An Experimental Test of the Core in a Simple N-Person Cooperative Nonsidepayment Game

• Author: Peter C. Ordeshook,Richard D. McKelvey,Mark D. Winer,Janet E. Berl
• Published date: 01 September 1976
• Date: 01 September 1976
• DOI: http://doi.org/10.1177/002200277602000304
• Subject Matter: Articles

An

Experimental Test

of

the Core in

a

Simple

N-Person Cooperative

No

nside

pa

ymen

t

Game

JANET

E.

BERL

RICHARD D.

hlcKELVEY

Scliool

of

Urbari

aiid

Public Affairs

Grnegie-hlellon University

PETER

C.

ORDESIIOOK

Center

for Adsaticed

Study

br

the

Behavioral Sciences

Stanford

University

MARK

D.

WlNER

Sclrool

of Urban arid Public Affairs

Gniegie-Alelloii

Uiiiversity

This essay reports on seventeen experiments

that

tcst the validity of the

Core

as

a

solution

to

n-person cooperative games in

a

nontransferable utility contest. Money is

used

to

induce preferences, but subjects

are

not

permitted

to

ncgotiatc about nor

transfer money amongst themselves. Instead, usin; majority rule, subjects must

ncgotiatc

over

and choose some policy in

a

two-dimensional “issue” space. Five

5-person games are run in which the

subjects’

utility is a function of the Euclidean

distance from their ideal policy. Twelve 3-person games

are

run using

a

city-block

rcprescntation of preferences.

Both

series

of

espcriments strongly

support

the

Core

3s

a

solution concept when

it

csists.

Experimental research desigied to evaluate n-person cooperative

ganie

theory focuses on solution concepts that treat

games

without Cores-such

as the V-solution, the Kernel, the Shaplcy value, and

the

several Bargaining

sets. Little attention, however,

is

paid to the Core itself.’

We

attribute this

focus, first, to the fact that, unlike say the Shapley value

or

the Kernel for

1.

One esception

is

the current experimental rew.;5cli of Fiorina

and

Plott

(1976).

Their research antedates ours in conception and,

in

fact, an earlier

JOURNAL OF CONFLlCT RESOLUTION,

Vol.

20

No. 3.

September

1976

01976

Sage

Publications,

Inc.

14541

JOUR

NI~

I,

OF CONFLICT

RESOL

UTION

garrics with sidepaynients, the

Core

does not exist for

large

classes of

games and, hence, is not

a

universally applicable concept.. Second,

designing an expcriniental game with

a

Core

niay render tlie solution

trarisparcnt to subjects and, tlierefore, uninteresting. Vie

Core,

nevertlie-

less, is important because of its intuitive appeal and because the notions of

dominance tliat define it are used also to defiiie otlicr solutions. Any

failure by the Core

to

exhibit empirical validity should, then, underniine

our coiifidence in these related solutions.

A

second deficiency with experimental research is its focus on the

special case of games with sidepayiiiaits and transferable utility. The

critical assumptions defining this case, wliicli admittedly is tlie most well

developed and analyzed version of n-person theory, are: (1)

a

coalition’s

value can be represented by a single number

tliat

corresponds

to

the

amount of

some

divisible transferable comniodity

(c.g.,

money) the

coalition can secure for its members and

(2)

each player’s utility for the

commodity is linear, and Iience transferable as well (c.f. Luce and Raiffa,

1957;

Iiapoport, 1970; and

O\vcii,

1968).

Using this paradigm, solution

theory is tested by assigning dollar values to coalitions, where subjects seek

to form coalitions arid negotiate advantageous divisions of their respective

coalition’s value, and where the outcomes of the game are tlicn analyzed

with the assuniption tliat each subject’s utility for money is linear (c.f.

Riker, 1967; Riker and Zavoina, 1970; Kalin and Kapoport, 1972;

llorowitz and Rapoport, 1974; Bucklcy and Westen, 1971

;

hlascliler,

1971).

We do not object

to

the use of money

to

induce preferences

experirnentally. But inducing preferences witli money is distinct from

requiring money to be the sole transferable commodity of

a

game. Thus,

as

the simple spatial

ganics

we discuss later illustrate, the form of tliesc

experiments in general and tlie transferable utility assumption in particular

hits

the

social relevance of the resultant research. hlathcmatically,

Iiowever, the notions of dominance, characteristic function, Core, V-set,

Bargaining set, and

so

on can be redefined for tlie

riiore

general case of

games without sidepayments (tlie Kernel,

though,

is

undefined without

transferable utility).’ Hence, there is

no

theoretical reason to restrict

rcscarcli to

a

traditional, special case.

preliminary presentation by

Plott

influenced our efforts. Whilc

the

details of their

cspcrimcnts diffcr from ours in several minor ways, their conclusions are essentially

idcntical

to

ours.

2.

Gamcs c3n bc classificd into

tluee

categories of diminishing niatliem3tical

generality: without sidepayiiients .and transferable utility. with sidcpaymcnts but