gamesmanship vs. fairness: experimental results from two-period alternative bargaining games

8/14/2019 Gamesmanship Vs. Fairness: Experimental Results from Two-Period Alternative Bargaining Games

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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.

Bibliography:Binmore K. A. Shaked and Sutton. 1985. Testing Noncooperative Bargaining Theory: A

Preliminary Study, The American Economic Review, 75 (5): 1178-1180.Binmore, Ken, Avner Shaked and John Sutton. 1989. An Outside Option Experiment,

The Quarterly Journal of Economics 104(4): 753-770.Bolton, Gary E. 1991. A Comparative Model of Bargaining: Theory and Evidence,

The American Economic Review 81(5): 1096-1136.Camerer, Colin and Richard H. Thaler. 1995. Anomalies: Ultimatums, Dictators and

Manners, The Journal of Economic Perspectives, 9(2): 209-219.Camerer, Colin F. 2003.Behavioral Game Theory, New York: Russell Sage Foundation,

& New Jersey: Princeton University Press.Davis, Douglas D. and Charles A. Holt. 1993.Experimental Economics, New Jesery:

Princeton University Press.Guth, Werner, Steffen Huck, and Peter Ockenfels. 1996. Two-level ultimatum

bargaining with incomplete information: an experimental study, The EconomicJournal 106 (436): 593-604.

Khan, Lawrence M. and J. Keith Murnighan. 1993. A General Experiment onBargaining in Demand Games with Outside Options, The American Economic

Review 83(5): 1260-1280.Nash, John F. 1950. The Bargaining Problem,Econometrica 18(2): 155-162.

Neelin, Janet, Hugo Sonnenschein, and Matthew Spiegel. 1988. A Further Test ofNoncooperative Bargaining Theory: Comment, The American Economic Review

78(4): 824-836.Ochs, Jack and Alvin Roth. 1989. An experimental study of sequential bargaining, The

American Economic Review 79(3): 355-384.Prasnikar, Vesna and Alvin E. Roth. 1992. Considerations of fairness and strategy:

experimental data from sequential games, The Quarterly Journal of Economics107(3): 865-888.

Rabin, Matthew.1 993. Incorporating Fairness into Games theory and Economics, TheAmerican Economic Review 8395): 1281-1302.

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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)

gamesmanship vs. fairness: experimental results from two-period alternative bargaining games

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