Arbitration Experiments+
Cary Deck - University of Arkansas
Amy Farmer - University of Arkansas
Dao-Zhi Zeng – Kagawa University
& Zhejiang University
”Arbitration and Bargaining Across the Pacific”
“Amended Final Offer Arbitration Outperforms
Final Offer Arbitration”
+Thank
you NSF (SES0350709)
Roadmap for Talk
Arbitration and
Bargaining Across
the Pacific
AFOA
Outperforms
FOA
Culture
Japan
US
Dispute Resolution
Two parties have a dispute regarding how to
split a pie.
- Litigation
- Mediation
- Arbitration
C substantial cost savings
C restrictions on discovery
C shorter hearing length
C information can remain private
Use of Arbitration
Lipsky and Seeber (1998) surveyed the legal counsels of
the 1000 largest US corporations and found that 79%
of respondents had used arbitration.
Dell Computer’s Online Policy States: “ANY CLAIM,
DISPUTE, OR CONTROVERSY … SHALL BE
RESOLVED EXCLUSIVELY AND FINALLY BY
BINDING ARBITRATION…”
http://www1.us.dell.com/content/topics/global.aspx/policy/en/policy?c=us&l=en&s=bsd&~section=012&cs=04
In Circuit City Stores Inc. vs. Saint Clair Adams, US
Supreme Court ruled that employers can force
employees to use arbitration to settle labor disputes.
Economics Approach to Arbitration
Theoretical Modeling
• Each party has a belief about the distribution of
arbitrator’s preferred outcome, fi(z).
• A disputant faces a cost ci of going to arbitration.
• A party is willing to settle pre-arbitration for an
outcome O if u(O) > u(A,ci) where A is what they
expect to receive in arbitration and is dependent on
fi(z).
Economics Approach to Arbitration
Theoretical Modeling
• Each party has a belief about the distribution of
arbitrator’s preferred outcome, fi(z).
• A disputant faces a cost ci of going to arbitration.
• A party is willing to settle pre-arbitration for an
outcome O if u(O) > u(A,ci) where A is what they
expect to receive in arbitration and is dependent on
fi(z).
Under standard assumptions this yields a contract
zone [A-c1,A+c2] which both parties prefer to
arbitration.
Economics Approach to Arbitration
Experimental Economics
• Experimenter controls the institution (rules of the
game, information flows) and the environment
(payoffs, costs, arbitrator’s preferences)
• Subjects make salient choices that are observed by
the experimenter.
• Enables replication and direct comparisons across
institutions and environments.
Forms of Arbitration
Conventional Arbitration (most commonly used)
- arbitrator can implement any allocation
- no strategic behavior by disputants
- disputants should settle and save costs
- many disputes are arbitrated
- 50% agreement rates in the laboratory
(Ashenfelter et al. 1992, Dickinson 2004, Deck and
Farmer 2005)
Forms of Arbitration
Final Offer Arbitration
- each side proposes an allocation
- arbitrator must pick one of the proposals
- incentive to make an extreme offer
- increases risk of going to arbitration
Final Offer Arbitration
Widely Studied Empirically
• Naturally Occurring World
– Used in Major League Baseball
• Laboratory
– More Strategic than Conventional
– Agreement Rates less than 50%
But (almost) Exclusively in US
even though arbitration is used to resolve
international disputes as well.
Do Cultural Differences Matter?
Bercovitch and Elgström (2001) find that cultural
differences lower mediation success.
Fu et al. (2002) find that Chinese and Americans exhibit
differences in choosing mediators.
Lew and Shore (1999) find cultural differences in cross
examination procedures.
Gans (1997) advocates informal procedures prior to
invoking formal arbitration procedures due to cultural
differences.
Cultural Differences
Growing Experimental Literature on Culture
(Roth et al. 1991, Henrich 2000, Buchan et al. 2004)
Kilbourne et al. (2005) identify differences in
materialism across cultures.
Brandts et al. (2004) found differences in spite and
cooperation behavior in voluntary contribution
mechanisms.
Buchan et al. (in press) examine the role that culture
plays in trust, reciprocity and altruism.
US and Japan
1) Similar Economies
Both Modern Industrialized Economies
Major Trading Partners for Several Decades
(Graham and Sano, 1989)
Societies exhibit high levels of trust
(Slemrod and Katuščák
2005)
2) Culturally Diverse
“collectivism” to “individualism”
(Hofstede 1991, Oyserman et al. 2002)
Differing views of fairness and power
(Buchan et al. 2004)
Shares of Imports
by Country of Origin
Importing Country
Exporting
Country
US
Japan
China
Australia
US
-
19.1%
8.6%
20.0%
Japan
12.0%
-
15.2%
13.2%
China
9.6%
15.0%
-
8.9%
Australia
0.5%
3.9%
1.6%
-
Data from Feenstra et al. (2004)
Hofstede’s Scales
PDI - Power Distance Index , IDV –Individualism,
MAS – Masculinity, UAI- Uncertainty Avoidance Index,
LTO-Long-Term Orientation
Experimental Design
A pair of subjects had $EXP 100 to allocate.
Treatments:
UU- both subjects from University of Arkansas
JJ- both subjects from Kagawa University in Japan
UJ- one subject from each university
Show up fee of $EXP 500
$EXP 100 = $US 1 & $EXP 100 = ¥100
Experimental Design
Written Directions
Comprehension Handout
Periods 1-15 forced arbitration
Bargaining Directions
Periods 16-25 bargaining prior to arbitration
Random rematching of anonymous counterparts each
period.
Experimental Design
Arbitrator's preferred outcome ~U[0,100].
Let x and y denote the shares for disputant 1
by disputants 1 and 2 respectively
if x<y then offers are compatible
payoffs are (x+y)/2 and 100 - (x+y)/2
if x>y then offers are incompatible
payoffs are x and 100-x if |z-x|<|z-y|
and y and 100-y otherwise
Brams and Merrill (1983) show that
unique Nash Equilibrium is x=100 and y=0.
Experimental Design
 Expected Payoff in Arbitration = 50
Periods 1-15 (arbitration only): c = 0
Periods 16-25 (pre-arbitration bargaining): c = 15 
Contract Zone [35,65]
4 replicates of each treatment (12 total sessions)
4 subjects in UU & JJ
6 subjects in UJ
Sessions lasted one hour.
Experimental Design Cultural Concerns
Same experimenters present for each session.
Web cameras employed in UJ treatment
as described by Eckel and Wilson (2006).
Pictorial screen for UJ and JJ treatments.
Directions written in English and translated into
Japanese.
Subject Screen
Distribution of Offers
in Periods 5-15
0.3
0.3
0.25
0.25
Counterpart in US
Countepart in US
Counterpart in Japan
0.2
Counterpart in Japan
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0
0-9
10-19
20-29
30-39
40-49
50-59
60-69
Final Offers for Subjects in US
70-79
80-89
90-100
0-9
10-19
20-29
30-39
40-49
50-59
60-69
Final Offers for Subjects in Japan
70-79
80-89
90-100
Linear Mixed Effects Model of
Offers in Periods 5-15
Offerijt   0  ei   ij  1 JapSubi   2 JapCounti   3 JapSubi  JapCounti   ijt
Variable
Parameter
Value
Constant
0
56.3895
JapSub
1
4.1366
JapCount
2
10.5445
JapSub´JapCount 3
–12.5770
t-value
19.9404
0.9604
2.4480
–2.0472
p-value
<.0001
0.3424
0.0186
0.0678
Hypotheses of Lituchy (1997)
As America is individualistic and Japan is a collective
society, Lituchy argues that
Japanese - Ho: 2+3 = 0 will be rejected
in favor of Ha: 2+3 < 0.
Americans - Ho: 2= 0 will not be rejected
in favor of Ha: 2  0.
We do not find support for either claim
hypothetical payments
subject pool bias
Self-Negotiated Settlement Rate
by Session
100%
Wilcoxon Rank-Sum Tests
75%
UU v JJ
UU v UJ
JJ v UJ
50%
25%
0%
JJ
UJ
Treatments
UU
W = 19.5
W = 20
W = 25*
Self-Negotiated Settlement Rate
by Session
100%
Wilcoxon Rank-Sum Tests
75%
UU v JJ
UU v UJ
JJ v UJ
50%
W = 19.5
W = 20
W = 25*
25%
0%
JJ
UJ
Treatments
UU
We find substantially more
agreement than previous
laboratory studies.
Let’s Play Name That Distribution
Distribution #2
Distribution #1
27
73
58
51
50
74
47
43
45
40
54
29
75
43
25
67
50
65
66
49
37
73
36
60
20
40
60
33
42
46
52
53
43
61
45
48
57
65
49
49
39
21
70
84
48
39
31
62
55
36
69
44
41
70
57
46
48
50
38
32
52
55
50
50
34
45
48
50
68
58
57
59
47
80
48
53
64
26
57
76
45
42
56
84
48
36
33
41
71
61
37
77
52
52
52
50
30
36
22
21
62
72
29
33
47
28
46
49
43
79
86
66
63
48
82
85
57
60
33
15
48
29
29
75
39
42
31
77
26
72
Distribution #3
47
25
64
60
46
54
59
52
64
41
84
53
71
34
83
30
58
57
43
45
60
53
12
66
39
49
20
62
47
59
38
25
13
46
57
46
61
73
36
44
84
19
55
1
49
51
28
61
51
50
51
23
65
32
36
33
26
25
51
38
54
40
62
57
85
52
86
67
75
76
79
43
25
38
29
50
53
48
36
38
48
44
35
45
72
54
55
65
69
48
56
69
29
77
70
23
51
39
30
43
79
74
32
30
54
20
69
40
31
43
59
76
28
22
41
26
42
26
32
37
43
51
26
26
34
58
59
79
47
31
67
37
28
68
55
31
58
41
37
67
Random Effects Probit Model of
Settlements in Periods 16-25.
F(01UJj2JJj3AvgPayjp4UJjAvgPayjp5JJjAvgPayjpj)
Variable
Parameter
Model 1
Model 2
Constant
0
–0.9783
(0.4423)
–0.9076
(0.4082)
UJ
1
–0.3421
(0.5758)
–0.5864
(0.4813)
JJ
2
0.8405
(0.6459)
0.2819
(0.4790)
AvgPay
3
–0.0206
(0.0472)
---
UJ ´AvgPay
4
0.0826
(0.0744)
---
JJ ´AvgPay
5
0.1588
(0.0800)
---
Listed are the GEE parameter estimates. The standard errors in parentheses are the empirical estimates.
Allocation in Self-Negotiated
Settlements
0.8
0.7
Percentage
0.6
0.5
JJ
0.4
UJ
0.3
UU
0.2
0.1
0
50- 56- 61- 66- 71- 76- 81- 86- 91- 9655 60 65 70 75 80 85 90 95 100
NA
US
Japan
63.8
58.2
Japan (self) 61.6
65.6
Lion's Share
Contract Zone:
35-65
US (self)
Further Exploration
Risk Attitudes and Strategic Bidding
First Price Sealed Bid and Dutch Auctions
n = 5 bidders
values ~ U[0,15]
6 sessions (3 in each treatment ordering)
Observed Price/Risk Neutral Expected Price
Auction Order
Dutch – Sealed – Dutch
Sealed – Dutch – Sealed
Periods
1-10
2-20
3-30
1-10
2-20
3-30
Japanese
Subjects
1.16
1.14
1.06
1.10
1.22
1.16
Cox et al. (1982)
0.96
1.18
1.09
1.06
1.18
1.15
Further Exploration
Cooperation and Other Regarding Preferences
Public Goodsn=4
0.7
MPCR=.3,.75
0.6
w=10
0.5
periods = 10
0.4
4 sessions
0.3
(2 per
0.2
MPCR order) 0.1
Percent Contirbuted to Public Good
MPCR = 0 .75 IW
MPCR = 0.75
MPCR = 0.3
MPCR = 0.3 IW
0
1
2
3
4
5
Period
6
7
8
9
10
Cultural Conclusions
JJ and UU treatments yield similar behavior
But, intercultural disputes differ from domestic ones
Americans become more aggressive in international
arbitration. (UU v UJ)
Japanese become more willing to settle in international
bargaining. (JJ v UJ)
Explanations:
Social Distance? (Cox and Deck 2005, Buchan in press)
Cultural Representation?
Improving Arbitration
Performance of Mechanism is measured by how
often it is not used!
– Social welfare is higher when parties save
arbitration costs.
– Preference for self-negotiated
settlements.
Can we do better than FOA?
Forms of Arbitration
Tri Offer Arbitration
- each side (and a neutral third party)
proposes an allocation
- arbitrator must pick one of the 3 proposals
- designed to lower the likelihood of extreme
outcomes in arbitration
- increases incentive to be extreme
- used to settle public sector disputes in Iowa
- lower agreement rate in laboratory than CA
(Ashenfelter, et al. 1992)
Forms of Arbitration
Combined Offer Arbitration
(Brams and Merril 1986 )
-like FOA except that extreme choices by
arbitrator are implemented
0
C
Y
100
- theoretically encourages convergent offers
- agreement rates in the laboratory lower
than FOA (Dickinson 2001)
Forms of Arbitration
Amended Final Offer Arbitration (Zeng 2003)
- each side proposes an allocation
- arbitrator picks preferred proposal
as in FOA
- person placing relatively extreme proposal
pays penalty to the more reasonable party
- allocation is
2 x arbitrators preferred outcome
minus the “extreme” proposal
0
}
}
Amended Final Offer Arbitration
100
Random Draw =z Allocation=p1
Counterpart’s Offer =y
Your Offer=x
}
}
If z > (x + y)/2), then p1 = z + | z - y| = 2z – y and p2 = 100 – (2z – y)
0
100
Allocation
Random Draw
Counterpart’s Offer
Your Offer
If z < (x + y)/2), then p1 = z + | z - x| = 2z – x and p2 = 100 – (2z – x)
Amended Final Offer Arbitration
-Like a 2nd price auction
while FOA is like a first price auction
-Allocation is based upon arbitrator’s
preference and loser’s offer
-Own offer impacts
1) the probability that you win
2) your payoff if you loose
incentive to bid “reasonably”
Distribution of Arbitrator
Previous experiments (and most theory) dealing with
arbitration have utilized nice continuous distributions.
• nice mathematical properties
• appropriate in many situations
– amount of alimony
– appropriate pain and suffering
– level of wages
• inappropriate for other situations
– is the defendant liable?
– who should receive custody?
Distribution of Arbitrator
FOA
• Centered about median if density is continuous and
has mass about the median.
• Kilgore (1994) showed that with a binary distribution
there is no pure strategy equilibrium (unless further
restrictions are imposed).
AFOA
• Centered about mean of distribution.
• Zeng (2003) showed that optimal offer = mz
and this is robust to distribution.
Comparison of AFOA and FOA
FOA strategy depends on the shape of the
distribution (Kilgour 1994)
AFOA strategy is robust to distribution
FOA offers should diverge
AFOA offers should converge
FOA does not induce settlement
AFOA
Experimental Design
2x2 design
1) mechanism: FOA vs AFOA
2) f(z): u[0,100] vs 25 w/p =.5 and 75 w/p =.5
 E(z)=50
UU treatment =
FOA with Uniform distribution
Optimal Offers
FOA with uniform distribution
x=100, y=0 as before
FOA with binary distribution forcing offers to be  [0,100]
if x=100, when y[0, 50) then 2’s profit is (100-y)/2
if x=100, when y=50 then 2’s profit is (.5+.25)*50+.25*(0)
if x=100, when y(50, 100] then 2’s profit is 100-y.
Best choice for disputant 2 is y=0,
and similarly for disputant 1’s best choice is x=100.
Expected payoff in arbitration is 50.
Contract Zone is [50-c,50+c]
Optimal Offers
AFOA with uniform distribution
x=50, y=50
AFOA with binary distribution
x=50, y=50
Expected payoff in arbitration is 50.
Contract Zone is [50-c,50+c]
Experimental Design
4 sessions (replicates) per cell
4 subjects per session
random pairing each period
average payoff = $12.26 + $5.00
subjects recruited for 1 hour
2 phases per session
-15 periods of arbitration (c=0)
-10 periods with pre-arbitration bargaining
(c=15)  Contract Zone = E(z) ± c =
[35,65]
Subject Screen
Experimental Results
0.18
0.35
0.16
0.3
0.14
0.12
0.25
0.1
0.2
0.08
0.15
0.06
0.1
0.04
0.05
0.02
0
0
0
10
20
30
40
50
60
70
FOA with Binary
Optimal Offer =100
80
90
100
0
10
20
30
40
50
60
70
80
AFOA with Binary
Optimal Offer =50
90
100
Experimental Results
0.16
0.14
0.14
0.12
0.12
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0
0
0
10
20
30
40
50
60
70
FOA with Uniform
Optimal Offer =100
80
90
100
0
10
20
30
40
50
60
70
80
AFOA with Uniform
Optimal Offer =50
90
100
Experimental Results
FINDING 1. Observed behavior in AFOA is consistent
with the theoretical predications of the model.
However, behavior in FOA is not consistent with the
theoretical prediction for the mechanism.
Offerijt  m  ei   ij  1 FOAi   2Uniformi   3Uniformi  FOAi   ijt
Parameter
m
1
2
3
Value
51.58480
4.65417
-0.99731
1.08503
Std. Error
2.966176
4.253991
4.202240
6.118946
DF
576
12
12
12
t-value
17.39101
1.09407
-0.23733
0.17732
p-value
<0.0001
0.2954
0.8164
0.8622
Experimental Results
FINDING 2. AFOA generates greater pre-arbitration
settlement than does FOA. (p-value is 0.014)
Statistical Significance based on Mack Skillings test
(2)
100%
(2)
50%
AFOA Bin
AFOA Uni
FOA Bin
FOA Uni
Experimental Results
0.5
0.4
0.3
Contract
Zone
FOA 83% in Contract Zone
AFOA 90% in Contract Zone
0.2
0.1
0
=50 51- 56- 61- 66- 71- 76- 81- 86- 91- 95- NA
55 60 65 70 75 80 85 90 95 100
Frequency of Settlements
in Bargaining Phase with Binary Distribution
Experimental Results
0.5
0.4
0.3
Contract
Zone
FOA 88% in Contract Zone
AFOA 86% in Contract Zone
0.2
0.1
0
=50 51- 56- 61- 66- 71- 76- 81- 86- 91- 95- NA
55 60 65 70 75 80 85 90 95 100
Frequency of Settlements
in Bargaining Phase with Uniform Distribution
AFOA Conclusions
AFOA outperforms standard FOA in several ways
1) Behavior in AFOA is consistent with theory
but behavior in FOA is not.
2) The shape of the distribution of arbitrator
realizations does not influence behavior in FOA but
does in AFOA.
3) Offers in AFOA have less variance than offers
in FOA making outcomes more predictable.
4) Settlement rates and therefore efficiency are
higher with AFOA.
5) The contract zone is a good predictor of the
location of agreements for both AFOA and FOA.