risk orientation as a predictor in the prisoner's dilemma

Risk Orientation as a Predictor in the Prisoner's DilemmaAuthor(s): F. Trenery Dolbear, Jr. and Lester B. LaveSource: The Journal of Conflict Resolution, Vol. 10, No. 4 (Dec., 1966), pp. 506-515Published by: Sage Publications, Inc.Stable URL: http://www.jstor.org/stable/173140 .

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I. Introduction The Prisoner's Dilemma is a mixed-motive situation in

which noncooperative short-

run maximizing behavior is inconsistent with

long-run (cooperative)

maximization.

It

has been investigated experimentally

un-

der various conditions, and

the

literature is summarized

in Lave (1OO$),

Rapoport and

Orwant (1OO2),

and Gallo and

McClintock

(1005). One version of

the

situation is

illus-

trated in Matrix I of

Table

1. The payoffs

to

player

A,

identified

by the

strategies of A and

B

respectively,

can

be ranked from

the

most to

the

least preferred: (2,1), ( 1,1 ), (2,2),

and

(1,2). This ranking shows the structure

of

the game: no matter which strategy

the

other player chooses, a subject prefers

the

payoffs resulting from strategy 2. In a

one-trial

game, (2,2) begins to take on the character of a unique solution. In an iterated game, dynamic considera-

tions

may upset this argument. When

the

game

is

repeated, there are

only

two posi- tions that might be expected to prevail

for

a

majority of

trials: (1,1)

and

(2,2). Since

the

former

is

preferred

to

the latter,

the

iterated game may be thought

of

as involving

two

tasks: deciding whether it is desirable (prof- itable) to

attempt

to

get

to (1,1) and,

ff it

is, selecting a technique (strategy)

for

achieving this goal. With verbal and written communications barred,

the only

way to suggest mutual cooperation is

to

choose strategy 1. Experi- mentally (in Prisoner's Dilemma games with money payoffs), different tendencies

to

choose strategy

i

have been observed in

dif-

ferent

subjects. These differences have been attributed to personality variables such as competitive orientation and sex difference, and have been measured by

the F scale,

the Internationalism

scale,

and a measure

of

"flexible

ethicality."

(However,

the

effects are

not

always significant when replicated; see

Pilisuk et al., 1965.) It would

seem to

us

that, in addition

to

these factors, differences in attitude toward risk across

subjects

should explain differences in behavior. Tradition-

ally,

this factor

has

been ignored under an assumption that utilities

of

payoffs

in

money are linear

(Luce

and

Raiffa, 1957,

p. 95).

But the

literature on lottery experiments (e.g.,

Dolbear, 1963),

as

well

as a tradition that goes back to Bernoulli

(1738),

suggests that attitudes toward risk cannot be repre- sented accurately by a linear utility function. This research was supported in

part

by

Ford

Foundation Grant 1-40055

to the

Carnegie In- stitute

of

Technology

for

research on organiza- tional behavior.

~

On leave

to the

Graduate School

of

Busi- ness, Stanford University,

1966-67.

CONFLICT RESOLUTION

VOLUMEX NUMBER4

Risk orientation as a predictor in the Prisoner's Dilemma

F. TRENERY DOLBEAR, JR.,2 and

LESTER

B. LAVE

Graduate School

of

Industrial Administration, Carnegie Institute

of

Technology



RISK

ORIENTATION AS A PREDICTOR

507

We

set out,

therefore, to assess experimentally

the

importance

of

attitudes toward risk in explaining behavior in

the

Prisoner's

Di-

lemma. A subject who chooses strategy 1 in

the

iterated Prisoner's Dilemma has little

infor-

mation as to whether cooperation

at (1,1)

will result and

little

information even that his choices will be perceived as communications.

Since

the player faces a high likeli- hood

of

getting the

least-desired

payoff

(1,2),

choosing strategy 1 in an effort to

get

to

(1,1) may

be regarded as a gamble. More precisely,

fi'equent

choice

of

strategy i will increase

the

chances

of

getting a large aggregate payoff because one's opponent-partner may be induced

to

"cooperate"; but it also increases the chances of getting a

small

(perhaps negative) payoff ff the opposite player turns

out

to be unco- operative. On the other hand, repetitive selection

of

strategy 2 removes

the

chances

of

large loss, since there

is

no possibility

of

getting

the least

preferred payoff. At

the

same time, it minimizes

the

chances

for large

gains, since

the joint

maximum payoff cannot be

reached.a

Since

the

achievement

of

a sequence

of

payoffs has an effect on a player's wealth, we may regard

the

iterated Prisoner's Dilem- ma as a "grand" lottery

in

which

the

probabilities

of

various sequences

of

payoffs are

influenced

by a player's selection

of

strategies. Given a

subject's

view

of the

chance

of

getting cooperation,

the

number

of

times he tries

to

signal his desire

for

cooperation

by

choosing strategy 1 provides a crude measure

of his

willingness to take risk-- which might result in either large gains or large losses. The less

risk-averse

subjects would tend,

ceteris paribus,

to

be

more willing

to

experiment with strategy 1. Lottery choice experiments offer perhaps

the

most widely used method of measuring attitudes toward risk. The explicit measure

which

we propose is discussed in section IV.

At

this point, however, we should remark that the relationship between risk attitudes and strategy 1 choices in

the

Prisoner's Di- lemma might be obscured by

the

personality factors mentioned earlier.

If

subjects with similar risk preferences differ with respect to other factors affecting cooperation, they will differ in

the

number

of

strategy 1 choices they make.

But if the

attitude toward risk is an important factor,

the con-

jectured

relation between risk attitudes and strategy 1 choices should

appear.~

II.

Hypotheses To

get

maximal use

out of

our data,

we used

a highly structured Prisoner's Dilemma experiment. (Subjects actually played against a stooge who always picked strategy 2 in

the

early trials; thus there was no chance

of

achieving

cooperation.)

Therefore, the hypotheses

below

are strictly relevant

only

to this

structttre.

(1) The principal hypothesis to be tested

was

that the number

of times

a

subiect

chose strategy I

in the

Prisoner's Dilemma would be

negatively correlated

with the number

of risk-averse

choices in

the

lottery experiment. (These variables are precisely defined

in

section

IV.)

(2) Several subsidiary hypotheses about

the

Prisoner's Dilemma were

also

tested. Several

of

these related to differences

in

behavior which might be associated with three different payoff matrices such as Ma- trix

I,

Matrix

II, andMatrix III

in

Table

1.

a

Few subjects are willing

to

continue choosing strategy 1 in

the

face

of

persistent choices

of

strategy 2 by

the

other. Thus, as the number

of

trials increases (in view

of the

above argument that [1,2]

and [2,1]

are unstable posi-

tions

), either ( 1,1 ) or (2,2)

may

be expected to

preyaft.



TABLE 1

SOME

PAYOFF MATRICES

FOR

PRISONER'S DILEMMA Player B Player A Strategy Strategy

1

2 Strategy 1 8, 8 0, 9 Matrix

I

Strategy 2 9, 0 2, 2 Strategy

I

6, 6 -2, 7 Matrix

II

Strategy 2 7, -2 0, 0 _ Strategy i 3, 3 -5, 4 Matrix

III

Strategy 2 4,-5 -3,-3 Strategy i a,

a'

c,

b'

Generalized Matrix Strategy 2 b,

c'

d,

d'

508 F.TRENERY

DOLBEAR, JR.,

AND LESTER B. LAVE Matrix III was selected

from

among those used by Lave (1965) as one which seemed sensitive to attempts at cooperation. From this matrix, the other

two

were constructed by adding 3 cents to each payoff (Matrix

II)

and then adding another

2

cents to each payoff (Matrix I).

All

payoffs in Matrix

I

are nonnegative; thus a

subject

could never lose money with this matrix. Matrix

II

contains a negative payoff

for

a player who is

doublecrossed;

a subject can never lose money by choosing strategy 2.

In

Matrix

III

the only way a subject can avoid losing money is to achieve cooperation at (1,1). One hypothesis about these matrices is offered by the theory

of

games. Game theory presumes that behavior is based on the utilities

of

the payoffs and that a linear utility function

for

money is a good approxi- mation (at least over a small range). Con-

sequently,

adding a constant to

all

money payoffs should not affect behavior, since it will not alter the relationships among the utilities of the payoffs (see Luce and

Raiffa,

1957, p. 95). The theory

of

games, then, would offer the

null

hypothesis that there will be no difference in subject behavior due to the differences among the three matrices. Note that this hypothesis is stronger than hypothesis 3 below, and stronger than the prediction implied by Rapoport and Chammah (1965) that the mean degree

of

cooperation in

the

three matrices should be the same. However, we felt that negative payoffs would have an effect on

the

tendency to cooperate.

It

must be remembered that all

subjects

are faced with a stooge who con-

tinually

chooses strategy 2

for

the first 12 trials; thus no subject can gain cooperation during that period. Given the nature of the stooge, we

felt

that

subjects

using the second

and

third matrices

wouldmbecause of

the losses incurred by choosing the cooperative

strategy--rapidly

conclude that cooperation was unlikely. On the other hand, subjects with Matrix

I

might be expected to be more cooperative, since they could never lose money by choosing strategy 1.

It

was con-

jectured,

therefore, that the mean number

of

strategy

I

choices

would

be highest

for

Ma- trix I. Given the matrices and the nature

of

the

stooge,

it was possible to make conjectures about

the

variance

of

cooperative responses among subjects. We

felt

that there would be greater variance in the number

of

strategy

1

choices

for subjects in

Matrix

I since

there were no negative payoffs in that

matrix--consequently

a smaller incentive

to

settle on strategy 2 as a technique to minimize losses. This weaker incentive

could

result in a greater dispersion in the responses

of

subjects.

At the

other extreme,

subjects faced

with Matrix III would be losing money on

each

trial, and

each

sub-

ject

might be expected to

face

up

to

reality quickly. Thus, we expected variance in the number

of

strategy 1 choices

to

be highest

for

Matrix I and lowest

for

Matrix III. CONFLICT

RESOLUTION VOLUMEX NUMBER4



Yz 2..oo 1.25

o

k O50

FIo.

1. Example

of

lottery card used

in

the first and second sessions

of the

experiment. Another hypothesis seemed relevant to the third matrix. Subjects are caught in the dilemma that they can make money only by cooperating, yet they lose a large amount when faced with a noncooperative stooge. We conjectured that these subjects would make attempts to achieve cooperation ini- tially, and then quickly recognize failure

and fall back

on strategy 2. Consequently, a greater proportion

of

attempts at cooperation should

come

on the

early

trials

for

Matrix

III

than

for

either of the other matrices.

(3) A

final hypothesis is contained

in

Lave

(1960). It

states that attempts at cooperation in the

Prisoner's

Dilemma

will

be related to the number of trials (n) and the values of the payoffs. Take the generalized matrix in

Table 1. If

the following formula is satisfied, subjects

wfil

make substantial attempts to cooperate (three or more choices of strategy

1):

3(b-a) n> a~d

' III. Method Undergraduate freshmen and sophomores were recruited

&om

Carnegie

Teeh's place-

ment bureau and from an elementary

eco-

nomies course. They were

told

that they were volunteering for a

decision-making

experiment in which their winnings

would

depend on how they played

the

game

and

RISK ORIENTATION AS A PREDICTOR 509 on luck. They were also told that the aver- age person

would

win about $1.50 an hour.

Fifty-four

students participated in

the

first

of

three sessions (held on Tuesday, Thurs- day, and Saturday

of the

same week), but

for

one reason or another only 45 completed all three sessions.

a~E LOTTma? EXPERIMENT

In

the first two sessions, subjects were asked to make choices in a binary-choice lottery experiment. A sample choice card is shown in Figure 1.

If

a subject was con- fronted with this card, he would have to choose between the left

lottery--which

offers 1/2 chance

of

receiving $2.00 and 1/2 chance

of

receiving

nothing--and the

right lottery, which offers

1/2

chance of receiving

$1.25

and 1/2 chance

of

receiving $.50. One hundred choices were made in each session, or 200 in

all.

The

first

150 choice situations involved lotteries containing 1/2-1/2 objective probabilities, while the

last

50 involved 9/10-1/10 objective probabilities. Payoffs ranged from $2.50 to -$1.00. The first 50 lottery pairs are shown in

Table

2. A second group

of

50 lottery pairs was obtained by subtracting $.50 from each payoff shown in that table; this pro- duced pairs containing one negative payoff. A third group

of

50 lottery pairs was obtained by subtracting another $.50 from the original

payoffs.4

To provide appropriate motivation, sub-

jects

were

told

that at the conclusion

of

each session

two

of the

100

lottery situations would be drawn at random by the subject. (One card was drawn from each

of

two

4 Of

course, when these choice situations were presented to the subjects, lotteries

and

payoffs were

,xrranged

to insure

(1)

random positioning

of

payoffs within lotteries

and

of lotteries within lottery pairs; and (2) a stratified (with

re-

spect to signs) random order of lottery pairs.



TABLE 2 DESCRIPTION OF

FIRST FIFTY

LOTTERY

PAIRS*

Lottery

card 1/2

Payoff A 1/2 Payoff

B

pattern:

1/2

Payoff D

1/2

Payoff G Lottery Payoffs: A

B C D

group

1

0 $ .90

$1.00 $1.80-$2.50

in $

.10

steps

2

$

.15

$ .70

$1.10 $1.65-$2.45

in $

.10

steps

3

$ .25

$.65 $1.05 $1.35-$2.05

in

$.10

steps

4

$ .30 $ .60

$1.20 $1.50-$2.20

in $

.10

steps 5 $

.40

$ .55

$1.15 $1.30-$2.10

in $

.10

steps 6 $ .45 $ .50

$1.30 $1.55-$2.25

in $ .10 steps * The method

of

generating the two other lottery groups with 1/2-1/2

objective

probabilities is described

in

the text. 510 F. TRENERY DOLBEAR,

JR.,

AND LESTER B. LAVE baskets. The first basket contained duplicates

of

the first 50 lottery cards and the second basket contained duplicates

of the

second 50 cards.) After the two cards had been drawn, the

subject

actually "played" the lotteries which he had chosen on those cards. For example,

if

the subject had chosen the left lottery in Figure 1, this lottery would be played as follows: one card marked

'~rop"

and one card marked

"Bot-

tom" (representing probability 1/2 for the top payoff and 1/2

for

the bottom payoff) would be placed in a basket and mixed by an assistant. The subject would then draw one of these

two

cards at random.

If

he drew the card marked "Top" he would receive the top payoff (in this case, $2.00);

if

he drew the other card he would receive the bottom payoff (here, nothing). Actual payments

of

winnings were made after

the

second session. These procedures were ex- plained to

all

subjects before they made any choices. THE

PRISONER'S

DILEMMA EXPERIMENT In the third session, subjects played a Prisoner's Dilemma game

for

25 iterations. Three matrices were used: 14 subjects played Matrix I, 16 played Matrix II, and

15

played Matrix III. Three rooms were

used

simul- taneously with about eight subjects

to

a room. Each subject received a copy of the matrix he was to use, and the usual instruc- tions were given on

how

to play the game

(see

Lave,

1965). In

addition, each subject received a color-coded pad for recording his choices and

the

responses

of

his opponent. He was told that there was, in one

of

the other rooms, another player (whose identity was not

known

to him) with a pad

which

matched his color and that this player was his

"opponent-partner."

Each subject received an initial stake

of

$1.50.

He was told that after each

of

the

25

trials he would be informed

of

the outcome of that trial and would be paid

(or

would pay from his

stake)

the amount

of

his

win-

nings (or

losses)

on that trial.

At

the end

of the

session he would be allowed

to

keep whatever he

had

left.

Of

course his win- ings could

be

smaller or greater than his initial stake. The play

would

be managed

by

the experimenters and their assistants, who would serve as "runners" and

who

would match the choices

of

the

color-coded

pads.

Unbeknownst

to the players

(at

least at the

beginning),

they were not to play against another player in one

of the

other rooms.

For

control purposes,

we

had decided that all subjects

would

play against a stooge who would play strategy 2 for the first

12

CONFLICT RESOLUTION VOLUMEX

NUMBER4



RISK


511

rounds and then switch to strategy 1

for the final

13

rounds.5

This seemed to be re- quired, since our object was

to

compare

(rank)

subjects with respect to attempts at cooperation.

IV. Risk-Aversion

and

the

Tendency

to Cooperate

In section I it

was

argued that,

ceteris

paribus,

the more

risk-averse subjects

would tend to be less inclined to seek

the

cooperative solution

in

the iterated Prisoner's

Di-

lemma. Relative risk-aversion and tendencies to cooperate can be defined in various ways.

For our

purposes, however,

let us (crudely)

measure

risk-aversion

by

the

total number of

risk-averting

choices made by

the

sub-

ject in the 150

lottery choices with

1/2-1/2 probabilities.?

Taking

the

card shown in Figure 1,

for

example,

it

seems reasonable

to

argue that subjects who choose the

right-

hand lottery display more

risk-averting

behavior on this choice than those

who

choose

the leR-hand lottery.*

A similar argument can be made

for all

150 lotteries, since

each

has

the

characteristic

that

one lottery

con-

rains

the two

extreme payoffs and the other lottery contains the

two

middle payoffs (relatively

risk-averting). Since

there

is

no obvious way

to

weight

the

various lotteries in determining a measure

of

relative risk-aversion

which

will rank

subjects,

we use a

crude

ranking scheme

which

weights

all

lottery situations equally. Notice that we are not interested in whether, on balance, a

subject

should be called a risk-averter or a

risk-lover.

Rather, we want a ranking

o[

subjects

in

degree

o[

risk-

aversion.

For the Prisoner's Dilemma experiment,

we

need a measure of tendency to pursue cooperative behavior.

Let the

ranking

o[

tendency to cooperate be based on

the

number

of

times, during the

first 13

trials, in which the

subject

chose strategy

I

(remem- bering that he received no encouragement from his

"opponent-partner"

during this period). With these two

rankings---it

seems un- warranted to suggest that we have any information stronger than rank

data--a

rank correlation test (see Kendall, 1955)

can

be performed to test the null hypothesis that the difference in ranks can be attributed

to

chance. That is,

the

null hypothesis suggests that there is no underlying relationship between

the

two ranking variables. This would, of course, be a

one-tailed

test, since

we

are hypothesizing

that the

number of trials

in

which strategy I was chosen by

the

subject and the number

of risk-averting

choices he has made in the lottery experiment

will

be negatively correlated.

5

Originally we expected that

the

reactions

of

a subject

to the stooge's

switch to strategy 1

would

provide data relevant to cooperation. As

it

turned

out,

several subjects during that stage suspected that they were

not

playing against a

real

opponent.

Also,

some discovered that they could

"doublecross"

without

eliciting

any

response

from the opponent. Thus we do

not

report any results which include the last

lg

trials, though

our

conclusions are not markedly different when account

is

taken

of all

25 trials

for

each subject.

aT he 50

choices involving

9/10-1/10 prob-

abilities were omitted from this

part

of

the

anal- ysis because

of

probability "distortion" prob-

lems (see, for

instance, Edwards, 1953,

1954a, 1954b).

However, with these choices included

the

results were

not

substantially different.

*

We

do not

mean to suggest, however, that choice

of the

left lottery is evidence that can be used to classify

such subjects

as

"risk-lovers." Since the

left lottery has higher

actuarial

value, a

"risk-averter"

might still

pick

the left lottery, feeling that

the

higher

actuarial

value would compensate

him for the

increase in risk. The arguments are spelled out in

Dolbear

and

Lave (1966).



0 1 2 3

4

5 6 7 8

'"~' !

mean

=3,6 med|an=4 4-

MATRIX II

!

variance

= 3.8

3. I

!

I ! i

il l

_.

-

......

oi ~ ~ ~ ~, ~ ~ ~,

8

~ meclian=3

me

an=3.3 I

MATRIX I!! 7

i

variance = 0.7 6

J

,

! !J i

.. __

I 1. J

........_..

,..

t

! ..

.

-

.....: ~

.... ...

~.

512

F.TRENERY DOLBEAR,

JR.,

AND LESTER B. LAVE mean

and

median =

4

MATRIX I variance =

4,5

3 2

1

.I-.

O

e~

_Q

o

~9

_O

E

Z

0 1

2

3 4 ~

6 /

8

y Number

of

Strategy

1's

Chosen

FIO.

2. Number

of

times strategy i was chosen by subjects using each

of the

three payoff matrices. CONFLICT RESOLUTION

VOLUMEX

NUMBER 4



RISK ORIENTATION AS A PREDICTOR

513

TABLE

3

CHOICES or STRaTEC?

1

BY TataL AND MATreX

TABLE 4 RANK CORRELATIONS

OF

SEVERAL

VAIiIABLES

RELATED TO

LOTTERY CHOICES AND

CHOICES

OF

STRATEGY 1 Trial

1 2

3 4 5 6 7 8 9

10 11 12

13 Proportions

for

trials

1,

2,

and

3: Matrix I Matrix II Matrix III 7 11 9

10

9 10 5 8

10

4 6 3 5 6 3 5 2 3 3 2 2 2 3 0 4 2 2 3 3 4 i 4 3 4 0 0 3

I

1

22/56 ~s/5s 29/5o (39,%) (48%) (58%)

Definitions

of vanking

variables: RA 150--number

of

relatively risk-averse choices on 150

1/2-1/2

lottery pairs RA 50--number

of

relatively

risk-averse

choices on 50 9/10-1/10 lottery

pairs

RA 200 -- number

of

relatively risk-averse choices on

all

200 lottery pairs

S-l's T--total

number of strategy

1's

chosen in first 13 trials

S-l's

C -- number of consecutive strategy 1's chosen at beginning Banking

KendaWs

Number variables

tau ?%

S-l's

T

vs.

RA 150 -.065 .60 S-l's T vs. RA 50

-.017

.16

S-l's

T vs. RA 200 -.064 .59 S-l's C vs. RA 150 -.153 1.35 S-l's C vs.

RA 50

-.105

.92 S-l's

C vs. RA 200

-.161

1.42 V. Results Our third major hypothesis stated that, if

our

formula

held,

the majority

of

subjects should either succeed in reaching coopera-

tion

or make a strong attempt.

For

the three matrices we are dealing with, n (the number

of

trials) must be greater than one; since n -- 25,

all

subjects are expected to attempt cooperation. On

the

other hand, since our subjects were

actually playing

a stooge, cooperation was not possible. Figure 2 shows the distribution

of

subjects by the number of times they chose strategy i in the

first

13 trials.

An

inspection

of

data from paired subjects in this type of game

(Lave,

1960) indicated that a subject

who

chose strategy i three or more

times was

extremely likely to achieve cooperation. By this rather con-

servative

criterion, 76 percent of the subjects in

the

present experiment

made

a strong attempt at achieving cooperation during

the

first 13 trials. Our second hypothesis concerned differences in behavior associated with

the

three matrices: that the mean number of times strategy I was chosen in Matrix

I would

be greater than the means

for

the other

two

matrices; that the variance about this mean would be greatest for Matrix

I and

least

for

Matrix

III;

and that early trials

for

Matrix

III

would show a greater

proportion of

strategy

1

choices than would the other

two

matrices. The means

and

variances are given in Figure

2.

Both statistics display

the

order

we

hypothesized,

but

the differences are too small to be

significant--except

that Matrix

III

does have

the

least variance

and

it is clear that this difference is significant. The distribution

of

strategy

1

choices by trial is shown in Table 3 and the ranking is consistent with

the

hypothesis: on the first three trials, Matrix

III got

58 percent

of

the strategy

1

choices, Matrix

II

got

48

percent,

and

Matrix

I

got

89

percent. Since

the

selection

of

the cutoff point for "early trials" is arbitrary, it is not clear in this case what a test

of

significance would mean. However, it should be remarked that the ranking is



5.14

F.TRENERY DOLBEAR,

JR.,

AND LESTER B. LAVE not sensitive to

the

arbitrary definition

of "early

trials." It might be useful to pause here and summarize the evidence

for

this second hypothesis on the comparison

of

the three matrices. The mean cooperative response is

not

significantly different; thus we cannot reject the null hypothesis

of

no difference among these matrices. We might conclude that utility does

secm

to be approximately linear with money over the range in ques- tion. On the other hand, the third matrix shows a marked difference from the others both in the variance

of

choice and in choices on early trials. Our

first

hypothesis stated a negative relationship between the number

of risk-

averse choices in the lotteries and the number

of

strategy i choices in the Prisoner's Dilemma. When this hypothesis was tested with a nonparametric statistic,

Kendall's

tau measure

of

rank correlation (Kendall, 1955), the result

was

in the expected direction but statistically insignificant, as is shown in

Table

4. Several other correlations are

also

reported in Table 4. Two additional measures

of

relative

risk-aversion

were used: number

of

relative risk-averse choices on the 50

lot-

teries with 9/10-1/10 pairs, and number

of

relative risk-averse choices on

all

200 lottery pairs. Table

4

also includes an additional measure

of

tendency to cooperate: the number

of

consecutive strategy 1 choices at the beginning

of

the Prisoner's Dilemma experiment. Again, the results are in the expected direction but

not

statistically significant. An implication

of

our second hypothesis is that variation in matrix

for

the Prisoner's Dilemma should affect the above correlations to some degree. However, partition

of

subjects on the basis

of

which matrix they used seemed to make no significant differ-

ence.

The results

of

this exercise are

not

reported.

VI.

Discussion Our results indicate that data on

the

perception

of

risk are not good

predictors of

behavior in the Prisoner's Dilemma.

The

relations are in the direction hypothesized,

but

are not

significant.s

The lottery data were comprehensive enough that, were

we

to redesign the experiment, we would

con- centrate

on the Prisoner's Dilemma aspect. The dummy player may not have been

re-

sponsive enough to bring out subject

differ-

ences.

However, a contingent dummy strategy or even one involving some choices

of

strategy i is likely to produce data that are impossible to test or that embody too many aspects

of

individual interpretation to be a significant predictor. For example, a strategy I choice by the stooge on trial 5 might be viewed variously as an indication that he is

now

"reformed" or, by contrast, as a Machiavellian attempt to exploit

the

subject's

stupidity. Even were such inter- pretations distributed randomly with respect to risk preference, they would compound the difficulties

of

getting significant results. We must conclude that a

subject's

basic attitudes toward risk do not affect his behavior in a Prisoner's Dilemma situation. Or,

if

they do have an effect,

it

is

not

very large. Experimenters who have been forced to "assume away" differences among

sub-

jects'

attitudes toward risk may regard these results as support

for

such an assumption.

s Pilisuk

et

al.

(1965) report an attempt to identify a risk effect which can explain

coopera-

tive and noncooperative behavior in a two-person

mixed-motive

game. Among the personality variables they used were

two

measures of risk attitude: ( 1

)

a

set of

choices among monetary gambles, and (2) a measure of social risk preference (see

Kogan

and Wallach, 1961). No

sigmificant

effect was reported. CONFLICT RESOLUTION

VOLU/VIEX NUSfBER4



RISK


515

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N., and M. A. WALLACH? "The Effect

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Anxiety on Relations Between Subjective Age and Caution in an

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P. H. HocH and J. ZtmiN

(eds.),

Psychopathology

of

Aging.

New York: Grune and

Stratton, 1961.

LAVE, L.

"Factors Affecting Cooperation in

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Prisoner's

Dfiemma,"

Behavioral Science,

10 (1965),

26-38?

~. "Applications of

the Theory

of

Games to Economics." Unpublished A.B.

dis-

sertation, Reed College,

1960. LUCE,

R. D., and

H. RaIrrA. Games and Deci- sion,.

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M., P.

POTTEa,

A.

RAPOPORT, and J. WINTER.

"War Hawks and Peace Doves: Alternative Resolutions

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Experimental

Con- flicts," Journal of

Conflict Resolution, 9, 4

(Dec. 1965), 491-508. RAPOPORT,

A., and A.

C}rAMMAH.

Prisoner's Dilemma. Ann Arbor: University

of

Michigan Press, 1965. and C.

ORWANT.

"Experimental Games: A Review," Behavioral Science, 7 (1962), 1-37? REFERENCES

BERNOULLI,

D? "Exposition of a New Theory on the Measurement

of

Risk," translated by Louise Sommer,

Econometrica, 22

(1954), 23-36.

DOLBEAR,

F. T.,

JR.

"Individual Choice Under

Uncertainty--An

Experimental Study,"

Yale

Economic Essays, 3

(1963.), 419-69. and L. LAVE.

"Inconsistent Behavior

in

Lottery Choice Experiments,"

1966

(to appear in

Behavioral Science). EDWAlmS, W. "Probability-Preferences

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bling," American Journal of

Psychology, 66 (1953),

349-64.

?

"Probability-Preferences

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American Journal of

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GALLO, P., JR.,

and C.

McCLrNTOCK.

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tive

and Competitive Behavior in

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M. G.

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risk orientation as a predictor in the prisoner's dilemma

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