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Assessing the Predictive Accuracy of Two Utility-Based Theories in a Marketing Channel

Negotiation Context

Author(s): Jehoshua Eliashberg, Stephen A. LaTour, Arvind Rangaswamy and Louis W. Stern

Source:

Journal of Marketing Research,

Vol. 23, No. 2 (May, 1986), pp. 101-110

Published by: American Marketing Association

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JEHOSHUA

ELIASHBERG,

and LOUIS

W. STERN* STEPHEN

A. LaTOUR,

ARVIND

RANGASWAMY,

The

results

of the study

show the robustness of two utility-based

negotiation

the-

ories-group decision

theory and Nash's bargaining

solution-in accurately pre-

dicting

outcomes

of a marketing

Jiunnel laboratory

simulation

in which

power

and

information conditions were varied. Both theories

significantly

outper

formed

the pre-

dictions

of a random model. Nash's theory performed

better than group decision

theory.

Assessing

the

Predictive

Accuracy

of

Two

Utility-Based

Theories

in

a

Marketing

Channel

Negotiation

Context

Negotiations

between

marketing

channel members take

place

over

prices,

terms

of trade

(credit,

cash discounts,

etc.), delivery, inventory

levels, promotional

support,

and

virtually

all other

elements

of the marketing

mix. In

the marketing

channel

literature,

little attention has been

given to testing models capable

of predicting

the out-

comes of negotiations

under conditions

characterizing

channel

relationships

(exceptions

are articles

by Roer-

ing, Slusher,

and

Schooler

1975 and

Dwyer

and Walker

1981).' Most of the attention

to date has been focused

on aspects

related

to the processes of channel

negotia-

tion, such as those involving the use of power, influ-

ence, and conflict

management

mechanisms

(e.g., Brown

'Neslin and

Greenhalgh's

study

(1983)

predicting

outcomes focused

on media

purchasing,

not on channels.

*Jehoshua

Eliashberg

is Associate Professor and Arvind

Ranga-

swamy

is Assistant

Professor,

Department

of Marketing,

The Whar-

ton School, The University

of Pennsylvania.

Stephen

A. LaTour is

Associate

Professor and Louis W. Stern is John D. Gray Distin-

guished

Professor of Marketing,

J. L. Kellogg Graduate School of

Management,

Northwestern

University.

The authors thank Renee Florsheim,

Patrick

J. Kaufman,

Vaman

Shenoy Kudpi, Lalita Manrai,

Marjo-Riitta

Lehtisalo, and Donald

Yonenaga

for help in running

the simulation

reported

in the article.

They

are also grateful

for support

from a Xerox

Corporation

research

grant

at the J. L. Kellogg Graduate School of Management.

Com-

ments and suggestions

made by the anonymous

JMR reviewers are

gratefully acknowledged.

and

Day 1981;

Eliashberg

and Michie

1984;

Frazier

1983;

John

1984;

Lusch

and Brown

1982; Stem, Stemthal,

and

Craig

1973).

With advances in mathematically

based approaches,

increased interest has been shown in employing

utility-

based

theories for the

prediction

of outcomes

in a variety

of bargaining

situations

(e.g., Braithwaite

1955; Nash

1950;

Raiffa 1953; Shapley 1953). In the field of mar-

keting,

the

work

of Neslin and

Greenhalgh

(1983) is par-

ticularly important. They examined

the ability

of Nash's

bargaining

solution

(Nash 1950) to predict

the points

of

agreement

in a media

purchasing

simulation

using

MBA

students as subjects.

The research we report

is an ex-

tension of the line of inquiry they initiated. In addition

to using

Nash's

theory,

we assess

the efficacy

of another

utility-based

theory-group decision

theory

(Keeney

and

Kirkwood

1975;

Keeney

and Raiffa

1976;

Raiffa

1968)-

to predict

the

points

of agreement

in a marketing

channel

negotiation

simulation. In particular,

we examine the ro-

bustness of both theories for predicting

the outcomes of

negotiations

in settings

where there is partial

information

and/or

unequal

power

among

the parties.

Marketing

channel

interactions

provide

rich and ap-

propriate

contexts for testing

utility-based

theories

relat-

ing to negotiation.

Channels

of distribution conform to

the common "image" of the generalized bargaining

problem

addressed

by developers

of the theories,

that

is,

bargainers

need to reach some mutually

acceptable

set-

tlement

but also wish to settle on terms favorable

to

themselves

(Bacharach

and Lawler 1981). This mixed-

101

Journal of Marketing Research

Vol. XXII (May 1986), 101-10

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JOURNAL

OF MARKETING

RESEARCH,

MAY 1986

motive scenario has been adopted widely throughout

the

marketing

channel literature

(e.g., Coughlan 1985; Etgar

1976; Jeuland and Shugan 1983; McGuire and Staelin

1983; Stern and El-Ansary 1982).

In the next section we explain group decision theory

and compare its properties with those of Nash's solution

to the bargaining problem. We then describe the mar-

keting channel simulation employed in our study and de-

tail our results. Finally, we discuss the implications of

our results and suggest directions for future research.

THEORETICAL

BACKGROUND

Group Decision Theory

Group decision theory has its origin in individual de-

cision theory. (Its applied version commonly is known

as decision analysis; Howard 1968; LaValle 1978). The

theory prescribes how an individual should make deci-

sions in situations characterized as risky or riskless (in

the sense that the decision maker is either uncertain or

certain about the consequences of the decision). Individ-

ual decision theory first identifies and separates the two

major components needed to model this kind of prob-

lem, (1) the subjective probabilities that are used to

quantify the individual's assessment of the likelihood of

the risky outcomes and (2) the von Neumann-Morgen-

ster (1947) utility functions that represent the individ-

ual's risk attitudes and preferences for the various out-

comes. The theory then suggests that maximization of

individual expected utility be employed as the criterion

to choose the best action. Though individual decision

theory

is primarily

normative

in orientation,

models based

on it have been reported to yield promising predictive

results in marketing applications

(Currim

and Sarin 1983;

Eliashberg 1980; Hauser and Urban 1979).

In a similar fashion, group decision theory prescribes

that the group first aggregate the individual subjective

probabilities

of its members. This step generates a group

consensus probability

(Winkler 1968), which reflects the

group's assessment of the likelihood of the various joint

returns

the group may obtain. The theory suggests that

the group combines the members' often-conflicting util-

ity functions to arrive at an appropriate group utility

function, also known as a social welfare function (Ed-

wards 1977; Keeney and Kirkwood 1975). The group

utility function and the group consensus probability then

can be combined to choose the best action for the group

through

the criterion of maximization of the group's ex-

pected utility (Keeney and Kirkwood 1975). Raiffa (1968,

p. 233-7) provides an insightful discussion of the ad-

vantages and disadvantages of the group decision-theo-

retic approach in the case of differing individual prob-

ability

assessments.

If negotiation

is viewed as a collective

decision-making problem, when the negotiators know all

the negotiation outcomes with certainty, only the group

utility function needs to be estimated. In that case, the

only determinants of the conflict between the group

members (negotiators) are their incongruent preferences

for various negotiation outcomes.

The two most commonly studied forms for group util-

ity functions are additive and multilinear. Both forms are

derived axiomatically from different sets of conditions

that can be verified empirically (Harsanyi 1955; Keeney

and Raiffa 1976). If we denote the individual von Neu-

mann-Morgenster utility functions in a dyadic setting

as U1 and U2 and the group utility function as UG, the

additive group utility function is represented by

(1) UG = K1U1 + K2U2.

The Ki (i = 1,2) parameters

are to be interpreted

as an

index of the power of the parties relative to one another

in the specific collective decision-making situation (Kee-

ney and Raiffa 1976, p. 540). The relative power of the

parties thus has a central role in this theory.

The multilinear group utility function takes the fol-

lowing form.

(2) UG = K1U1 + K2U2 + Ke,UU2

Here, the coefficient K, moderates the power effect and

reflects the group

members' concern

for achieving equality

of utilities at settlement. The larger Ke, the higher the

group's collective desire for both parties to choose a set-

tlement yielding individual utilities that are more or less

equal to each other. (See Eliashberg and Winkler 1981

for further

interpretation

of the parameters

in a risk-shar-

ing context.)

Some promising empirical applications of group de-

cision analysis in the area of arbitration

(as opposed to

pure negotiation) have been reported in a variety of con-

texts, for example, space probes (Dyer and Miles 1976),

environmental concerns (Howard 1975; Keeney 1977),

and health issues (Torrance, Boyle, and Horwood 1982).

To our knowledge, however, there has been no empirical

test of the predictive ability of these functions in any

negotiation context, in general or in marketing set-

tings-in particular

those settings reasonably typical of

marketing channel interactions. The research we report

is an attempt

to advance this field of inquiry through its

application

to marketing

channel negotiations. In a long-

term channel relationship characterized

by trust and fre-

quent interactions, the negotiators may be considered

members of a "group" (as in group decision theory) or

as two bargainers with full information trying to reach

a just settlement (as in Nash's theory).

Nash Bargaining Solution and its Comparison with the

Group Decision-Theoretic Approach

Nash's bargaining

solution was the focus of Neslin and

Greenhalgh's study (1983) and they provide a useful de-

scription of the theory. Therefore, we only paraphrase

the basic concepts and parameters

of Nash's theory and

highlight key differences from group decision theory.2

2For further comparative discussion see Riddell (1981). Luce and

Raiffa (1957) and Roth (1979) provide important

discussions of Nash's

axioms.

102

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PREDICTIVE

ACCURACY

OF UTILITY-BASED

THEORIES

Like the group decision-theoretric

solution, Nash's

bargaining

solution

is an axiomatically

derived

outcome-

oriented

approach

and its prediction

focuses on the Pare-

to-optimal

subset.3

It has been widely employed

in sev-

eral studies to predict

outcomes of bargaining

experi-

ments

(e.g., Roth

and Malouf

1979). The Nash solution

to the dyadic

bargaining

problem

is the choice of U1

and

U2

by the two parties

to maximize

(3) (U, - Ulo)(U2 - U20).

Here, Ul0 and U20

are the utilities

corresponding

to the

no-agreement

point

for the two parties.

There are some key differences

between

Nash's and

the group

decision-theoretic

approach

to the bargaining

problem.

First, the Nash solution

does not require

in-

terpersonal

comparisons

of utilities, whereas

group

de-

cision

theory

explicitly

recognizes

such

comparisons.

This

is a controversial

issue. It involves questions

such as,

"Does one dollar

to a beggar

mean much more than a

million dollars to a billionaire?"

There have been ar-

guments

in the literature,

both pro and con, on the in-

terpersonal

comparison

of utilities

(Braithwaite

1955;

Is-

bell 1959;

Luce and

Raiffa

1957).

Luce and

Raiffa

(1957,

p. 137), for example, suggest

that

bargainers

are in fact

engaged

in comparing

individual

utilities. Empirically,

Nydegger

and Owen (1975) report

that

comparisons

of

utilities for negotiation

outcomes did take

place in their

experiments.

If one assumes

that utilities can be com-

pared

meaningfully,

the

utilities

corresponding

to the no-

agreement

outcome in the Nash model (U10,U20)

can be

interpreted

as representing

the bargainers'

relative ad-

vantages

(Luce and Raiffa 1957, p. 145).

The two bargaining

solution

approaches

also differ

in

their

treatment of the notion of equality

or fairness.

Group

decision

theory

treats this construct as a parameter

that

can

take

different

values

based on the parties'

subjective

feelings. Nash's approach,

in contrast,

requires

through

its symmetry

axiom

that

the solution

depend

only on in-

formation

contained in the model. In particular,

it re-

quires

that if all players

have the same outcome

possi-

bilities, they should get equal outcomes. The original

Nash model has been extended

theoretically

to incor-

porate

individual

differences and asymmetry

(Harsanyi

and

Selten 1972;

Kalai 1977) through

additional

param-

eters. One solution

concept

prescribes

that the negotia-

tors

maximize

(4) (U1 - Ulo)P'(U2 - U20)P2.

The

parameters

PI and

P2 represent

various

confounding

effects of factors

outside the model (see Roth 1979, p.

17)

such

as differences in bargaining

ability,

in the initial

3Informally, the Pareto-optimal subset is the locus of all settlements

such that moving from one to another will make one party better off

and at least one other party worse off. For relatively large negative

K, values, the multilinear utility function may not always predict a

Pareto-optimal

settlement. However, this uncommon situation did not

occur in our study.

distribution

of power, and

in the parties'

assessments

of

particular

"types"

of opposers.

In our

study,

we focus

on situational

bargaining

power

and

on amount

of available

information,

and

we consider

only the original

Nash model. We compare

it with the

group

decision-theoretic

approach

in making

predictions

of simulated

channel

negotiation

outcomes.

METHOD

Fifty-six executives and 140 MBA students

partici-

pated

in the study. Executives

were paired

with execu-

tives and students

with students.

In each session, one

person

was assigned

randomly

to the role of "sales

man-

ager"

for a manufacturer

of ski caps and

the other

to the

role of "buyer"

for a retailing

firm. Both the retailing

and

the manufacturing

firms

were said

to be major

com-

panies.

Both were described

as having

been in business

for a number

of years and being roughly equal

in size,

financial

performance,

stability,

and profitability.

This

description

was necessary

to make certain

the partici-

pants

did not attribute

unequal

situational

power to the

firms

at the outset.

The subjects

were

told they would

negotiate

the price

to be paid

for the ski caps and

the quantity

to be shipped

using a 9 x 5 price-quantity

matrix.4

Perceived

inter-

dependence

was induced

by conducting

a warmup

ne-

gotiation

session using an abbreviated

(4 x 3) price-

quantity

matrix.

This session served

to demonstrate

that

some cooperation

was necessary

to achieve a mutually

acceptable

agreement

that

was better

than

outside

alter-

natives.

The notion

of a long-term

relationship

was in-

duced

by informing

each

dyad

that it would

be given the

opportunity

to negotiate

a second

time and

that

the prof-

its generated

by each member

would be the average

of

the profits

obtained

in the two bargaining

sessions with

the

other

member.

We realize,

however,

that

most

chan-

nel relationships

are much

longer

in duration

and more

complex

than

that

simulated in our study.

After

the warmup

session, experimenters

assessed

the

utility

functions

of the "sales

manager"

and

the "buyer"

for various

levels of profit

within

the range

of the profit

dollars contained

in the price-quantity

matrices. The

method

used

was the standard

lottery-type

procedure

(for

further

details, see Swalm 1966 and

Keeney

and

Raiffa

1976).5

Independent Variables

Amount

of information. For group utility functions and

Nash's theory

to predict

outcomes accurately,

the ne-

4Each cell of the matrix contained the profit dollars that would be

realized by the buyer and seller if they agreed on a price and quantity

corresponding to that cell. The matrix used, as well as other simu-

lation materials (e.g., utility-assessment forms, instructions, etc.), are

available from the authors upon request.

5The utility functions were represented in graphic form. Once a

continuous utility function for profits is assessed, a negotiator's utility

corresponding

to any negotiation outcome can be determined from the

graph.

103

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JOURNAL OF MARKETING

RESEARCH,

MAY 1986

gotiating parties are supposed to have full information

about one another's utilities. Actual bargaining situa-

tions in marketing channels are unlikely to conform to

such a requirement. Therefore, in the simulation, we

created two conditions, one conforming to the dictates

of the theories (i.e., full information) and another more

in line with "real-world" channels (i.e., partial infor-

mation). In the full information condition, both matrices

(the sales manager's and the buyer's) were given to each

dyad

member.

The matrices

included information

on utility

values (on a 0 to 1 scale) for the parties to the negotiation

and for the "outside" alternatives

available to each party.

In the partial

information

condition, the matrices and the

utility information they contained were private. How-

ever, as in the full information condition, communica-

tion between the parties was not restricted during the

course of negotiation. Though it would have been pos-

sible to restrict such communications, we believed this

manipulation

of partial information more faithfully rep-

resented the conditions of most actual negotiations.

Relative

power. Power in a bargaining relationship

can

be varied as a function of several factors, including (1)

the outcomes available from no-settlement alternatives,

as in Thibaut and Kelley's (1959) comparison level for

alternatives, (2) the motivational investment of the par-

ties in the goals mediated by each of them, and (3) the

bargaining skill of the individuals. We elected to focus

on situational power, which we manipulated by varying

the no-settlement alternatives.

The utility levels corresponding to the no-settlement

alternatives

can be considered objective power parame-

ters in the Nash bargaining solution. For group utility

functions, the party with the better alternative

is less de-

pendent on the relationship and therefore should be per-

ceived to have greater situational power, all other things

being equal. To operationalize this situation, we in-

formed the subjects that, irrespective of whether they

reached agreement, they would be given an opportunity

to negotiate with another firm. In the unequal power

condition, one of the parties

had an alternative

that would

yield, on average, $65,000 in profit, whereas the other

had an alternative

that would yield only $25,000. In the

equal power condition, each party

was informed

that their

alternative

would yield, on average, $40,000 in profit.

Relative power perceptions and utilities were assessed

twice during the simulation-before and after the main

negotiation. Also, an extensive questionnaire was ad-

ministered after the negotiation, probing equality con-

siderations

(to determine the appropriateness

of the mul-

tilinear function), perceived power, and several related

factors. The responses to some of these questions served

as manipulation

checks (discussed subsequently).

Three features of the methodology used in our study

should be noted. First, the dependent measures are out-

comes measured

in terms of utilities, not in terms of profit

dollars. This approach

is consistent with the utility-based

nature of the theories examined. Second, the negotiation

was constrained by time; the negotiators were given 20

minutes to come to an agreement. Consequently there

was undoubtedly an end effect. Third, both perceived

power and utilities were assessed before and after the

main negotiation session to detect possible changes over

time. As Roth and Malouf (1979) note, in much of the

bargaining literature, studies assessing correspondence

between bargaining models and outcomes have inappro-

priately used postbargaining utilities when in fact the

bargaining may have affected the utilities. In our re-

search only the earlier assessments (hereafter called

"prenegotiation"

measures) are employed for model es-

timation. This approach is consistent with our focus on

situational power, but leads to a highly stringent test of

the theories, in particular

the group decision theory.

Procedures for Parameterizing the Group Utility

Functions

To assess utilities for the group utility functions, a

scaling procedure was used such that the individual and

group utilities were restricted to be between zero and

one. Perceived power was measured on a constant sum

scale whereby the negotiators were asked to divide 100

points between themselves and their opponents to reflect

their

relative bargaining power (cf. Huber 1974; Johnson

and Huber 1977).

Denote

Kbb = number

of points assigned

by buyer

to himself/her-

self,

Kb = 100 - Kbb,

Kss

= number of points

assigned by sales manager

to him-

self/herself, and

Ksb

= 100- Kss

For the additive group utility functions (UA = KbAUb +

KsAUs), KbA and KA were determined by averaging (Kbb,

Ksb)

and (Ks, Kbs),

respectively. KbA and KS can be in-

terpreted

as the dyadic perception of the relative power

of the parties. By averaging, each member's perception

is being given an identical weight. For the multilinear

functions (UM

= KbMUb

+ KsMUs

+ KUbUs), the follow-

ing set of simultaneous equations first was solved for the

buyer.

Kbb + Kbs + Kbe = 1,

Kbb/Kb,

= the ratio obtained from the constant sum

scale, and

Kbe = the buyer's response to the equality

equation

(discussed

hereafter).

A similar set of equations was solved for the seller. The

solutions for the buyer and sales manager then were av-

eraged to determine the parameters of the group utility

function.

To obtain the equality coefficients (Ke,, Kse) for the

individual multilinear utility functions, each negotiator

was asked (separately) to draw a line on a thermometer

scale ranging from -1 ("it was extremely important to

me that our utility numbers would be different") to + 1

104

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PREDICTIVE

ACCURACY

OF UTILITY-BASED THEORIES

("it was extremely important

to me that our utility num-

bers would be the same"). The equality parameter for

the group utility function also was computed as an av-

erage.

Of the 98 dyads participating in the study, five dyads

failed to reach an agreement and four dyads were not

included in the analyses because of missing data. The

analyses were performed on a total of 89 usable dyads.

A minimum of 20 and a maximum of 24 dyads were

assigned randomly to the four experimental conditions

created by the power and information manipulations.

RESULTS

We first present the results from the power measure-

ments. As mentioned before, perceived relative power

is a central construct in the group utility functions. We

then describe the predictive performance of the group

utility functions in comparison with the Nash bargaining

model and to two naive models.

Reliability and Validity of Power Scales

The reliability of the power scales was assessed by

obtaining three postnegotiation measures (using category

rating scales) of perceived power and comparing them

with a postnegotiation constant sum measure. For the

category rating-scale measures, subjects were asked to

rate their own and their negotiating partner's power on

9-point scales ranging from powerless to powerful, im-

potent to potent, and no control to complete control over

the profit of the negotiating partner. Cronbach alpha

coefficients (Cronbach 1951) of .83 for buyer's percep-

tions of power and .87 for seller's perceptions of power

were obtained. The correlation

between the constant sum

measure and the 3-item category rating scale averages

.82 across buyers and sellers. Therefore, the constant

sum measure appears to have sufficient reliability. Fur-

ther, the fact that the means of the constant sum measure

for the equal and unequal power conditions are different

in accordance with expectations (see next section) pro-

vides evidence for the construct validity of the measure.

Effectiveness of Power Manipulations: Pre- and

Postnegotiation Measures

Table 1 contains the perceived average "own" power

measured on the constant sum scale. In equal power con-

ditions, we would expect the average

perceived

own power

measure to be close to 50. On the basis of the prene-

gotiation measures of power, the obtained level is

significantly6 higher at 53.3 (t(88) = 3.50), probably

reflecting an egocentric bias. Though the mean values

of the prenegotiation measures for the equal, high, and

low power conditions are in the right direction, none of

the differences is significant. When postnegotiation mea-

sures are considered, however, all three differences are

significant. These results suggest that the subjects crys-

talized their perceptions more clearly after the negotia-

tion was completed. When power perceptions are ana-

lyzed separately for the buyer and seller, there are also

some notable differences. On the average, on the basis

of premeasures, buyers perceived that they had more

power than sellers (58.4 vs. 48.9; related samples t(88)

= 5.1). Furthermore,

these differences in perception

hold

significantly across all power conditions. There are no

significant

differences

in prenegotiation

perceptions

across

the power conditions in the case of the buyer. However,

in the case of the seller, the difference between high and

low power conditions as well as between equal and low

power conditions is significant. These results suggest that

the lack of overall significant differences in prenegotia-

tion measures is mainly the result of an egocentric bias

in power perception among buyers (i.e., some "role ef-

fect") before they actually experienced the power dif-

ference during the course of the main negotiations.

Predictive Performance of the Models

Individual outcomes. Both individual and dyadic

measures can be used to test predictions based on the

6Throughout

the Results section, all results reported as significant

are at the level of p = .05 or better for two-tailed tests and p = .025

or better for one-tailed tests.

Table 1

AVERAGE

SELF-PERCEPTION

OF POWER

FROM

CONSTANT

SUM

SCALEa

Self-perception Time of assessment

under Pre- Post- Difference Significant

condition of bargaining bargaining (pre - post) t-value

High

power

(n = 44) 56.7 61.5 -4.9 t(43) = -2.1

(14.7) (14.3) (15.6)

Low power

(n = 44) 51.5 40.3 11.1 t(43) = 4.8

(12.3) (15.3) (15.0)

Equal

power

(n = 90) 53.3 51.9 1.3 n.s.

(9.1) (9.6) (8.5)

All conditions

(n = 178) 53.6 51.4 2.2 t(177) = 2.2

(11.6) (14.5) (13.5)

'Numbers

in parenthesis

are standard

deviations;

n.s. denotes a nonsignificant

difference

(p < .05).

105

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JOURNAL OF MARKETING

RESEARCH,

MAY 1986

theories. However, problems arise with dyadic-level

analysis

because

of a lack of well-defined

goodness-of-

fit criteria.

Consider,

for example, the sum of utilities

of buyer

and seller

as a measure

of dyadic

outcome. The

deviation

of the predicted

sum

of individual utilities from

the sum at actual

agreement

can be used as a criterion

for the predictive

performance

of the theory. However,

small

deviations

do not necessarily imply accurate

pre-

dictions

because

they may mask large variations

in in-

dividual utilities.

Therefore,

even though dyadic analysis

may sometimes

be preferred

in marketing

channel

stud-

ies (see Stem and

Reve 1980), our emphasis

here is on

individual-level outcomes, supplemented with two

suggestive dyadic measures. (See Neslin and Green-

halgh 1984 for further

analysis

of this issue.)

Tables

2 and 3 compare

the relative

accuracy

of the

two group

utility

functions

and

the Nash bargaining

so-

lution in predicting

individual

negotiation

outcomes.

Predictions

of the theoretical

models are based

on iden-

tifying the settlements

above the no-settlement

point

which maximize dyadic utility score. The theoretical

models

also are

compared

with

two "naive"

models, (1)

an

equal-weights

additive

utility

model and

(2) a random

model

in which predicted

outcomes are selected

at ran-

dom (with

equal

probabilities)

from any cell of the 9 x

5 price-quantity

matrix.

The

equal-weights

additive

model sets the

power

coef-

ficients

equal

to .5 in the additive

utility

model described

before

and predicts

the settlement

at the cell that max-

imizes the group's

(dyad's)

score. It thus

provides

some

insight

into the usefulness

of assessing

the negotiator's

perceived

relative

power. The random

model is inde-

pendent

of any

theory

because

it makes

predictions

with-

out taking

into account

relative

power

or utilities.7

Table

2 contains

the correlation

coefficients

between

the actual and

predicted

utilities

(separately

for buyer

and

seller) for the five models considered.

All four utility-

based

models

predict

significantly

more

accurately

than

7It must be noted that the 9 x 5 price-quantity

matrices

do not

contain

any

settlement

(measured

in profit)

which is strictly

dominated

by either the unequal

power ($65,000, $25,000) or equal power

($40,000, $40,000) condition.

Hence, all 9 x 5 = 45 possible set-

tlements

are considered.

Table

2

CORRELATIONS

OF ACTUAL UTILITIES

WITH

PREDICTED

UTILITIESa

Model Buyer Seller

Additive

(A) .57 .52

Multilinear

(M) .59 .51

Equal-weight

additive

(E) .51 .46

Nash

(N) .66 .61

Random

(R) .25 .35

'All correlations

are significantly

greater

than

zero (p < .05).

Table 3

AVERAGE

ABSOLUTE

DEVIATIONS

OF PREDICTED

FROM

ACTUAL

UTILITIES

Partial Full

information information

Buyer

Unequal power .131 (A) .154

.135 (M) .136

.111 (E) .149

.141 (N) .124

.228 (R) .241

Equal

power .150 .161

.158 .146

.150 .169

.109 .081

.224 .236

Seller

Unequal power .122 .183

.145 .169

.122 .194

.140 .144

.282 .242

Equal power .152 .202

.162 .196

.173 .232

.133 .132

.149 .173

A is additive

utility

model, E is equal-weight

additive

model, N is

Nash

bargaining

model, M is multilinear

utility

model, and R is ran-

dom

model.

the random

model.8

There are

no significant

differences

in predictive

performance

between

Nash's

model and the

three

group

utility

models, except that the Nash model

performs

significantly

better

than

the equal-weights

ad-

ditive

model for the case of the seller. However,

at the

descriptive

level, as Table

2 indicates,

predictions

of the

Nash

model

have

higher

correlations

with the actual

out-

comes than

do those of the group

utility

models. Also,

all utility-based

models appear

to predict

more accu-

rately

for the buyer

than

for the seller. This result

rep-

licates a finding reported

by Neslin

and

Greenhalgh

(1983)

and is probably

the consequence

of the "role effect"

mentioned

before.

Table

3 reports

the average

absolute

deviations

of pre-

dicted

utilities from the actual

obtained

utilities, sepa-

rately

for

buyers

and

sellers,

under

the four

experimental

conditions

for the five different

models. Overall

(i.e.,

across

all experimental

conditions

and across

both buy-

ers and

sellers),

the improvement

gained

by using

a util-

ity-based

predictive

model

instead

of the random

model

ranges

from 37% for the equal-weights

additive

model

8The tests are based on the comparison

of correlations

from two

dependent

samples.

See, for example,

Roscoe (1975, p. 266).

106

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PREDICTIVE

ACCURACY

OF UTILITY-BASED

THEORIES

to 77% for the Nash model. The quality of the predic-

tions also can be ascertained by comparing the devia-

tions with the range of the values over which the pre-

dictions could actually fall. The average range is .86 (on

a scale of 0 to 1) for buyers' utilities and .82 for sellers'

utilities. After averaging over buyers, sellers, and ex-

perimental

conditions, the deviations computed from the

predictions of utility-based models range from 19.5% of

the range for the equal-weights additive model to about

15% of the range for the Nash model. In the case of the

random model, the average deviations are 26.5% of the

range.

To gain further insights, we submitted the deviation

scores to an analysis of variance. In no case were there

any effects involving the experimental variables. There-

fore, the results listed below hold across experimental

conditions.

1. The

utility-based

models

predicted

significantly

more ac-

curately

than the random

model

(additive

model,

F(1,85)

= 13.25; multilinear,

F(1,85) = 13.58; equal-weights

additive,

F(1,85) = 13.02; Nash, F(1,85) = 21.32).

2. The Nash model predicted

better than

both the additive

model, F(1,85) = 4.75, and the multilinear

model,

F(1,85) = 4.57.

3. There were no differences

in performance

between the

equal-weights

additive model and the unequal-weights

additive

model, a result

paralleling

that

found

in the in-

dividual

decision-making

literature

(Dawes

and

Corrigan

1974).

4. The Nash model and the equal-weights

additive

model

predicted significantly

better

for the buyer

than for the

seller (Nash, F(1,85) = 5.10; equal-weights

additive

model, F(1,85) = 7.75).

5. An analysis

of the "signed"

deviations

between

predicted

and actual utilities

(unlike

the absolute deviations in Ta-

ble 3) indicated

that all models significantly

overpre-

dicted the utility

achieved

by the seller at the agreement

point

(additive,

F(1,85) = 4.90; multilinear,

F(1,85) =

11.6; equal-weights

additive,

F(1,85) = 28.35; Nash,

F(1,85) = 22.6). The Nash model also underpredicted

in the case of the buyer

(F(1,85) = 4.20). The under-

Table 4

AVERAGE DEVIATIONS

OF ACTUAL

FROM

PREDICTED

UTILITIES USING MODEL

FUNCTIONAL

FORM

Partial Full

information information

Unequal power .049 (A) .050

.052 (M) .046

.055

(E) .044

.042 (N) .041

Equal

power .045 .052

.047 .052

.044 .058

.028 .025

A is additive

utility

model,

M is multilinear

utility

model,

E is

equal-weight utility

model,

and N is Nash

bargaining

model.

Table 5

PREDICTIONS OF RANK

ORDER

OF BUYERS'

AND

SELLERS' UTIUTIES

Model

Additive

Multilinear

Equal-weight

Nash

Random

No. dyads

with

correct

prediction

of rank

order

56

61

55

63

48

Percentage

(of 89 dyads)

63

69

62

71

54

prediction

for buyers

and overprediction

for sellers by

the Nash model

parallel

Neslin and

Greenhalgh's

(1983)

findings.

Dyadic outcomes. Table 4 lists deviations between

predicted

outcomes and actual outcomes obtained by the

following procedure. First, the functional form of each

model was used to compute the values of the functions

at the predicted and actual cells in the price-quantity

ma-

trix. Next, the deviations (predicted minus actual) were

computed for each dyad and then averaged under each

experimental condition. It is important to note that the

deviation measures developed are not independent of the

model and, hence, no meaningful comparisons can be

made between models. However, predictions made by

the same model can be compared across the four ex-

perimental conditions.

An analysis of variance of these dyadic deviations

showed no differences between experimental conditions

for the predictions of the group utility functions, sug-

gesting that their predictions are robust across the ex-

perimental conditions. In the case of the Nash model,

however, the predictions are significantly better under

conditions of equal power than unequal power (F(1,85)

= 3.99).

Another

dyadic criterion of predictive

performance

that

may be of interest is the percentage of dyads (of 89) in

which the models correctly predict the rank

order of buy-

ers' and sellers' utilities at the agreement cell. This per-

centage gives a measure of a model's performance in

correctly predicting whether the buyer or seller would

achieve higher utilities at agreement. The results in Ta-

ble 5 suggest that on this criterion, the multilinear group

utility model and the Nash bargaining model perform

equally well and outperform the other three models.

DISCUSSION

Our major finding is that, in the marketing channel

simulation chosen as the research setting, both group de-

cision theory and Nash's bargaining solution performed

well in predicting

the outcomes of the negotiations

across

all conditions. This finding indicates that these utility-

based theories are robust even in circumstances which

threaten their application, such as partial

iffoilation and

unequal power.

107

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JOURNAL OF MARKETING

RESEARCH,

MAY

1986

Another

important

finding

is that Nash's theory pre-

dicted outcomes more

accurately

than did the group

util-

ity functions,

even though

the simulation

apparently

vi-

olated the symmetry

condition

specified

by Nash's

theory.

One

reason for the inferior

performance

of the

group utility

functions in relation to Nash's theory may be that the

prenegotiation power

measure failed

to show significant

differences between

the equal and unequal

power con-

ditions.

The weak induction

may have been due to the

fact that

the availability

of alternatives

was merely an

abstraction

before the negotiations

actually

commenced.

As indicated

before,

we are

suspicious

of the use of post-

negotiation

perceived

power

measures

in the group

util-

ity functions

because

postnegotiation

perceptions

could

be a rationalization

for the outcome

actually

achieved.

Had we measured

power

perceptions

at some point

dur-

ing the course

of the negotiations

when

the parties

were

actually

experiencing

their

effects, the predictive

accu-

racy

of the group

utility

functions

might

have matched

that

of Nash's theory. (Recall that the power measure

for Nash

is more

objective

because

it comes

directly

from

the utilities

associated

with

the available

alternatives

rather

than

indirectly,

via the

perceptions

of the

parties.)

Clearly,

this area

should be subjected

to further

research,

which

should

include measures

of bargaining

skill as well as

improved

measures

of situational

power.

In terms of ease of operationalization,

group utility

functions are

more

difficult

to operationalize

than Nash's

theory.

When

the former

are

used, one must

work with

a number of perceptual

measures.

The time and effort

required

to collect such data

and

to check for reliability

and

validity may

be worthwhile

if the models

are

clearly

superior

to competing

models. Such

was not the case in

our

study.

Nash's

theory's

relative

merit

is that it is more

parsimonious

than group decision theory. In addition,

the fact that the unequal-weights

additive

group

utility

function

did not

significantly

outperform

the

equal-weights

additive

model suggests

the effort

expended

in measur-

ing power

differences

may not have been

justified.

The

critical

variables

in predicting

negotiation

outcomes

thus

appear

to be the utilities, not perceptual

measures

of

power. This is also an important

subject

for future

re-

search.

A third

major

finding

is that both theories

predicted

accurately

even when the full-information

requirement

was violated.

This finding

seems to indicate that

during

the course

of the negotiations,

the parties

shared

enough

relevant

information

to enable them to achieve settle-

ments

close to the normative

solutions.

Such a phenom-

enon

may

be even more

prevalent

in "real-world"

chan-

nel relations, especially in those that are highly

interdependent,

long-term,

and

characterized

by trust

(as

opposed

to opportunistic

behavior).

This possibility

also

poses questions

for further

research.

Finally, the theories

predicted

better

for buyers

than

for sellers.

This finding

suggests

that

buyers

are able to

achieve

outcomes

closer to the normative

ones recom-

mended

by the models. Interestingly,

all of the utility-

based models tended

to overpredict

the utilities

achieved

by sellers at agreement

(as well as underpredict

in the

case of buyers). Supporting

the dominance

of the buyer

is the fact that the average profit

achieved

by buyers

was

$69,850

whereas

for sellers the

average

was

only

$63,990.

This finding

indicates

that there

may be significant

role

bias in perfectly symmetric

negotiations.

(See Bazer-

man, Magliozzi, and Neale 1985 for similar

findings.)

This is another

subject worthy

of future research.

CONCLUSION

Any technique

that facilitates

predicting

the outcomes

of negotiations undoubtedly

would be appreciated by

management, irrespective

of the issue (e.g., labor

rates,

advertising

space

charges,

allocation of retail shelf space,

etc.) involved.

Theories

developed

in economics and

the

decision

sciences can be applied

in solving such prob-

lems. We have applied

two utility-based theories-group

decision theory and Nash's bargaining

solution-to a

marketing

channel

simulation

in an effort to assess the

accuracy

and robustness of their predictions

in such a

context.

Our

research shows both theories to be superior

to a

random model that

does not consider

utilities. This find-

ing indicates

that utility-based

theories, at least in the

setting

chosen for our

study,

can be helpful

in generating

insights

into negotiation

outcomes.

Of particular

impor-

tance is the fact that the theories

predict

well under

a

variety

of information

and relative

power

conditions.

Our research

also shows that the more parsimonious

model derived

from Nash's theory

is superior

to group

utility

functions

in terms

of predictive

accuracy.

How-

ever, the richness

of the perceptual

data demanded

by

the group utility

functions

may provide

management

with

deeper insights about the bargaining processes. We fo-

cused only on outcomes. Given some of the difficulties

associated

with the measurement

of power

during

a ne-

gotiation,

further

comparisons

of the theories

with better

power

measures

may be profitable.

We point out several

issues for future research.

The

true

test of the theories,

however,

will be when

they are

taken into the field and used to predict

the outcomes

of

actual channel

negotiations.

Despite our efforts

to sim-

ulate channel interactions

in the laboratory,

we do not

claim to have captured

the true levels of intensity,

in-

terdependency,

and trust

of long-term,

on-going

channel

relationships.

The

managerial implications

of our research

obviously

must be based on the laboratory

study. Extrapolation

to

the "real

world"

is probably

not appropriate

at this

junc-

ture.

However,

if one could

extrapolate

(i.e., if our

find-

ings held up in the field or if we were able to develop

a richer channel

simulation

in the laboratory

and achieve

the same

results),

we would

argue

that

the measurement

and sharing

of information

on utilities relating

to pro-

jected outcomes of the negotiations

(via face-to-face

communications

or through

an intermediary)

might pro-

vide

channel members

with an input

they

need to predict

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PREDICTIVE

ACCURACY

OF UTILITY-BASED

THEORIES

the likely negotiation outcome and evaluate its fairness.

This input should make the bargaining process more ef-

ficient and perhaps more effective as well. Because of

the amount of time that might be wasted in an attempt

to elicit such information via informal means, more at-

tention to formal utility-based theories seemingly would

enhance the productivity of all parties engaged in the

process.

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