening offer that is too cooperative, i.e. that leaves too
little space for the bargaining to follow, almost always destines the bargainer to
a meager profit. For example, consider a buyer who offers b1 = 170 when
holding value vB = 200. Suppose that the seller counters with s1 = 210 as is
typical. Bargaining is now confined to the 170-210 range, and it is a fair bet
that the final price will be in the middle of this range, near 190, leaving the
buyer a profit of 10. This is considerably less than the buyer should expect to
get on average. After all, the average seller value is 150, so the available total
profit from an agreement is 50 on average. To have a chance of securing its fair
profit share (25), the buyer must stake out enough room (say open with b1 =
145) for the subsequent “negotiation dance.” The experimental evidence
indicates that a bargainer does best by making an extreme opening offer, but
not one so extreme as to compromise all credibility. One cannot “win” the
negotiation by making the right opening. But one can lose it with an offer that
stakes out too little bargaining room.
Like Sherlock Holmes’ dog that didn’t bark in the night, the key
observation about the middle game is the absence of stratagems that deliver a
clear profit advantage. In principle, a stubborn pattern of slow concessions
(conceding more slowly than one’s partner) might be expected to reap profit
dividends. The experimental evidence shows that most pairs of bargainers
make concessions at roughly the same rate. One side’s slow concessions beget
matched slow concessions from the other. (Of course, a small number of
subjects make the mistake of a large initial concession, giving away profit to
the other side.) Whether slow or fast, if concessions are equally matched, the
final agreement (if there is one) can be expected in the neighborhood of the
midpoint between the sides’ opening offers. Of course, the farther apart are the
opening offers, then the greater are the number of offers and counter-offers it
takes to reach agreement.
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In the negotiation exercise, a good prediction for the price of a final
agreement is provided by the equation:1
P = .43[(vB + vS)/2] + .38[(b1 + s1)/2] + .19[178].
According to this equation, price is determined as a weighted average of the
three bracketed terms. (Note that the weights .43, .38, and, .19 sum to one.)
The first term is the midpoint of the reservation values, an obvious point of
attraction for the final price. The second term is the midpoint of the opening
offers. As we noted, if concession rates are roughly equal, then the final price
will gravitate toward this point (subject, of course to the influence exerted by
the bargainers’ reservation prices. The third term represents the influence of the
ranges from which reservation prices are drawn. Both sides know that these are
drawn from the overlapping ranges 100-200 and 150-250. Since the midpoint
of the combined range is 175, we would expect this value to act as a center of
gravity for final prices.
Since more than half of all agreements were concluded in the last two
minutes of the allotted time, one might expect the end play to be important.
The main finding here is that almost all students are willing to make
significant last moment concessions rather than fail in reaching an agreement.
In fact, the clearest evidence of this behavior is provided by the pairs whose
reservation prices precluded agreement. These subjects exchanged offers
relentlessly (though fruitlessly), typically conceding within five units of their
true reservation prices before giving up or running out of time. As a result of
this behavior, pairs were very successful at attaining agreements – reaching on
average 9 of 10 possible agreements accounting for some 96% of the potential
bargaining profit.
The cooperative negotiation behavior of subjects produces high marks for
efficiency but does not constitute equilibrium behavior. A bargainer could
increase his expected profit by departing from average behavior – by being
much more aggressive. This means beginning with an extreme opening offer,
making slow concessions in the middle game, and out-waiting one’s bargaining
11 The equation was estimated from the experimental data using ordinary least
squares regression. The form of the equation is implied by the hypotheses that
(i) the reservation price coefficients are equal and (ii) the offer coefficients are
equal. Both of these hypotheses were supported by the data.
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partner in the last minute. For instance, a smart bargainer knows that a typical,
cooperative-minded partner will concede nearly to his true value in the end
game. By holding out for a substantial profit and waiting for the partner’s final
concessions before time expires, the bargainer can obtain a better price. In fact,
a direct way to improve a subject’s profit performance is to tell him a “wrong”
reservation price. For instance, consider a buyer whose true value is 200 and
earns an average profit from bargaining. If she is told instead that her value is
180, she will bargain more aggressively and earn a significantly greater profit
on average. (Profit continues to be computed based on the true value 200.) This
is true even though there is a greater chance of missing efficient agreements
(for instance, when the seller’s value is above 180). Similarly, a seller will earn
greater profit if he is told a tougher (i.e. higher) value than his true one.
In terms of pure self-interest, the key to more profitable bargaining
behavior is to act as if one holds a tougher value than is the case. To quote the
immortal words of the movie producer Sam Goldwyn, “The most important
thing in acting is honesty. Once you’ve learned to fake that, you’ve got it
made.” But a move to self-interested behavior on the part of both bargainers
inevitably risks missing potentially beneficial agreements.
B. Buying and Selling a Maine House. In this negotiation, price is the main
issue (so distributive bargaining is emphasized), but not the only one. A second
part of the deal is whether the sale should be for all 17 acres of land or for only
14 acres. This introduces an “integrative” element. Each bargainer knows his or
her own reservation prices but not those of the other side.
According to the information sheet, the buyer’s reservation price is
$150,000 if he or she purchases the house and all 17 acres and $127,000 if the
deal is for 14 acres (whereby the seller retains three acres on the outskirts of
the property. Seller information sheets (see below) come in two different
versions. The instructor should distribute version one of the seller information
sheet to odd-numbered sellers and version two to even-numbered sellers. In the
first version, the seller’s reservation price is $120,000 for a 17-acre sale and
$107,000 for a 14-acre sale. In the second version, the seller’s reservation price
remains $120,000 for 17-acres, but is only $85,000 for 14 acres.
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The accompanying figure shows the zones of agreement for 17-acre and
14-acre deals. For a 17-acre sale, the zone of agreement (ZOA) stretches from
$120,000 to $150,000, implying a total trading gain of $30,000 to be split
between the players depending on the final negotiated price. How does a
14-acre deal compare? For odd-numbered pairs, a 14-acre deal offers an
inferior zone of agreement with total trading gains of only $20,000. (See the
middle ZOA in the figure.) The explanation is straightforward. Retaining the 3
outlying acres has a value of $120,000 - $107,000 = $13,000 to the seller. But,
it reduces the buyer’s reservation value by $150,000 - $127,000 = $23,000. The
cost to the buyer is greater than the gain to the seller, so having the seller retain
the 3 acres makes no sense.
Things are just the reverse for even-numbered pairs. Now, a 14-acre deal
offers a superior zone of agreement (stretching from $85,000 to $127,000,
implying $42,000 in total trading gains). Thus, if all negotiation pairs diligently
explore both 17-acre and 14-acre deals, they should reach agreements where the
most total money is to be had – odd-numbered pairs closing 17-acre deals and
even-numbered pairs 14-acre deals. In practice, about 80% of odd-numbered
pairs reach the efficient outcome, but only about 65% of even-numbered pairs
do so. (It seems harder to budge from the 17-acre deal status quo.)
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In the debriefing, the following questions should be addressed:
1. How did you arrive at your given agreement (14 acres or 17 acres)? Was
your outcome efficient? Did you “lay your cards on the table” or “play things
very close to the vest?”
2. Describe the negotiation dance. What was the opening offer? The counter
offer? Were concessions fast or slow? What bargaining strategies seemed to
work well? Is it an advantage to make the opening offer?
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| | | | | | |
80 90 100 110 120 130 140
| | | | | | |
80 90 100 110 120 130 140
House + 17 acres
vS = 120, vB = 150
| | | | | | |
100 110 120 130 140 150 160
vS = 107, vB = 127
House + 14 acres
vS = 85, vB = 127
135
117
106
Total Profit = 30
Total Profit = 20
Total Profit = 42
In keeping with the earlier discussion (pp. 9-11), opening offers are crucial. The
biggest mistake is to be too generous in ones opening offer (or offer response).
It is imperative to leave enough “room” in the negotiation dance. For instance,
suppose the buyer opens with b1 = $132 (not aggressive enough) for a 17-acre
deal. Then, a likely seller response is s1 = $160. From here, matching offer
concessions from the players would result in a final price of $146, leaving only
$4 thousand in profit for the buyer!! A poor initial offer has led directly to a
low-profit outcome.
Buying a Maine House
After reading these instructions, you will participate in a negotiation
exercise involving two parties, a buyer (you) and a potential seller (a
bargaining partner to be assigned). The description of the bargaining setting
and information about your role as buyer are outlined below.
You and your spouse are in your late thirties and live outside New York
City. For the last five years, you have been renting a cottage near a lake in an
isolated and unspoiled part of Maine. Recently, you were contacted by the
owner of a nearby summer house who has decided to sell the cottage and a
considerable parcel of land surrounding it. Since the owner’s spouse died two
years ago, the house has been unused and unattended. You and your spouse
went to college with the owner’s son and remember the house from a visit three
summers ago. You were both taken with the cottage, so taken that you asked to
be called if it ever were put up for sale. A week ago over the phone, you and
the owner agreed to meet at the house, tomorrow (Memorial Day weekend) to
explore the terms of a possible sale. As yet neither side has even mentioned a
price; both sides prefer to discuss and negotiate in person. You remember the
owner (whose age you guess is near 65) as something of a “Yankee Trader”
and probably a good negotiator. You also acquired negotiating experience in
your former job as a purchasing agent.
The rambling “cottage” sits on a bluff overlooking a river and gorge. The
house is in the Cape Cod style but is equal to the size of two Capes. The first
floor has kitchen, bathroom, storage room, small dining room and an
impressive, 40-foot living/family room with a fine view of the river below. The
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second floor has three normal bedrooms and one “dormitory size” bedroom
over the living room, with no bathroom. A good euphemism for the cottage is
“rustic”; the carpentry, appointments, kitchen appliances, plumbing and
electrical systems all date from forty-five years ago. There are two first floor
fireplaces, one on the second floor, but no central heat. The cottage is located
six miles from the nearest (small) town, and the final turnoff consists of two
miles of unpaved road. (There is one, poor quality, year-round house at the
junction of the dirt road and highway.) Besides the house, there are 17 acres of
surrounding land, wooded except for two acres of lawn around the house. The
lawn and former flower gardens have been untended for two years.
Over the phone, you and the owner agreed to be prepared to discuss two
sale options: (1) sale of the house and all 17 acres, or (2) sale of the house and
14 acres allowing the owner to retain 3 acres (separated by a small knoll from
the house). The owner explained that keeping a small part of the land in the
family as a link to the beloved spot would be appealing.
Prior to the negotiations, you have done two important bits of
homework. First, you have explored with your spouse the maximum amount of
money that you are willing to pay for the house. You prize the site, the view,
and the cottage’s wonderful downstairs rooms. On the other hand, the kitchen
and upstairs bedrooms (and adding a bathroom) mean considerable trouble and
expense. You are also thinking about converting it to all-year use, since you are
avid skiers and there is terrific skiing nearby. Accounting for these expenses,
you come to the conclusion (after long thought) that your walk-away price for
the house and all 17 acres is $150,000. You will never pay more than this
price. Of course, you hope to pay a price below this level (and as small a price
as possible). Acquisition of only 14 aces is obviously less desirable than getting
all 17. After hard thought, you figure that giving up the 3 acres reduces your
value for the house and property by $23,000. That is, you would be willing to
pay at most only $127,000 for the house and 14 acres.
Second, you have tried to imagine the kind of price the owner might
demand for the house and land. To your mind, the house, because of its
condition and isolation, will be very difficult to sell locally. You also realize
that the owner’s personality and circumstances will probably have as much
influence on an acceptable selling price as the quality of the house itself. You
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know very little and would like to know much more about the owner. On a note
pad, you have listed the following, possibly pertinent facts: (1) The owner
seems to be in the middle-income bracket and may need the sale income for
later retirement. (2) None of the owner’s three children are interested in
retaining the house. (3) Question: how much is retaining the 3 acres worth to
the owner? All in all, your best guess concerning the owner’s minimum
acceptable price (the least he would be willing to accept) for the house and 17
acres is that it ranges between $100,000 and $160,000, all values in between
equally likely.
You will have 15 minutes to negotiate possible sale terms with your
bargaining partner representing the owner. Negotiations are conducted by
offers and counteroffers. You may accept the other side’s offer at any time and
this ends the negotiations. Either side can make the first price offer. The main
bargaining ground rules are:
1) You may not show this information sheet to your partner. In particular,
it is not permitted to show the other side your walk-away price. However, you
and your partner are free to discuss and argue about agreement terms. Besides
exchanging offers, you may also make general statements such as, “I can’t go
higher” or “I can’t afford to pay that price.”
2) Offers must alternate between the players. A bargainer’s offer cannot
get any worse (buyer offers cannot fall nor seller demands rise over time). The
bargainer is free to repeat his previous offer, i.e. make no concession.
Your final profit from any agreement is the difference between your
reservation price and the price you pay. Example: if you purchase the house
and 14 acres for $115,000, your profit is 127,000 - 115,000 = $12,000.
(Remember, you are not allowed to pay more than your walk-away price!) If
no agreement is reached, your profit is zero.
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