1. Alternative-offer bargainging
2009
Alternative-offer bargainging
-An Experiment based on the students of Peking University
Yang Cao, Bachelor candidate for Economics, PKU
Yang He, Bachelor candidate for Finance, PKU
Lisha Fu, Bachelor candidate for Economics, PKU
Aug. 6th, 2009

2. Agenda 2009 Background Review Experiment Design Purpose & Innovation
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Agenda
2009
Background Review
Experiment Design
Purpose & Innovation
Make sense of the Data
Drawbacks & Improvement
Q & A 9

3. Stahl/Rubinstein prediction
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0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Background Review
2009
Standard Model
Ultimatum Game
Binmore,Shaked
& Sutton(1982)
Guth & Tieze(1987)
Neelin, Sonnenschein
& Spiegel(1988)
Ochs & Roth(1989)
Developed by Stahl(1972)&Rubinstein(1982):
(1)Two bargainers decide how to divide K .
(2) Discount factors:δ1 and δ2 (represent the time value of the bargainers)
Solution:
(Two-period Game)
(1) The solution of the bargain strictly follows the logic of the backward
induction;
(2) The game would end in the first period;
(3) Only the discount factors influence the division outcome.
Standard Model
Stahl/Rubinstein prediction 9

4. Background Review 2009 Ultimatum Game Standard Model Ultimatum Game
Binmore,Shaked
& Sutton(1982)
Guth & Tieze(1987)
Neelin, Sonnenschein
& Spiegel(1988)
Ochs & Roth(1989)
One-period bargaining game designed by Guth et.al.
The results deviated from the theoretical prediction.
The subjects often rely on what they consider a fair or justified result.
Furthermore, the ultimatum aspect cannot be completely exploited since
subjects do not hesitate to punish if their opponents ask for “too much”.
——Guth
Consideration of fairness and being afraid of the punishment.
(further proved by Dictator Game)
Ultimatum Game

5. Background Review 2009 Binmore,Shaked & Sutton(1982) Standard Model
Ultimatum Game
Binmore,Shaked
& Sutton(1982)
Guth & Tieze(1987)
Neelin, Sonnenschein
& Spiegel(1988)
Ochs & Roth(1989)
Two-period game experiment;
At the beginning of the experiment, the results are similar to the Ultimatum Game conducted by Guth;
when the experiment was conducted again with the role of the players reversed , most of the opening offers become very close to the prediction of the theoretical model.;
some simple learning experience would help the results approach the theoretical model.
Binmore,Shaked
& Sutton(1982)

6. Background Review 2009 Guth & Tieze(1987) Standard Model
Ultimatum Game
Binmore,Shaked
& Sutton(1982)
Guth & Tieze(1987)
Neelin, Sonnenschein
& Spiegel(1988)
Ochs & Roth(1989)
It is because the discount factor applied by Binmore et.al. is too moderate that the results of the experiments could be close to the theoretical prediction.
——Guth & Tieze
Introduce two treatments with two extreme discount factors and 0.9 into their design to test the predictive power of the Stahl/Rubinstein through the comparison between the two treatments.
The results of the second treatment seriously deviate from the Stahl/Rubinstein prediction.
Guth & Tieze(1987)

7. Background Review 2009 Neelin, Sonnensc- -hein& Spiegel(1988)
Standard Model
Ultimatum Game
Binmore,Shaked
& Sutton(1982)
Guth & Tieze(1987)
Neelin, Sonnenschein
& Spiegel(1988)
Ochs & Roth(1989)
2-period, 3-period and 5-period experiments;
Nor the Stahl/Rubinstein or the equal-split model predict the bargaining behavior observed in our experiments. A convenient summary of what we observed is that in each game the sellers offer the buyers the value of the second-round pie.”
——Neelin et.al
Neelin, Sonnensc-
-hein& Spiegel(1988)

8. Background Review 2009 Ochs & Roth(1989) Standard Model Ultimatum Game
Binmore,Shaked
& Sutton(1982)
Guth & Tieze(1987)
Neelin, Sonnenschein
& Spiegel(1988)
Ochs & Roth(1989)
A consistent first-mover advantage is observed in both of the first-period and subgames in all the treatments;
The discount factor of player1 was observed to influence the outcome of the two-period game ,which contradict the prediction of the mainstream theory;
Though, according to the theoretical prediction, the game should end in the first period, a large percentage of opening offers were rejected in the experiments;
The observed mean agreements deviate from the equilibrium predictions in the direction of equal split;
A substantial rejected opening offers were followed by disadvantageous counterproposals, which means that the rejection in the first period is impossible to bring the buyer a larger utility in the subgames.
Ochs & Roth(1989)

9. Agenda 2009 Background Review Experiment Design Purpose & Innovation
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Agenda
2009
Background Review
Experiment Design
Purpose & Innovation
Make sense of the Data
Drawbacks & Improvement
Q & A 9

10. Experiment Design 2009 4 treatments
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Experiment Design
2009
Experiment A
Experiment B
Experiment C
Experiment D
Period
Player 1
Player 2 1 10 2 3 7 -
0.9 4
0.27 5
0.081
Discount factor
0.3
0.7
Nash equilibrium
(7, 3)
(3, 7)
(7.9, 2.1)
(7.7, 2.3)
4 treatments
Randomization
16 participants (students from different departments)
60 observations for each treatment 9

11. Agenda 2009 Background Review Experiment Design Purpose & Innovation
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Agenda
2009
Background Review
Experiment Design
Purpose & Innovation
Make sense of the Data
Drawbacks & Improvement
Q & A 9

12. 2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Purpose & Innovation
2009
Through the comparison among treatment A, B and C to observe people’s decisions in experiments involving different periods. (Neelin et.al,1988)
Innovation: discount factor & Revenue chart
Through the comparison between treatment A and B to observe people’s decisions in experiments involving different discount factors. (Guth & Tieze,1987)
Innovation: design of our discount factor (0.3/0.7)
Replicate the alternative-offer experiment in China to observe whether there are culture differences among participants from different countries.
Test the behavior routines established by Ochs & Roth(1989), and make our own conclusions about the opening-offers, rejection rate, disadvantageous counterproposals, first-mover advantages and the differences of decisions among people having different genders and degrees. 9

13. Agenda 2009 Background Review Experiment Design Purpose & Innovation
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Agenda
2009
Background Review
Experiment Design
Purpose & Innovation
Make sense of the Data
Drawbacks & Improvement
Q & A 9

14. Opening Offers in Experiments A,C and D
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0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Opening Offers Analysis
2009
Opening Offers in Experiments A,C and D
Most offers of player 1 are between the subgame
perfect Nash equilibrium offer and even division,
and the closer to subgame perfect Nash
equilibrium offer it is, the higher for the rejection
rate.
In three-period game, player 1 are more likely to
offer fifty-fifty, while player 1 in five-period game
are more likely to choose subgame perfect Nash
equilibrium offer. 1

15. Opening Offers in Experiments A and B
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0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Opening Offers Analysis
2009
Opening Offers in Experiments A and B
In Experiment A, discount factor for players are
both 0.3, while in Experiment B, the discount
factor for player 1 is 0.3 and for player 2 is 0.7.
Player 2 in Experiment B is more powerful than
those in Experiment A. Because subgame perfect
Nash equilibrium for Experiment A and B is (7,3)
and (3,7), respectively. The results for each
experiment are closer to their own equilibrium.
In Experiment B, player 1 has first-move
advantage, so even subgame perfect Nash
equilibrium is (3,7), he will not get less earnings
than player 2 1

16. perfect equilibrium offer ————————— actual offer
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Opening Offers Analysis
2009
Opening Offers of the experienced players
··········
perfect equilibrium offer
————————— actual offer
Figures show the opening offers of experienced players. Experienced players refer to the one who have played
the specific game for the most time.
the subgame perfect Nash equilibrium may not be a good prediction. Because most offers tend to move to
equal division, and only the player in Experiment D tend to offer as subgame perfect Nash equilibrium. 5

17. Source: Euromonitor International 2007 data
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Opening Offers Analysis
2009
Testing predictive power of Nash equilibrium
Test for the opening offers in each experiment
The direction of the difference corresponds to
the theoretically predicted direction in 5 of the
6 groups.
Source: Euromonitor International 2007 data 5

18. 2009 Rejected Opening Offers Analysis Offers &Responses in Experiments
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Rejected Opening Offers Analysis
2009
Offers &Responses in Experiments
Disadvantageous counters are referred
to the situation that player rejects the
opening offer and make a
counterproposal, he will not get as
much as he can if has been accepted.
In Experiment A,C,D, the subgame
perfect Nash equilibrium is (7,3),
(7.9,2.1), (7.7,2.3), respectively. our
subjects failed to reach equilibrium
prediction in the first period, with 8
percent of opening offers rejected. 5

19. 2009 Rejected Opening Offers Analysis
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
Rejected Opening Offers Analysis
2009
Rejection rate and disadvantageous counterproposal rate in previous experiments
The pattern of rejections and
counterproposals observed in the
experiments is quite similar to
those in the previous experiment
discussed above.
One explanation is that players
usually have limited calculation
ability, they cannot figure out
where Nash equilibrium
locates. Another is that players’
utility is not measured by their
monetary payoff. 5

20. Average opening offers and Average earnings
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First-move advantage and earnings
2009
Average opening offers and Average earnings
Although player 1 has first-move advantage, it
doesn’t mean that he can get highest earnings
when making most generous offers, because the
reject rate is also very high
The fitted line between average earnings and
average offers, we find that it’s like cubic
polynomial, which indicates that average
earnings increase first and then decrease as
average offers increase 1

21. 2. Data after semicolon mean percentage in the row
Legend: 1. Data before semicolon mean percentage in the column
2. Data after semicolon mean percentage in the row
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Other factors analysis——Gender and Education
2009
Variance Table of Opening Offers
Opening Offers Rejection Rate
These two factors both have significant influence
on the opening offers, no matter separately or as a
whole
Men and postgraduates usually leave themselves
less earnings in the first period and are also more
likely reject opening offers, while women and
graduates usually leave themselves more earnings
and seldom reject opening offers 5

22. Agenda 2009 Background Review Experiment Design Experiment Process
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
2009
Agenda
Background Review
Experiment Design
Experiment Process
Make sense of the Data
Drawbacks & Improvement
Q & A 9

23. Agenda 2009 Background Review Experiment Design Experiment Process
2019年2月1日星期五6时11分5秒
0c8eee_ChinaLife_CICC_DiscussMaterials_1202.ppt
2009
Agenda
Background Review
Experiment Design
Experiment Process
Make sense of the Data
Drawbacks & Improvement
Q & A 9