gamesmanship vs. fairness: experimental results from two-period alternative bargaining games
TRANSCRIPT
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(Forthcoming: Economic Literature, 2010)
Gamesmanship Vs. Fairness: Experimental Results from Two-Period
Alternative Bargaining Games
Mani Nepal*
AbstractUsing two-period alternating offer bargaining games, we find that the participants chose
to move towards the fairness equilibrium, not towards all or nothing type subgameperfect equilibrium. The introduction of the costs of delay did not affect the fairness
outcomes either. We use the extra-credit points as an incentive for the student-participants. About 48% of the first round offers were 50-50 split. Any offer below 35%
was rejected indicating that responders wanted to be treated fairly, and proposers leanedto distribute the points more evenly in the second-time. However, this deviation towards
even-split may be due to the fear of rejection as one-third of the proposers increased theiroffers once their low offers were rejected in the first-time.
Keywords: Bargaining games, alternating offer, dictator games, fairness, sub-game
perfect equilibrium, and experimental economics.
___________________________________________________________________
* Dr. Nepal is an Associate Professor at the Central Department of Economics,Tribhuvan University, Kathmandu. Address for correspondence:
[email protected]. The paper was written when the author was at theDepartment of Economics, University of New Mexico, Albuquerque, 87131 NM, USA.
He wishes to thank students at the University of New Mexico who took his class onstatistics and econometrics, and voluntarily participated in the experiment. Dr. Kate
Krause provided valuable inputs while running the experiment. Usual disclaimer applies.
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Gamesmanship Vs. Fairness: Experimental Results from Two-Period
Alternative Bargaining Games
I. Introduction
Alternating offer bargaining game is an extension of the ultimatum game. In the
ultimatum game, two players (player 1 and player 2) have to divide a pie of size K.
Player 1 (proposer) divides the pie, such that x1 + x2 = K, and 0 xi Kfor i = 1, 2.
Player 2 (responder) has two options: accept the division so that she gets x2, and player 1
gets x1, or reject the division in which both players receive nothing. Game theory predicts
that this game has a unique subgame perfect equilibrium: player 1 demands almost
everything, and player 2 accepts all such minimal offers (under the rationality
assumption) such that she gets very little (or nothing).
In the case of such one sided ultimatum games, the responder is powerless. In real
life, proposer and responder interact each other with offers and counter offers before
reaching an agreement. In experimental settings, we can give player 2 bargaining power
by allowing her to make a counter offer in case she rejects the first proposal by player 1
for whatever reason. In the case of two-round alternating offer bargaining game, the
second round becomes the ultimatum game. Game theory predicts that the player 2 has
all the power to determine the outcome of the game, and she receives the entire pie if
both players are rational, and if there is no costs of delay.
If there is a cost of delaying the agreement, then the pie shrinks in the second
round by an amount c. In that case, game theory predicts that player 2 demands (K-c) in
period 2 if player 1 demands more than c in the first round, which player 2 rejects. Using
the backward induction, the unique subgame perfect equilibrium (SPE) is that player 1
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demands c, and player 2 receives (K-c) in the first round and the game ends. This
prediction indicates that player 1s payoff increases with the increment in the cost of
delay. If the cost of delay approaches to the size of the pie, the alternating offer
bargaining game becomes the ultimatum game in which the first mover gets all or most
of the pie. This indicates that the higher the cost of delays the better the payoffs to the
first mover. The game-tree of both ultimatum and alternating offer bargaining games are
presented in appendix-D.
Experimental results of the ultimatum-bargaining games do not support the
theoretical prediction that the ultimate proposer gets almost everything and the responder
gets very little or nothing. It has been recorded that the median and modal ultimatum
offers are usually 40 to 50 percent of the pie, and the mean offers are 30-40 percent.
Offers less than 20% are rejected most of the time (Camerer, 2003).
Binmore, Shaked and Sutton (1985) first time used two period ultimatum
bargaining games with shrinking pie to see if the observed behavior resembles with the
theoretical prediction. In their experiment, the cost of delay was 75%. The average first
round demand was 57% of the pie, which is considerably less than theoretical prediction
of 75%. In their experiment when the first round responders were given the role of
proposer in the subsequent games, they tend to optimize the payoffs to bargaining
problems. The inference from Binmore et al. paper is that experience is sufficient to turn
fairmen into gamesmen. If we allow playing the same game with changing the roles of
the responder as proposer, they will learn the gamesmanship instead of fairness,
meaning that once small changes are made, experienced subjects tend to optimize their
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payoffs in the bargaining ultimatum games supporting the Stahl/Rubinstein subgame
perfect equilibrium outcome.
Neelin, Sonnenschein and Spiegel (1988) reported the results from
experiments design to respond Binnmore et al. (1985) results from alternating bargaining
ultimatum games with shrinking pie. They ran an experiment more than two rounds, and
found that experience did not play role in the subsequent rounds, and the subjects behave
as fairmen. The results from more than two-round games showed that neither backward
induction type results nor equal-split results did hold. This result remained unchanged
with higher stack games, indicating that agents didnt learn to become Stahl/Rubinstein
gamesmen through repeated play, nor they prefer equal-split.
Matthew (1993) analyzed experimental results that incorporated fairness
(emotions or reciprocity) in the game-theoretic framework in economics and derived the
fairness equilibrium. Both battle-of-sexes and prisoners dilemma games were
considered. The paper tries to analyze the issue: Fairness by choice or fairness by fear?
This paper revolves around three stylized facts: a) People are willing to sacrifice their
own material well being to help those who are being kind. b) People are willing to
sacrifice their own material well being to punish those who are being unkind. c) Both
motivations A and B have a greater effect on behavior as the material cost of sacrificing
becomes smaller. This paper develops the concept of fairness equilibrium or the role of
intentions in behavior in which people like to help those who help them and hurt those
who hurt them (tit-for-tat strategy).
From the incentive viewpoint, this paper is different from others. Instead of
paying dollar amounts we chose to award extra credit points for their statistics and
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econometrics course-work. For students, it is assumed to be a better incentive than the
monetary benefits. The main objective of this paper is to examine the predictions about
the subgame perfect equilibrium made by game theory using experimental results from
two-period alternating offer bargaining games. The main interest is to see if the
participants choose to behave as predicted by subgame prefect equilibrium or they choose
to behave as predicted by fairness equilibrium. Using two period alternating offer
bargaining games, we do not find support to the prediction about the subgame perfection.
It seems that participants prefer fairness to the subgame perfection.
The paper is organized as follows. With detailed background in section I, the
experimental design is described in section II. The experimental procedure is outlined in
section III. Experimental results are analyzed in Section IV. Final section concludes.
II. Experimental Design
We consider two-period alternating offer bargaining game in which player 1 was
given 100 points and asked to divide the given points between herself and her unknown
partner (player 2). Player 2 has to decide whether to accept or reject the first round offer.
If the offer is accepted the game ends and the players receive their shares of 100 points
proposed by player 1. If the first round offer is rejected the game enters to the second
round. In the second round, player 2 gets chance to make the division of the given points
between two players, but this time the number of points to be divided shrinks by c points
such that 0< c < 100. Once player 2 makes a counter offer, player 1 gets a chance to
decide whether to accept the offer. If the second round offer is rejected both players get
zero points, and if the offer is accepted both players get points proposed by player 2.
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In this game, the SPE predicts that the ultimate division depends on the cost of
delay. If the cost of delay is less than half of the size of the pie, the second player will be
in advantageous position. If the cost of delay is over half of the total size of the pie, then
the first player will get most of the pie. For example, ifc=25, then subgame perfection
predicts that in the first round if player 1 proposes less than 75 to player 2, she rejects and
counter offers almost nothing or very little to player 1 in the second round. Knowing that,
it is in the best interest of player 1 to propose 75 points to player 2 in the first round and
get 25 points for herself which player 2 accepts and game does not enter into the second
round. Theory predicts that player 1 always offer subgame perfection split and player 2
always accepts it such that game should always be ended in the first round. The
behavioral aspects of the game theory predict fairness equilibrium, not the subgame
perfect equilibrium such that fairness equilibrium ends up around 50-50 splits.
III. Experimental Process
The experiment was conducted in a classroom at the University of New Mexico.
The participants were junior and senior students in a basic statistics and econometrics
course. In the experiment, 21 participants showed up. As we only need an even number
of participants, we asked students if they wanted to volunteer not to participate in the
game. It was announced that the incentive for not playing the game was average class
earnings. The student who showed up late volunteered to stay out of the game and
observed the entire process. He received the class average earnings of 30 points1.
1Out of four games played, game-3 was selected randomly to award the extra credits for the players. In that
game two pairs of players got 0 points due to the lack of agreements in the bargaining process. So the class
average went down to 30 points in that game.
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The 20 participants were randomly divided into two groups, and assigned group
names A and B through coin toss. They were asked to sit in two different sides of a
relatively big classroom so that one group could not see the decision made by another
group. Each student received a written instruction about the rules of the game. Those
instructions were read loudly and students were asked to follow through. Those
instructions and other materials used in the experiments are reproduced in an appendix-B.
In game-1 participants in Group A were given a sheet of paper with 100 points
and possible division of it between two people (a sample sheet is reproduced in appendix-
C). They were asked to divide those 100 points between him/her and an unknown partner
from group B such that the points should be divisible by 5. Once they chose the division,
paper sheets were collected and distributed to group B participants without revealing the
identity of their proposer (partner) from group A. Group B participants were asked to
respond the offer made by group A participants by placing yes or no to the offer.
Those who chose to accept the first round offer were asked to keep the sheet of paper for
a while with them. Those who chose no to the offer were asked to make counter offer to
their unknown partners from group A. But this time, there was a fixed cost of delay (c),
which was not same to all participants2, but it was a common knowledge to both of the
partners. So those who rejected the first time offer got a chance to counter offer to the
first time proposers. They propose the division of(100-c) points between them and their
first time proposer from group A. The sheets of paper with the yes/no decision and
counter offers were returned to the respective participants from group A. If the first round
offer were accepted, both players got the points proposed by the first round proposer.
Those who got counter offers from their unknown partners from group B were asked to
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choose yes or no to the counter offers. If they said yes to the counter offer, both got
the points based on the counter offer. If no was chosen, both got zero point in that
game.
The game was repeated four times. The only change in the subsequent games is
that the roles of the players were reversed alternatively. In game-2 group B players were
asked to be the first round proposer. Rest of the processes was same as in the game-1.
Participants were told that they would play with anonymous and different partners in
different games. In the end, game-3 was randomly chosen for awarding extra credit
points to the participants
3
.
IV. Experimental Results
IV.1. General Results
In the experiment, each player got chance to be a first-round proposer twice:
group A got such chances in game-1 and game-3, while group B got the chance to be a
first round proposer in game-2 and game-4. While analyzing the data, we frequently term
first-time offer and second-time offer. First-time offer means offers in game-1 and game-
2 in which players got the first chance to be a proposer in round 1, and the second-time
offer means offers made in game-3 and game-4. The raw data from the experiment are
reported in table A1 (appendix-A). Table 1 summarizes the initial demand, relative
frequency and the rejection rate in the first round offers. The maximum opening generous
offer was 60 points and the minimum offer was 10 points. Put differently, the minimum
2The cost of delay was assigned randomly and it was 15, 25, and 35 points.
3A participant was asked to roll an eight-sided die to choose a game for awarding the extra credit points.
The probability of selecting any of the four game is 0.25.
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first round demand by the proposers was 40 points and the maximum first round demand
was 90 points.
Table 1: Opening Demand, Frequency and Rejection Rate
Demand Relative Frequency Rejection Rate
40 0.03 0.00
45 0.08 0.00
50 0.48 0.11
55 0.10 0.50
60 0.18 0.71
65 0.05 1.00
70+ 0.10 1.00
In the experiment all offers of 35 points or less were rejected and all offers of 55
points or more were accepted. About 48% of the first time offers were 50-50 split
indicating that participants were leaning towards the fairness split of 50-50. The
interesting part of the experiment is that such 50-50 splits were rejected 11% of the time
indicating something else was also going on in the mind of those participants.4
The
results from table 1 are exhibited graphically in the fig 1.
4On possible explanation for those who rejected 50-50 split in the first round is that they wanted to earn
more extra credit points to make up for their relatively lower grade in the course work as those who
rejected the even-split of 100 points counter offered very low (only 6% to 29% of the remaining points
after deducting the cost of delay) in the second round.
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Fig 1: First Time Demand, Relative Frequency and the Rejection Rate
0.00
0.05
0.10
0.15
0.200.25
0.30
0.35
0.40
0.45
0.50
40 45 50 55 60 65 70+
Demand
RelativeFrequency
0.00
0.20
0.40
0.60
0.80
1.00
1.20
RejectionRate
Relative Frequency Rejection Rate
IV. 2. Evidences of fairness
Table 2 shows the average offer in each game, standard deviation, t-value in
which the null hypothesis is 50-50 splits, and acceptance rate of the first time offers.
Table 2: Average demand, standard deviation, t-value and acceptance rate of first-round offers
Game-1 Game-2 Game-3 Game-4 Over-all
Average opening demand 60.50 55.00 52.00 52.00 54.88
Sdt. Deviation 12.12 8.50 5.87 7.53 16.26
t-value 2.74*** 1.86 1.08 0.84 1.90
Acceptance Rate 0.50 0.60 0.60 0.80 0.63
1. The null hypothesis for the t-value is 50-50 splits in the opening round in each game.
2. The critical t-value is 2.262 with 9 df, and it is 2.021 with 39 df (two-tailed values)
Table 2 shows that average opening offer was moved towards the fair-offer of 50-
50 split in the subsequent games. In game-1, the average offer was 60.5 points, which
was significantly different from 50-50 split as indicated by t-value of 2.74. The average
demand, however, declined towards the middle and was not statistically different from
expected 50-50 splits in games 2, 3 and 4. Also, the overall average first-round offer was
not significantly different from fairness splits. As the opening offers moved towards the
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middle, the acceptance rate for the first round offers went up from 50% in the game-1 to
80% in the game-4. The overall the acceptance rate in the first round was 63%. It seems
that this acceptance rate is lower than what have been reported in the literature (Camerer,
2003).
IV.3. Fairness or fear of rejection
Why did the participants move towards 50-50 split? Is that purely due to fairness
or due to the fear of rejection? To analyzefair vs. fear, we split the sample into two parts.
In the first category, we put all the observations in which first round offers were
accepted, and in second category, we put all observations in which first round offers were
rejected. Fig 2 exhibits the second time offer by the same participants given that his/her
first time offer was accepted.5
In this diagram we can see that almost all second-time offers were either the same
as the first-time offer or higher than the first-time offer given that the first-time offers
were accepted. There was only one exception in which one participant chose to offer low
in the subsequent game given that first-time offer was accepted. This results show that
fear of rejection was not necessarily the primary cause of moving towards 50-50 splits.
5Here second-time offer refers to the game-3 for group A participants, and game-4 for group B participants
as those games provided them second chance to be a first-round proposers.
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Fig 2: Accepted First Time Offer and Second Time Offer
45 4550
5550 50 50
40
5060
55
0
20
40
60
80
40 45 50 50 50 50 50 50 50 50 50
First Time Offer
SecondTim
eOffer
Figure 3 shows the second-time offer conditional on the fact that the first-time
offers were rejected. Out of 20 participants, the first-time offers of nine participants were
rejected. Given that their first-time offers were rejected, seven participants chose to
increase their second-time offers. It can be interpreted that such higher offer in the
second-time may be due to thefearof rejection.
Fig 3: Rejected First-Time Offer and Second-Time Offer
55
45 50
35
50
35
50 5040
0
10
20
30
40
5060
10 30 30 30 40 40 40 40 50
First Time Offer
SecondTimeOffer
Two participants chose to lower their second-time offer even though their first-
time offers were turned down. It is to be noted that one participant offered 50-50 split in
the first-time and was rejected. As the evenly split offer was turned down he opted for
lower offer in the second round. This might be due to the fact that he wanted to hurthis
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partner in the second-time offer by offering less as his evenly split offer was rejected in
the first-round supporting Mathew (1993). Overall, it is hard to conclude that the sole
motivation of moving towards 50-50 splits was the sense offairness. The element of the
fearof rejection was clearly present with those player whose first-time offers were turned
down.
IV.4. Gamesmanship or tit-for-tat?
Another aspect of the experiment is to analyze the behavior of the responders.
Following figure presents the initial percentage offers and rejection percentage counter-
offers in all four games. Out of 40 opening offers (four games with 10 offers in each
games) 15 were rejected in the first round (37.5%). Three responders counter offers were
towards the fairness split (over 46% were offered after rejecting the offers of 40-45%).
Fig 4: Rejected Offers and Counter Offers
0.06 0.07
0.29
0.40
0.29 0.29
0.08
0.33
0.40
0.46 0.47
0.40
0.47
0.13
0.38
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.10 0.30 0.30 0.30 0.35 0.35 0.40 0.40 0.40 0.40 0.40 0.45 0.45 0.50 0.50
Initial Offers (%)
CounterOffe
rs(%)
However, after rejecting the first-round offer, majority of the responders opted
counter offers much lower than what they were offered in the first-round. The average
counter offer in the second-round was below 30% of the total available points, which is
much lower than the first-round average offer of over 45%. This evidence suggests that
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players in the second-round try to follow the gamesmanship, not the fairness. Still, the
less than 30% average counter offer does not support the SPE, which predicts that the
counter offer should be very little or nothing.
IV.5. Costs of delay effects
The basic idea of introducing differential costs of delay is to see if the participants
will follow the SPE strategy. The SPE predicts that higher the cost of delay, the better the
bargaining power of the first mover in the two-round alternating offer bargaining games.
Table 3 presents the results about the costs of delay, the opening demands, acceptance
rate, and counter offers. With the increasing costs of delay, the initial demand has no
definite trend. The SPE predicts that the initial demands in this experiment should be in
neighborhood of the costs of delay itself.
Table 3: Effect of costs of delay in the opening demand and counter offer
Cost of Delay Initial Demand Acceptance Rate Counter Offer
Acceptance
Rate
% Offer in
Round-2
15 53.13 0.69 24.00 0.80 0.28
25 57.81 0.56 23.57 0.57 0.31
35 52.50 0.63 20.00 0.67 0.31
Table 3 shows that the prediction is nowhere near to such prediction as the average
opening demands were 52 points or more where as the average cost of delay was 25
points only. The correlation coefficient between the costs of delay and the initial demand
is also very low (0.03) indicating that the experimental results do no support the SPE.
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In order to figure out the motivating factors of initial demands, we computed the
correlation coefficients between first-time demands, whether first-time demands were
accepted, second-time demands, and the participants expected GPAs.
Table 4: Correlations between first and second-time demands, response to first-time
demand, and expected GPAs
Demand-2 Accept Demand-1
Accept -0.345
Demand-1 0.087 -0.685
EGPA 0.128 0.101 -0.261
From table 4 we can see that the correlation coefficients between acceptance rate and the
expected GPA are negative with first-time demand indicating that if participants EGPA
was higher, they demanded lower points, and if the proposer demanded lower points,
those demands were accepted. However, after learning in the first two games, they
demanded more even if their expected GPA was higher.
IV.6. learning to be fair
Is there any significant difference between first-time offer and the second-time
offer? Table 5 shows that the mean difference in first-time offer and the second-time
offer was significantly different from zero (t-statistic is significant) implying that the
participants learned to be fair in the subsequent games.
Table 5: t-Test for Paired Two Sample for Means
First offer Second Offer
Mean 57.75 52.00
Variance 111.78 43.16
Observations 20 20
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Hypothesized Mean Difference 0.00
df 19
t Stat 2.15** (Significant at 5%)
P(T
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Table 6: Poisson regression results
Dep. Var.
First round demand
Coefficients Std. Errors t-value p-value
Constant 3.89 0.175 22.30 0.000
Cost of delay 0.0017 0.003 0.55 0.582
Game# Dummy1
-0.1049 0.0427 -2.45 0.014
Expected GPA 0 .0015 0.002 0.68 0.499
Sex 0.050641 0.054 0.94 0.348
1
1 if game-3 and game-4, 0 otherwise.
In the experiment, about 37.5% first-round offers were rejected in which mean
offer was over 45 points. The rejection rate was surprisingly high as compared to the
existing literature. In order to see the probable reason of such high rejection rate, we use
the logit regression. The regression results are presented in table 7.
Table 7: Logit regression results (dependent variable: categorical variable for
acceptance =1, 0 otherwise)
Coefficient Std. Error t-value p-value
Constant 20.3938 7.7971 2.62 0.009
Demand -0.3365*** 0.1043 -3.23 0.001
Cost 0.0113 0.0737 0.15 0.879
EGPA -0.0319 0.0764 -0.42 0.676
Sex 0.3504 1.1508 0.30 0.761
*** Significant at 1% level
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After controlling for the cost of delay, expected GPA, and sex of the participants the
opening demand appears to be the only significant variable to affect the decision whether
to accept the offer or reject it. The negative sign of the Demand coefficient indicates
that the probability of accepting the offer declines with higher demand in the first-round
meaning that responders wanted to see the fair distribution.
V. Concluding Remarks
This paper deals with experimental results of alternating offer bargaining game.
Irrespective of the acceptance or rejection of the first-time offer, most of the participants
chose to offer more in the second-time offer. The opening offers were not affected by the
costs of delay. This implies that the observed distributions were towards fairness
equilibrium, not towards what the SPE predicts.
One possible reason why participants chose to be fair while dividing the extra
credit points would be that they were from a small class of students; all were known to
each other. By the time the experiment was run, only 40% of the course work was
completed in terms of homework, quizzes, and the exams. It was hard for the majority of
the students to infer about their final grade so early. That may be one possible
explanation why they chose to split the sum towards 50-50, and there was a huge
rejection rate for those offers not close to the equal splits.
There are some limitations of this experiment to draw some meaningful
inferences. The sample size was quite small. Another point to be noted is that participants
received extra credit points as an incentive to play the game, not monetary benefits,
which is different from the other experiments. In order to see how robust is the findings
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from this experiment, on possible extension would be to run it with the same setting but
with more students in the class, and in the beginning of the semester. That might dilute
the personal relations to each other and student might be more self-interested, and might
demonstrate gamesmanship as predicted by SPE.
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Appendices
A: ProtocolWelcome to the experiment. Please do not communicate to each other. It is extremely important
to listen to the instructions carefully.
Today we are going to play some games. In these games you will get chances to earn extra credit
for Econ 309. You can earn up to 100 extra points depending on how you and your unknownpartner will play the game. These 100 points will be equivalent to 7% of your semester credits.
Here you are playing for extra credits. So your semester work is still 100%. Ill add these extrapoints to your semester totals to assign your final letter grade. In participating in todays game,
you will not get hurt in terms of your final grade. You will be benefited depending on how you
and your unknown partner will play.
Here is how it works: If you earn 100 points in todays game, and you get 90% from your
semester exams, homework, quizzes, labs, etc, then your final grade points would be 97%. If you
earn 60 points today, and got 90% in your course works, you will get 90%+4.2% = 94.2% foryour final grade. If you get 100% in your course work, and earn 100 points in todays game, then
your final grade point will be 107% (sure A+ !!!)
We will play this game more than once. However, you will be given points for one game only.
We will draw a lottery to decide which round is used for giving you points. So, all rounds are
equally important for you. Play as if there is only one round in the game.
Now Im going to tell you the rules of the games. Ill divide you in two groups. Half of you are
going to be proposers and half responders. Each of you will have a partner from the other group,
but we will not tell you who is your partner, and your partner will not know you either. We willdecide who is a proposer and who is a responder by chance in the beginning.
The proposer will get 100 points that is to be divided between you and your secret partner orresponder. If you want you can keep all 100 points with you or you can give all 100 points to
your partner, or you can divide that 100 points between the two of you. Remember, you areallowed to divide the 100 points in amounts that are divisible by 5. For example you can keep 100
for you and 0 for the responder, 95 for you and 5 for your responder, or 90 for you and 10 foryour proposer, or 0 for you and 100 for your responder, 5 for you and 95 for your responder, 10
for you and 90 for your responder and so on such that the two numbers must add to 100 points.
But dont worry, Ill provide a table that gives you all the possible division between two of you(appendix C).
Once you made your proposal of dividing the 100 points between you and your unknownresponder, your partner (the responder) gets the chance to decide. The responder can do two
things. Accept the proposal of the proposer or reject it. If the responder accepts the proposal, the
game ends in which proposer and responder will get the points divided by the proposer. If the
responder rejects the first proposal of the proposer, then the responder gets a chance to be aproposer. This time you will be playing the game with the same unknown partner, but your roles
are just reversed.
The proposer of the first round becomes the responder in the second round if the game is not over
in the first round. But this time, the total points to be divided between you and your unknown
partner will be less than 100 points. The total point will diminish according to the rule: (100- C)where C is some number less than 100 and greater than 0. For example, if C is 5, then the second
proposer will divide (100-5) = 95 points between you and your unknown partner if he/she rejects
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the first proposal. If c is 40, the second proposer will divide (100-40) = 60 points between the two
of you. The C may be different for each group. In this second round, if the responder accepts thedivision, both of you will get the points chosen by the second proposer. If the responder rejects
the proposal, both of you will get 0 points (nothing) and the game ends.
Any questions so far? Lets see a slide for example.
B: Games [1] & [3]
Round 1: Group A (Proposer)
You all are the proposer. You each have a responder from group B that you dont know. And the
responder does not know who you are. I will not reveal the identity of any one of you. Now Illgive you 100 points to divide. You will decide how to divide the points between you and your
unknown responder from group B. If the responder accepts, or says yes to how you divide the
points, then you each will get the agreed upon points. If your responder rejects your proposal,
then your responder gets a chance to be the proposer. Now take a look in the table that you havenow. Make your choice by putting a check mark (in the third column) by the pair of numbers that
you choose. Dont show your choice to others. I will give you 1 minute to make your decision.
Dont check your choice until I tell you to do so. Put your ID #. Now mark your choice and giveme back the form.
Round 1: Group B (Responder)
You are the responder. You will decide whether to say yes or no to the offer. If you say yes andaccept the offer, then you will get the points that your proposer offered to you and he/she gets
what was proposed to him/her. If you say no and reject the offer then the game enters in the
second round. Take a look in the form. It shows you what your proposer has proposed to you. Ill
give you 1 minute to think. Check your choice (yes/no). If you check yes, please give me theform.
Round 2: Group B (Proposer)
Those who choose to say no in group B: If you say no to the first round offer, now you are goingto divide (100-C) points, not 100 points, between you and your unknown responder. Ill give you
30 seconds to make your decision. Once you decide, put a check mark next to the pair of numbersthat you choose, and give the paper back to me.
Round 2: Group A (responder)Now you are the responder. You will decide if to say yes or no the offer. If you say yes and
accept the offer, you will get the points that the proposer offered to you and the proposer will get
the points he/she proposed for himself/herself. If you say no and reject the offer then you and theproposer both will get zero points. The form above shows you what the proposer has offered for
you. Take 30 seconds and put yes or no in your choice (last column).
C: Games [2] & [4]Now we are ready to play the game again. This time group B is the proposer, and group A is the
responder. Again, you will not know who your partner is (remaining part of the instruction is the
same as for Games [1] and [3], and removed from here to save some space.
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C. Sample of a table provided to participants to make their bargaining decision (Cost of delay was 15, 25 and 35)
Proposers ID # ( ) Responders ID # ( )Round -1 Round- 2
Proposers
points (A)
Responders
points (B)
Proposers
Choice
Response
(Yes or No)
If NO in round-1, Play the following round
100 0 C= 15, So split the
following
Bs choice As Response
(Yes or No)95 5
90 10
Keep for B Give to A
85 15 85 0
80 20 80 5
75 25 75 10
70 30 70 15
65 35 65 20
60 40 60 25
55 45 55 30
50 50 50 35
45 55 45 40
40 60 40 45
35 65 35 50
30 70 30 5525 75 25 60
20 80 20 65
15 85 15 70
10 90 10 75
5 95 5 80
0 100 0 85
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D: Game Tree1. Ultimatum Game
2. Alternating Offer Bargaining Games
((XX,, 110000--XX ))
AA
RR
11
22
(X, 100-X)
((XX,, 110000-- XX ))
A
RR
11
22
21
(X, 100-X)
(Y, 100-C-Y)
(Y, 100-C-Y)
(0,0)
(0,0)