Arbitration Experiments + Cary Deck - University of Arkansas Amy Farmer - University of Arkansas Dao-Zhi Zeng – Kagawa University & Zhejiang University.

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.