Deep Thought
.
(Translation: Today is another lesson teaching you how to get the best deal for yourself from bargaining.)
BA 445 Lesson B.2 Sequential Bargaining and Impatience 1

Readings
Baye “Sequential Bargaining” (see the index)
Dixit Chapters 1, 2, 3
BA 445 Lesson B.2 Sequential Bargaining and Impatience 2

Overview
BA 445 Lesson B.2 Sequential Bargaining and Impatience 3

Overview
Best Alternative to No Agreement is added to a bargainer’s share of the fixed positive gain from an agreement. — So, a seller can increase her price from a sale by finding alternative buyers.
Mutual Alternatives to No Agreement are added to both bargainers’ shares of the gains from an agreement. — So, a union seeks alternative employers and management alternative employees.
Manipulating Alternatives to No Agreement can be profitable even when alternatives decrease, depending on the relative decrease. — So, a union strikes as long as it costs management more.
Bargaining and Impatience interact like bargaining and depreciation. They should lead to an agreement before the gains from the agreement actually depreciate in the perception of the bargainers.
Relative Patience is profitable because bargaining is affected by the possibility of depreciation in the perceived gain from an agreement. — So, China gains when it is more patient than the US.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 4

Best Alternative to No Agreement
BA 445 Lesson B.2 Sequential Bargaining and Impatience 5

Best Alternative to No Agreement
Overview
Best Alternative to No Agreement is added to a bargainer’s share of the fixed positive gain from an agreement. — So, a seller can increase her price from a sale by finding alternative buyers.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 6

Best Alternative to No Agreement
Comment: When solving any Bargaining Game, a bargainer’s share of the fixed positive gain from an agreement is added to their Best Alternative To No
Agreement (BATNA) . In particular, a bargainer can increase their total payoff from an agreement by increasing their BATNA.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 7

Best Alternative to No Agreement
Question: Suppose Buyer Bob values the bag of fresh beans in front of him at 1 dollar and Seller Sabitha , in an effort to improve her bargaining position, has taken the time to find an alternative buyer would would pay $0.60. That drops the gains from a trade between Bob and Sabitha from $1.00 to $0.40.
As before, suppose there is only enough time before his tour bus leaves for Buyer Bob to make one offer to Seller
Sabitha for the bag of beans. Seller Sabitha must either accept or reject that offer, and if Sabitha rejects then she can sell to the alternative buyer for $0.60. Will trade occur between Bob and Sabitha? If so, at what price to Bob?
BA 445 Lesson B.2 Sequential Bargaining and Impatience 8

Best Alternative to No Agreement
Answer: The gain from Bob trading with Sabitha is $0.40. To consider all possible price offers (offers by Bob to buy or counteroffers by
Sabitha to sell), consider a bargaining payoff table.
The game lasts only one round, and gains are measured as a percentage of the $0.40 gain from Bob trading with Sabitha.
Rounds to
Game End
Offer by
T otal Gain to Divide
Bob's Gain
Offered
Sabitha's
Gain
Offered
?
1 Bob 100 ?
As before, Sabitha should accept anything as being better than nothing.
So, Bob can get away with 100 percent of the gains minus a pittance.
That leaves Bob with $0.40 gains from trade, and Sabitha with $0.00, meaning Bob pays $1.00-$0.40 = $0.60 to Sabitha, and Sabitha receives $0.60+$0.00 = $0.60 from Bob.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 9

Best Alternative to No Agreement
Comment: In any Bargaining Game, a bargainers’ shares of the fixed positive gain from an agreement depends solely on the sequence of who makes offers and on any depreciation of the gains from an agreement over the bargaining rounds. In particular, the bargainers’ shares are independent of the level of the gain from an agreement, and of the BATNAs of the bargainers.
Rounds to
Game End
1
Offer by
Bob
T otal Gain to Divide
100
Bob's Gain
Offered
100
Sabitha's
Gain
Offered
0
BA 445 Lesson B.2 Sequential Bargaining and Impatience 10

Bilateral Alternatives to No Agreement
BA 445 Lesson B.2 Sequential Bargaining and Impatience 11

Mutual Alternatives to No Agreement
Overview
Mutual Alternatives to No Agreement are added to both bargainers’ shares of the gains from an agreement. — So, a union seeks alternative employers and management alternative employees.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 12

Mutual Alternatives to No Agreement
Question: Consider union-management wage bargaining during
Thanksgiving Weekend at Medieval Times Dinner Theatre. The extended weekend lasts Thursday through Sunday. On the Wednesday before the weekend, the employee’s union confronts the management over wages. The union presents its demand. The management either accepts or rejects it and returns the next day with a counteroffer. Offers alternate thereafter. Each day Medieval Times operates with union labor, Medieval Times makes a profit of $10,000 before paying union wages. Each day without an agreement with the union, Medieval
Times makes a profit of $3,000 after paying for expensive scab (nonunion) labor, and union labor earns $2,000 from outside employment.
What initial wage demand should the union make? Should management accept that demand?
BA 445 Lesson B.2 Sequential Bargaining and Impatience 13

Mutual Alternatives to No Agreement
Answer: To consider all possible wage offers (offers by the Union to sell labor or offers by Management to buy labor), consider another bargaining payoff table . The game ends if an offer is accepted or if the weekend ends without an accepted offer. Gains are measured as a percentage of the 4x(10-3-2) = 20 thousand gain from accepting the
Union’s offer at the beginning.
Rounds to
End of
Game
1
2
3
Offer by
T otal Gain to Divide
Union's Gain
Offered
M.'s Gain
Offered
Management
Union
Management
25
50
75
?
?
?
4 Union 100 ?
BA 445 Lesson B.2 Sequential Bargaining and Impatience
?
?
?
?
14

Mutual Alternatives to No Agreement
Starting 1 bargaining round from the end of the game and
Rounds to
End of
Game
1 rolling back to the beginning
2 determines optimal offers and 3
4 counteroffers.
Offer by
Management
Union
Management
Union
T otal Gain to Divide
Union's Gain
Offered
25
50
75
100
0
25
25
50
M's Gain
Offered
25
25
50
50
The Union’s initial wage demand should give it 50% of the
$20,000 gains from trade, or $10,000, and management should accept that demand. Since the BATNA for Medieval
Times is $3,000x4 = $12,000 profit from scab labor and the
BATNA for union labor is $2,000x4 = $8,000 from outside employment, the initial wage demand by the union should be $8,000+$10,000 = $18,000, and management should accept that demand, and so earn $12,000+$10,000 =
$22,000 profit.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 15

Manipulating Alternatives to No Agreement
BA 445 Lesson B.2 Sequential Bargaining and Impatience 16

Manipulating Alternatives to No Agreement
Overview
Manipulating Alternatives to No Agreement can be profitable even when alternatives decrease, depending on the relative decrease. — So, a union strikes as long as it costs management more.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 17

Manipulating Alternatives to No Agreement
Comment: When a strategic bargainer observes that a better outside opportunity translates into a better share in a bargain, he will look for strategic moves that improve those outside opportunities. And he will notice that what matters is his outside opportunity relative to that of his rival. He will do better in the bargaining even if he makes a commitment or a threat that lowers both parties’ outside opportunities, as long as that of the rival is damaged more severely.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 18

Manipulating Alternatives to No Agreement
Question: Reconsider the outcome of the original unionmanagement wage bargaining for Thanksgiving Weekend at Medieval Times Dinner Theatre, where each day
Medieval Times operates with union labor, Medieval Times makes a profit of $10,000 before paying union wages, and each day without an agreement with the union, Medieval
Times makes profit $3,000 from scab labor and union labor earns outside income $2,000.
Compute how outcomes change if the union gives up $500 per day of outside income to intensify their picketing and, thereby, reduces Medieval Times profit from scab labor by
$1,000 per day.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 19

Manipulating Alternatives to No Agreement
Answer: The bargaining payoff table is not affected by changing the BATNA for each bargainer.
Rounds to
End of
Game
Offer by
T otal Gain to Divide
Union's Gain
Offered
M's Gain
Offered
1
2
3
Management
Union
Management
25
50
75
0
25
25
25
25
50
4 Union 100 50 50
In particular, the Union and Management reach an agreement on the first round, and each get half of the gains from an agreement.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 20

Manipulating Alternatives to No Agreement
Originally, the Union’s initial wage demand should give it 50% of the
$20,000 gains from trade, or $10,000, and management should accept that demand. Since the BATNA for Medieval Times is $3,000x4 =
$12,000 profit from scab labor and the BATNA for union labor is
$2,000x4 = $8,000 from outside employment, the initial wage demand by the union should be $8,000+$10,000 = $18,000, and management should accept that demand, and so earn $12,000+$10,000 = $22,000 profit.
But with intensified picketing, the BATNA for Medieval Times is
$2,000x4 = $8,000 and the BATNA for union labor is $1,500x4 =
$6,000 and the gains from trade is $26,000. So, the initial wage demand by the union should be $6,000+$13,000 = $19,000, and management should accept that demand, and so earn $8,000+$13,000
= $21,000 profit. The Union does better.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 21

Bargaining with Impatience
BA 445 Lesson B.2 Sequential Bargaining and Impatience 22

Bargaining with Impatience
Overview
Bargaining and Impatience interact like bargaining and depreciation. They should lead to an agreement before the gains from the agreement actually depreciate in the perception of the bargainers.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 23

Bargaining with Impatience
Comment: Now consider a different kind of cost of delay in reaching an agreement. Suppose the actual monetary value of the total gains from an agreement does not depreciate, but bargainers have a “time value of money” and therefore prefer early agreement to later agreement.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 24

Bargaining with Impatience
Question: Compute a bargaining payoff table for
Bargainers A and B making alternating offers over 5 bargaining rounds, with Bargainer A making the first offer,
A discounting 10% between each period, and B also discounting 10% between each period.
That is, both bargainers believe that having only 90 cents right now is as good as having $1 one round later.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 25

Bargaining with Impatience
Answer: A bargaining payoff table for Bargainers A and B making alternating offers over 5 bargaining rounds, with
Bargainer A making the first offer:
Rounds to
End of
Game
3
4
1
2
Offer by
A
B
A
B
T otal Gain to Divide
100
100
100
100
A's Gain
Offered
(10% dis.)
?
?
?
?
5 A 100 ?
BA 445 Lesson B.2 Sequential Bargaining and Impatience
B's Gain
Offered
(10% dis.)
?
?
?
?
?
26

Bargaining with Impatience
Starting 1 bargaining round from the end, B
Rounds to
End of should accept anything as being better than
Game nothing. After deducing that, A’s best acceptable
1 offer to B is a pittance, leaving A with 100.
2
Offer by
A
B
T otal Gain to Divide
100
100
A's Gain
Offered
(10% dis.)
100.00
90.00
B's Gain
Offered
(10% dis.)
0.00
10.00
3 A 100 91.00
9.00
Rolling back to 2 rounds from the end, A could
4 B 100 81.90
18.10
reject any offer and get 100 in the next round, which after A’s 10% discount is worth 90 in the
5 A 100 83.71
16.29
current round. After deducing that, B’s best acceptable offer to A is 90 plus a pittance, leaving B with 10.
Rolling back to 3 rounds from the end, B could reject any offer and get 10 in the next round, which after B’s 10% discount is worth 9 in the current round. . After deducing that,
A’s best acceptable offer to B is 9 plus a pittance, leaving A with 91.
Rolling back to 4 rounds from the end, A could reject any offer and get 91 in the next round, which after A’s 10% discount is worth 81.9 in the current round. After deducing that, B’s best acceptable offer to A is 81.9 plus a pittance, leaving B with 18.1.
Rolling back to the beginning, B could reject any offer and get 18.1 in the next round, which after B’s 10% discount is worth 16.29 in the current round. . After deducing that,
A’s best acceptable offer to B is 16.29 plus a pittance, leaving A with 83.71.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 27

Bargaining with Impatience
Comment: When both
Rounds to
End of
Game bargainers discount the same percent, the division of the gains
2
1 from trade is the same as if the 3
4 object itself were depreciating
5 by that percentage.
Offer by
A
B
A
B
A
T otal Gain to Divide
(10% dep.)
65.61
72.90
81.00
90.00
100.00
A's Gain
Offered
65.61
65.61
73.71
73.71
83.71
B's Gain
Offered
0.00
7.29
7.29
16.29
16.29
In the current problem, on the one hand, if there are 5 bargaining rounds and if A and B each discount 10%, then
A’s best acceptable offer to B is 83.71% plus a pittance, leaving A with 16.29%. On the other hand, if there are 5 bargaining rounds and the object itself depreciates 10% per round, then A’s best acceptable offer to B is, again, 83.71% plus a pittance, leaving A with 16.29%.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 28

Relative Patience
BA 445 Lesson B.2 Sequential Bargaining and Impatience 29

Relative Patience
Overview
Relative Patience is profitable because bargaining is affected by the possibility of depreciation in the perceived gain from an agreement. — So, China gains when it is more patient than the US.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 30

Relative Patience
Comment: We now see that more patience (less discounting) translates into a better share in a bargain. So a strategic bargainer will learn patience.
The Chinese symbol for patience can also mean restraint and control. It is formed by 2 different characters with the image of blade on the heart.
The word connotes how difficult it is to practice patience.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 31

Relative Patience
Question: Compare outcomes from 5 rounds of bargaining in three different scenarios:
1) Both bargainers discount the money payoff from an agreement 10 percent each round.
2) The first mover (the first to make an offer) discounts the money payoff from an agreement 10 percent each round, but the second mover discounts 20 percent.
3) The first mover (the first to make an offer) discounts the money payoff from an agreement 20 percent each round, but the second mover discounts 10 percent.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 32

Relative Patience
Answer: A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 5 bargaining rounds, with A discounting 10% between each period, and with B discounting 20% between each period.
Rounds to
End of
Game
3
4
1
2
Offer by
A
B
A
B
T otal Gain to Divide
100
100
100
100
A's Gain
Offered
(10% dis.)
?
?
?
?
5 A 100 ?
BA 445 Lesson B.2 Sequential Bargaining and Impatience
B's Gain
Offered
(20% dis.)
?
?
?
?
?
33

Relative Patience
Starting 1 bargaining round from the end, B
Rounds to
T otal Gain
A's Gain B's Gain
End of Offer by Offered Offered should accept anything as being better than to Divide
Game (10% dis.) (20% dis.) nothing. After deducing that, A’s best
1 A 100 100.00
0.00
acceptable offer to B is a pittance, leaving A
2 B 100 90.00
10.00
with 100.
3 A 100 92.00
8.00
Rolling back to 2 rounds from the end, A could reject any offer and get 100 in the next round, which after A’s 10% discount is
4
5
B
A
100
100
82.80
86.24
17.20
13.76
worth 90 in the current round. After deducing that, B’s best acceptable offer to A is 90 plus a pittance, leaving B with 10.
Rolling back to 3 rounds from the end, B could reject any offer and get 10 in the next round, which after B’s 20% discount is worth 8 in the current round. . After deducing that,
A’s best acceptable offer to B is 8 plus a pittance, leaving A with 92.
Rolling back to 4 rounds from the end, A could reject any offer and get 92 in the next round, which after A’s 10% discount is worth 82.8 in the current round. After deducing that, B’s best acceptable offer to A is 82.8 plus a pittance, leaving B with 17.2.
Rolling back to the beginning, B could reject any offer and get 17.2 in the next round, which after B’s 20% discount is worth 13.76 in the current round. . After deducing that,
A’s best acceptable offer to B is 13.76 plus a pittance, leaving A with 86.24.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 34

Relative Patience
A bargaining payoff table for Bargainers A and B, with
Bargainer A making the first offer, with 5 bargaining rounds, with A discounting 20% between each period, and with B discounting 10% between each period.
Rounds to
End of
Game
3
4
1
2
Offer by
A
B
A
B
T otal Gain to Divide
100
100
100
100
A's Gain
Offered
(20% dis.)
?
?
?
?
5 A 100 ?
BA 445 Lesson B.2 Sequential Bargaining and Impatience
B's Gain
Offered
(10% dis.)
?
?
?
?
?
35

Relative Patience
Starting 1 bargaining round from the end, B
Rounds to
T otal Gain
A's Gain B's Gain
End of Offer by Offered Offered should accept anything as being better than to Divide
Game (20% dis.) (10% dis.) nothing. After deducing that, A’s best
1 A 100 100.00
0.00
acceptable offer to B is a pittance, leaving
2 B 100 80.00
20.00
A with 100.
3 A 100 82.00
18.00
Rolling back to 2 rounds from the end, A
4 B 100 65.60
34.40
could reject any offer and get 100 in the next round, which after A’s 20% discount is
5 A 100 69.04
30.96
worth 80 in the current round. After deducing that, B’s best acceptable offer to A is 80 plus a pittance, leaving B with 20.
Rolling back to 3 rounds from the end, B could reject any offer and get 20 in the next round, which after B’s 10% discount is worth 18 in the current round. . After deducing that, A’s best acceptable offer to B is 18 plus a pittance, leaving A with 82.
Rolling back to 4 rounds from the end, A could reject any offer and get 82 in the next round, which after A’s 20% discount is worth 65.6 in the current round. After deducing that, B’s best acceptable offer to A is 65.6 plus a pittance, leaving B with 34.4.
Rolling back to the beginning, B could reject any offer and get 34.4 in the next round, which after B’s 10% discount is worth 30.96 in the current round. . After deducing that,
A’s best acceptable offer to B is 30.96 plus a pittance, leaving A with 69.04.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 36

Relative Patience
Summary: Compare outcomes from 5 rounds of bargaining in three different scenarios.
1) Both bargainers discount the money payoff from an agreement 10 percent each round. Outcome: First mover A’s best acceptable offer to B is 16.29%, leaving A with 83.71%.
2) The first mover (the first to make an offer) discounts the money payoff from an agreement 10 percent each round, but the second mover discounts 20 percent. Outcome: A’s best acceptable offer to
B is 13.76%, leaving A with 86.24%.
3) The first mover (the first to make an offer) discounts the money payoff from an agreement 20 percent each round, but the second mover discounts 10 percent. Outcome: A’s best acceptable offer to
B is 30.96 plus a pittance, leaving A with 69.04.
A does best when his is more patient (discounts less) than B.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 37

Relative Patience
Comment: When a strategic bargainer observes that more patience (less discounting) translates into a better share in a bargain, he will seek partners less patient than himself and avoid those more patient.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 38

Summary
BA 445 Lesson B.2 Sequential Bargaining and Impatience 39

Summary
A bargainers’ shares of the fixed positive gain from an agreement depends solely on the sequence of who makes offers and on any depreciation of, or discounting of, the gains from an agreement over the bargaining rounds. In particular, the bargainers’ shares are independent of the level of the gain from an agreement.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 40

Summary
A bargaining payoff table for Bargainers A and B, with
Bargainer A making the first offer, with 5 bargaining rounds, with A discounting 30% between each period, and with B discounting 40% between each period.
Rounds to
End of
Game
3
4
1
2
Offer by
A
B
A
B
T otal Gain to Divide
100
100
100
100
A's Gain
Offered
(30% dis.)
100.00
70.00
82.00
57.40
B's Gain
Offered
(40% dis.)
0.00
30.00
18.00
42.60
5 A 100 74.44
BA 445 Lesson B.2 Sequential Bargaining and Impatience
25.56
41

Summary
A bargaining payoff table for Bargainers A and B, with
Bargainer A making the first offer, with 5 bargaining rounds, with A discounting 40% between each period, and with B not discounting. (If A did not discount, he would have 100% of the gains from an agreement.)
Rounds to
End of
Game
Offer by
T otal Gain to Divide
A's Gain
Offered
(40% dis.)
B's Gain
Offered
(0% dis.)
3
4
1
2
A
B
A
B
100
100
100
100
100.00
60.00
60.00
36.00
0.00
40.00
40.00
64.00
5 A 100 36.00
BA 445 Lesson B.2 Sequential Bargaining and Impatience
64.00
42

Review Questions
Review Questions
 You should try to answer some of the following questions before the next class.
 You will not turn in your answers, but students may request to discuss their answers to begin the next class.
 Your upcoming Exam 2 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 43

Review 1: Relative Impatience
BA 445 Lesson B.2 Sequential Bargaining and Impatience 44

Review 1: Relative Impatience
Comment: TheFasterTimes.Com posts an account of bargaining for a tiny glass bottle covered in a landscape painting at Shanghai’s Yuyuan market.
The games began at a whopping 380RMB, or about $56US. Over the course of 20 minutes, the buyer brought the price down by pointing out design flaws and pretending to be distracted by a porcelain doll in a red silk dress. When the shopkeeper refused to go below 80RMB, the buyer walked away, slowly. “Come back,” the saleswoman cried, racing after her. “You can have it for 60.” Deal, at just under $9US, or about
1/6 of the asking price.
Bargaining in China is an art form that requires a lot of patience, and a willingness of the buyer to signal their patience by spending time.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 45

Review 1: Relative Impatience
Question 1. Consider negotiations over the price of a tiny glass bottle covered in a landscape painting at Shanghai’s
Yuyuan market. Buyer Betty values the bottle at $65, and
Seller Shen’s cost of supplying the bottle is $5. S makes the first offer, with 4 bargaining rounds of alternating offers, and with S discounting 2% between each period.
Compare bargaining outcomes when B discounts 10% between each period with B discounting only 1% between each period, and with B discounting 100% between each period (which is absolute impatience).
BA 445 Lesson B.2 Sequential Bargaining and Impatience 46

Review 1: Relative Impatience
Answer 1: A bargaining payoff table for Bargainers B and
S, with Bargainer S making the first offer, with 4 bargaining rounds, with B discounting 10% between each period, and with S discounting 2% between each period.
Rounds to
End of
Game
1
2
3
4
Offer by
B
S
B
S
T otal Gain to Divide
100
100
100
100
B's Gain
Offered
(10% dis.)
100.00
90.00
91.20
82.08
S's Gain
Offered
(2% dis.)
0.00
10.00
9.80
17.92
BA 445 Lesson B.2 Sequential Bargaining and Impatience 47

Review 1: Relative Impatience
A bargaining payoff table for Bargainers B and S, with
Bargainer B making the first offer, with 4 bargaining rounds, with B discounting only 1% between each period, and with
S discounting 2% between each period.
Rounds to
End of
Game
1
2
3
4
Offer by
B
S
B
S
T otal Gain to Divide
100
100
100
100
B's Gain
Offered
(1% dis.)
S's Gain
Offered
(2% dis.)
100.0000
0.0000
99.0000
1.0000
99.0200
0.9800
98.0298
1.9702
BA 445 Lesson B.2 Sequential Bargaining and Impatience 48

Review 1: Relative Impatience
A bargaining payoff table for Bargainers B and S, with
Bargainer B making the first offer, with 4 bargaining rounds, with S discounting 100% between each period, and with S discounting 2% between each period.
Rounds to
End of
Game
1
2
3
4
Offer by
B
S
B
S
T otal Gain to Divide
100
100
100
100
B's Gain
Offered
(100% dis.)
100
0
2
0
S's Gain
Offered
(2% dis.)
0
100
98
100
BA 445 Lesson B.2 Sequential Bargaining and Impatience 49

Review 1: Relative Impatience
Summary: In the first case, when B discounts 10% between each period, B captures 82.08% of the $60 gains from trade, or about $49.25, leaving S with about $10.75. Buyer Betty thus makes an acceptable offer of $65-$49.25 =
$15.75, leaving Seller Shen with gain $15.75-$5 = $10.75.
On one extreme, when B discounts only 1% between each period, B captures
98.0298% of the $60 gains from trade, or about $58.82, leaving S with about
$1.18. Buyer Betty thus makes an acceptable offer of $65-$58.82 = $6.18, leaving Seller Shen with gain $6.18-$5 = $1.18.
On the other extreme, when B discounts 100% between each period, B captures 0% of the $60 gains from trade, or $0, leaving S with $60. Buyer
Betty thus makes an acceptable offer of $65, leaving Seller Shen with gain $65-
$5 = $60. It is just as if Seller Shen made a take-it-or-leave-it offer.
Buyer Betty does better when she is more patient. In an extreme, she gets no gains when she has no patience.
BA 445 Lesson B.2 Sequential Bargaining and Impatience 50

BA 445 Managerial Economics
BA 445 Lesson B.2 Sequential Bargaining and Impatience 51