Arbitration Experiments + Cary Deck - University of Arkansas Amy Farmer - University of Arkansas Dao-Zhi Zeng – Kagawa University & Zhejiang University.
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Arbitration Experiments+
Cary Deck - University of ArkansasAmy Farmer - University of ArkansasDao-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
Culture
Japan US
Mechanism
Arbitr
ator
Behav
ior
AFOA Outperforms
FOA
Dispute Resolution
Two parties have a dispute regarding how to split a pie.
- Litigation - Mediation - Arbitration substantial cost savings
restrictions on discovery shorter hearing length 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 EconomiesBoth Modern Industrialized EconomiesMajor 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
US Japan China Australia
Exporting Country
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 ArkansasJJ- both subjects from Kagawa University in JapanUJ- one subject from each university
Show up fee of $EXP 500
$EXP 100 = $US 1 & $EXP 100 = ¥100
Experimental Design
Written Directions Comprehension HandoutPeriods 1-15 forced arbitration Bargaining DirectionsPeriods 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 respectivelyif x<y then offers are compatible
payoffs are (x+y)/2 and 100 - (x+y)/2if 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 = 0Periods 16-25 (pre-arbitration bargaining): c = 15
Contract Zone [35,65]
4 replicates of each treatment (12 total sessions)4 subjects in UU & JJ6 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
0.05
0.1
0.15
0.2
0.25
0.3
0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100
Final Offers for Subjects in US
Countepart in US
Counterpart in Japan
0
0.05
0.1
0.15
0.2
0.25
0.3
0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100
Final Offers for Subjects in Japan
Counterpart in US
Counterpart in Japan
Linear Mixed Effects Model of Offers in Periods 5-15
ijtiiiiijiijt JapCountJapSubJapCountJapSubeOffer 3210
Variable Parameter Value t-value p-value Constant 0 56.3895 19.9404 <.0001JapSub 1 4.1366 0.9604 0.3424JapCount 2 10.5445 2.4480 0.0186JapSubJapCount 3 –12.5770 –2.0472 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 claimhypothetical paymentssubject pool bias
Self-Negotiated Settlement Rate by Session
0%
25%
50%
75%
100%
JJ UJ UU Treatments
Wilcoxon Rank-Sum Tests
UU v JJ W = 19.5 UU v UJ W = 20 JJ v UJ W = 25*
Self-Negotiated Settlement Rate by Session
0%
25%
50%
75%
100%
JJ UJ UU Treatments
Wilcoxon Rank-Sum Tests
UU v JJ W = 19.5 UU v UJ W = 20 JJ v UJ W = 25*
We find substantially more agreement than previous laboratory studies.
Let’s Play Name That Distribution
27 54 37 52 39 69 52 57 4573 29 73 53 21 44 55 59 4258 75 36 43 70 41 50 47 5651 43 60 61 84 70 50 80 8450 25 20 45 48 57 34 48 4874 67 40 48 39 46 45 53 3647 50 60 57 31 48 48 64 3343 65 33 65 62 50 50 26 4145 66 42 49 55 38 68 57 7140 49 46 49 36 32 58 76 61
37 62 79 48 56 79 59 43 6777 72 43 44 69 74 76 51 3752 29 25 35 29 32 28 26 2852 33 38 45 77 30 22 26 6852 47 29 72 70 54 41 34 5550 28 50 54 23 20 26 58 3130 46 53 55 51 69 42 59 5836 49 48 65 39 40 26 79 4122 43 36 69 30 31 32 47 3721 79 38 48 43 43 37 31 67
47 84 60 38 84 51 54 86 4825 53 53 25 19 23 40 66 2964 71 12 13 55 65 62 63 2960 34 66 46 1 32 57 48 7546 83 39 57 49 36 85 82 3954 30 49 46 51 33 52 85 4259 58 20 61 28 26 86 57 3152 57 62 73 61 25 67 60 7764 43 47 36 51 51 75 33 2641 45 59 44 50 38 76 15 72
Distribution #1 Distribution #2
Distribution #3
Random Effects Probit Model of Settlements in Periods 16-25.
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 20.8405
(0.6459)0.2819
(0.4790)
AvgPay 3–0.0206(0.0472)
---
UJ AvgPay 40.0826
(0.0744)---
JJ AvgPay 50.1588
(0.0800)---
Listed are the GEE parameter estimates. The standard errors in parentheses are the empirical estimates.
UJjJJjAvgPayjpUJjAvgPayjpJJjAvgPayjpj
Allocation in Self-Negotiated Settlements
Contract Zone:
35-65
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
50-55
56-60
61-65
66-70
71-75
76-80
81-85
86-90
91-95
96-100
NA
Lion's Share
Per
cent
age
JJ
UJ
UU
US Japan
US (self) 63.8 58.2
Japan (self) 61.6 65.6
Further Exploration
Risk Attitudes and Strategic Bidding First Price Sealed Bid and Dutch Auctions
n = 5 biddersvalues ~ 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
JapaneseSubjects
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 Goods-
n=4MPCR=.3,.75 =10periods = 104 sessions (2 per MPCR order)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10
Period
Per
cen
t C
on
tirb
ute
d t
o P
ub
lic
Go
od
MPCR = 0 .75 IW
MPCR = 0.75
MPCR = 0.3
MPCR = 0.3 IW
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
- theoretically encourages convergent offers- agreement rates in the laboratory lower than FOA (Dickinson 2001)
0 100C Y
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
Amended Final Offer Arbitration
}}
Random Draw =z Allocation=1 Counterpart’s Offer =y Your Offer=x
0 100
}}
Allocation Random Draw Counterpart’s Offer Your Offer
0 100
If z > (x + y)/2), then 1 = z + | z - y| = 2z – y and 2 = 100 – (2z – y)
If z < (x + y)/2), then 1 = z + | z - x| = 2z – x and 2 = 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 win2) 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 = z
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 divergeAFOA offers should converge
FOA does not induce settlement AFOA
Experimental Design
2x2 design 1) mechanism: FOA vs AFOA2) f(z): u[0,100] vs 25 w/p =.5 and 75 w/p =.5
E(z)=50
UU treatment =FOA with Uniform distribution
Mechanism
Arbitr
ator
Behav
ior
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)/2if 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 cell4 subjects per session
random pairing each periodaverage payoff = $12.26 + $5.00subjects 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
FOA with BinaryOptimal Offer =100
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 10 20 30 40 50 60 70 80 90 100
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 10 20 30 40 50 60 70 80 90 100
AFOA with Binary Optimal Offer =50
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 10 20 30 40 50 60 70 80 90 1000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 10 20 30 40 50 60 70 80 90 100
Experimental Results
FOA with UniformOptimal Offer =100
AFOA with Uniform Optimal Offer =50
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.
ijtiiiiijiijt FOAUniformUniformFOAeOffer 321
Parameter Value Std. Error DF t-value p-value 51.58480 2.966176 576 17.39101
<0.00011 4.65417 4.253991 12 1.09407
0.29542 -0.99731 4.202240 12 -0.23733
0.81643 1.08503 6.118946 12 0.17732
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
AFOA Bin AFOA Uni FOA Bin FOA Uni
(2)(2)100%
50%
Experimental Results
Frequency of Settlements
in Bargaining Phase with Binary Distribution
0
0.1
0.2
0.3
0.4
0.5
=50 51-55
56-60
61-65
66-70
71-75
76-80
81-85
86-90
91-95
95-100
NA
FOA 83% in Contract ZoneAFOA 90% in Contract Zone
Contract Zone
Experimental Results
Frequency of Settlements
in Bargaining Phase with Uniform Distribution
0
0.1
0.2
0.3
0.4
0.5
=50 51-55
56-60
61-65
66-70
71-75
76-80
81-85
86-90
91-95
95-100
NA
FOA 88% in Contract Zone
AFOA 86% in Contract Zone
Contract Zone
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.
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