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Free-Rider Problems in the Production of Collective Goods

Jean Hampton

Economics and Philosophy / Volume 3 / Issue 02 / October 1987, pp 245 - 273

DOI: 10.1017/S0266267100002911, Published online: 05 December 2008

Link to this article: http://journals.cambridge.org/abstract_S0266267100002911

How to cite this article:Jean Hampton (1987). Free-Rider Problems in the Production of CollectiveGoods. Economics and Philosophy, 3, pp 245-273 doi:10.1017/S0266267100002911

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Economics

and

P hilosophy, 3,1987, 245-273. Printed in the United States of America.

FREE RIDER PROBLEMS IN THE

PRODUCTION OF COLLECTIVE

G O O D S

JEAN HAMPTON

University of Pittsburgh

There has been a pers isten t tendency to identify w hat is called the free-

rider problem in the production of collective (or public) goods with the

prisoner's dilemma. However, in this article I want to challenge that

identification by presenting an analysis of what are in fact a variety of

collective action problems in the production of collective goods. My

strategy is not to consult any intuitions about what the free-rider prob-

lem is; rather I will be looking at the problematic game-theoretic struc-

tures of various situations associated with the production of different

types of collective goods, thereby showing what sorts of difficulties a

com munity concerned with their voluntary production would face. I call

all of these dilemmas free-rider problems because in all of them certain

individuals find it rational to take advantage of others' willingness to

contribute to the good in a way that threatens its production. Some

readers may feel that the term 'free-rider problem' is so identified with

the prisone r's dilemma th at my extension of the term in this way jars ;

if so, I invite them to coin another word for the larger phenomenon. My

aim is not to engag e in linguistic analysis but to attempt at least a partial

analysis of the com plicated structu re of collective good produ ction.

In fact, free-rider prob lem s of this sort are neither pu rely m athem ati-

cal nor purely practical difficulties; they are a function of both the mathe -

matical structu re of the situation and of hum an psychology. If we believe

that human beings act in ways that are primarily, or even exclusively,

The author would like to thank David Gauthier, Isaac Levi, Alan Nelson, Christopher

Morris, Yoram Gutgeld, Jon Elster, a referee for Economics and Philosophy, and Russell

Hardin (whose work sparked these speculations) for their very helpful comments on

earlier drafts of this pape r.

© 1987 Cambridge University Press 0266-2671/87 $5.00 + .00 2 4 5

http://journals.cambridge.org/





46

JEA N H A M P T O N

self-interested, then producing these goods becomes problematic when

the game-theoretic structures underlying their production present to

people exploitative opportunities that are individually rational but collec-

tively irrational for them to take. So, once we understand these various

mathematical structures, we will see when and how human self-interest

can derail the production of these goods.

But it turns out that self-interest is not as much the enemy of their

production as traditionally thought. I will argue that many collective

action problems are (or can be transformed to become) coordination rather

than conflict dilemmas, so that the production of collective goods in

many situations need not require help in the form of sanctions from the

long arm of the state. Hence my analysis should be good news to those

who wish to encourage politically uncoerced cooperation.

I. THE CLASSIC

BUT

INCORRECT

PD

ANALYSIS

OF

FREE

R I D I N G

Stating the nature of the free-rider problem in English appears easy: any

public good which is indivisible but nonexcludable would seem to be

one whose benefits an individual can enjoy without paying for them, but

if too many people try to take this "free ride," either no amount of the

good, or else only a less than socially optimal amount, will be produced.

Nonetheless, this statement of the nature of the problem is blurry.

Rawls (1971, p.267) makes an attempt to get a better statement of it as

follows:

where the public is large and includes many individuals, there is a tempta-

tion for each person to try to avoid doing his share. This is because what-

ever one man does, his action will not significantly affect the amount

produced. He regards the collective action of others as already given one

way or the other. If the public good is produced his enjoyment of it is not

decreased by his not making a contribution. If it is not produced his action

would not have changed the situation anyway.

1

Russell Hardin (1971; 1982, chapter 2, esp. pp. 25ff) has constructed the

game-theoretic matrix suggested by Rawls's remarks, and it is repro-

duced in Figure 1. It depicts a situation in which the collective good will

not exist unless at least two people work to produce it; and the more of

them who produce it, the less the cost of production to each. In this

matrix, the individual's preferences are compared with the preferences

of the rest of the group. For our purposes, only the individual's prefer-

ences are important, hence they are underlined (1 is most preferred, 4 is

least preferred). Note that they match the preferences of any participant

of a prisoner's dilemma. In this situation, it is rational for the individual

1.

This passage

is

also cited

by

Richard Tuck

(1979, p.

147).






L i

L 2

4 3

3_ 3

FREE RIDERS

ND

COLLECTIVE

GOODS 47

THE COLLECTIVE

Pay Not Pay

THE

INDIVIDUAL

Pay

Not

Pay

FIGURE 1

not to pay, no matter what the others do (assuming standard probability

assessments). And since every other individual would have the same

preferences relative to the rest of the collective, then it seems that it isn't

rational for any of them to pay the cost of production. Hardin concludes

that the voluntary production of collective goods can only succeed when

this PD interaction is part of a series of such interactions, or when it is

embedded in a wider set of interactions such that the cooperative action

dominates (1982, chapters 9-12). (Note that it might also be solved if

each player has the rather unusual probability judgment that the others

are likely to do what she or he does.

2

)

However, a number of theorists, including Hardin

himself,

have

questioned the strict equation of free-rider problems with prisoners'

dilemmas.

3

1 will now argue that they are right to do so.

II. DEFINING COLLECTIVE GOODS

Collective goods can be defined as goods that benefit a collective and

that are indivisible or in joint supply, that is, making them available

to one person in the community makes them available to all. Free-rider

problems arise in the production of these goods when benefits from

them are either difficult or impossible to exclude from people who do not

2.

For more on this possible (but controversial) solution to PD games, see Jeffrey (1965).

3.

See Hardin (1982, chapter 4, pp. 58-61). Taylor and Ward (1982) want to argue that

many free-rider problems are not PD's but chicken games. Frohlich, Oppenheimer, and

Young (1971) suggest that the PD is not the correct game-theoretic structure, and

Frohlich and Oppenheimer (1970 and 1978) show that there are situations in which

voluntary production of these goods is individually rational. This argument is extended

and deepened in Frohlich, Hunt, Oppenheimer, and Wagner (1975), which is discussed

in footnote 4.






248 JEAN HAMPTON

Amount

of

Good

9(x)

T o t a l C o n t r i b u t i o n s

F I G U R E

2

contribute to their production. I will contend in this paper that under-

standing particular free-rider problem s depen ds upon un ders tand ing the

relationship between

th e prod uction structu re of the collective good in ques-

tion and the individual grou p m em ber's expected costs and benefits asso-

ciated with its production. My strategy for revealing these problem s m ust

therefore beg in with a technological definition of different kinds of

collective goods: tha t is, I will define them not by aggregating individual

contributions an d benefits, but by aggregating produc tion contributions

(regardless of who pays) and amounts of the good thereby generated.

4

As Hardin (1982, chapter 4) has discussed, some collective goods

only exist after a substantial amount has been contributed to their pro-

duction, and then do not increase in quantity or quality if any further

contributions are m ade . Figure 2 depicts such a good. These goods have

been called pu re step go od s (or lum py goods ) because their creation

4. I am ind ebted to Jack Hirschleifer for this characterization of my approach . I developed

this approach, as well as the arguments in this paper, in ignorance of the trailblazing

paper of Frohlich et al. (1975), who also insisted that free-rider problems have to do

with the shap e of [individu als'] utility functions and of the production function go vern-

ing the supply of the collective good (p. 328). However, to make this point, they

followed Schelling (1973) in employing a graphical representation of n-person, binary

choice games with externalities in which the number of contributions to the good is

represented on the horizontal axis and an individual's benefit from the good is repre-

sented on the vertical axis. Although this technique enabled them to show that some

free-rider problems are not prisoner's dilemmas, it did not allow them to show that,

dep end ing upo n the extent to which a collective good is (or can be) produced in larger

or smaller increments, a variety of (primarily coordination) problems can arise in con-

necting possible producers to the good's (naturally or artificially defined) increment(s).

In this paper I am ex perimenting with the use of a different technique in order to make

this general p oint.






FREE RIDERS ND COLLECTIVE GOODS

49

Aaount

of

Good

Total Contributions

FIGURE

3

involves taking

one big

production step

and no

more. Examples

of

these

goods include

the

election

of a

political candidate

and

objects such

as

bridges (half

a

bridge

is no

bridge

at

all). We

can

define this type

of

good

using

the

following step function: 8 x)

=

0

for x < c; = k for

x

2 c.

Other goods come into existence in degrees of quantity or quality,

and successive contributions to their production result in further incre-

ments of the good (in quantity or quality). I call such goods increm ental

collective go od s. They can vary from being quite ste pp y, as the graph

in Figure 3 represents, so that a certain fairly large contribution level

must be reached in order for an increment of the good to be produced

(for example, the co nstruction of railway lines connecting small towns),

to being completely continuous such that any contribution, no matter

how small, will result

in

some increase

in the

good (e.g., clean

air or

clean w ater), until some n atural bo und ary is reached.

Let

us

define

the

function

in

Figure 3

as

follows: G

v

=

o

2 A#° where v is

the total number

of

increments produced

(at a

given contribution level)

and Ag

a

is the ath

increment

of the

good. Note that

we can

define

a

continuous incremental good

as a

function

of

contribution level (c)

in the

following

way:

G c) = dg(c')

c'=0

where g is a function which takes contribution levels as arguments and

which measures the rate of increase in the amount of the good being

produced.

Finally, collective goods

can

have

a

mixed structure .

For

example,

bringing

a

collective good into existence

can

initially require

a

large






250 JEAN HA MP TO N

production step bu t increasing this good in quality or quan tity thereafter

can require only small contributions over a certain range. Hence, al-

though creating a minimally effective bridge over a river is a step good,

this bridge's strength and effectiveness might be increased by reinforc-

ing its structure up to a certain point, so that after a certain large step

such as the one represented in Figure 2, the good subsequently has the

sort of incremental or continuous structure which is represented in Fig-

ure 3, and which we could describe using the following step function:

dx

=0 for

x <

c;

= f(x)

for

x

5= c where f x) is a function with /(c) =

k

a nd

which monotonically increases (where it may or may not be continuous).

Or we might have a partial step good in reverse , that is, a good which

exists naturally at some level and which does not decrease with con-

sumption until some critical consumption point is reached. This good

can be defined with the following function: O(x) = k for x =£ c and 0(x) =

C(x)

for

x > c

where / ' is a monotonically decreasing function whose

maximum value is k. (A gain /' may or may not be continuous.)

A pure step good is really just a collective good with only a single

increment, and a mixed good is just an incremental good whose incre-

ments are vastly unequal in size. So we might say that all collective

goods are incremental in different ways: some have only one increment

(these are step goods); some have more than one increment, where the

size of the increme nts can vary and w here there may or may not be some

natural bound on how many increments can be produced; and some

goods have increm ents that are infinitesimally small (continuous goods).

But for purposes of understanding the problems involved in producing

collective goo ds, there is a significant distinction betw een w hat I will call

step goods, which have only one increment, and what I will call incre-

mental goods, which have more than one increment (and which include

mixed goods and continuous goods). This two-part classification is what

I will be primarily re lying upo n in the res t of this article.

I I I .

TH E BATTLE-OF-THE-SEXES PROBLEM IN THE SELECTION

OF PRODUCERS OF STEP GOODS

We begin by examining free-rider problems involved in step good pro-

duction. There are two places in which these problems can occur: In this

section w e will explore prob lems involved in the selection of producers to

produce the good; and in the next section we will look at problems

involved in the actual

production

of the good by those selected to do so.

To show that w ha t are called Battle-of-the-Sexes problem s are in-

volved in the selection of producers of a step good, I will use as an

example of the production of such a good, Hume's meadow-draining

project:






FREE RIDERS

AND

COLLECTIVE

GOODS

251

Two neighbours may agree to drain a meadow, which they possess in

common; because 'tis easy for them to know each other's mind; and each

must perceive, that the immediate consequence of

his

failing

in

his part, is,

the abandoning of the whole project. But 'tis very difficult, and indeed

impossible, that a thousand persons shou'd agree in any such action; it

being difficult for them to concert so complicated a design, and still more

difficult for them to execute it; while each seeks a pretext to free himself of

the trouble and expense, and wou'd lay the whole burden on others. (Ill,

ii,

vii

[1978,

538])

I will interpret Hume's remarks so that the situation has the following

structure.

1. Draining the meadow is a collective good: i.e., it is indivisible, non-

excludable, and a benefit to the grou p.

2. It is a step good. It does not make sense to say that the drained

meadow can be increm entally increased in either quan tity or quality

after it comes into existence.

3. Individual production costs and benefits from the good are well de-

fined and commonly known, so that individual preferences for pro-

ducing the good are commonly know n.

4.

The group involved in producing the good is what Olson (1965, pp.

22-36 and 48-50) calls laten t as opp osed to privileged because

there is no individual in the group for whom V, — C

T

>

0. Here and in

the rest of the paper V, is the amount of benefits to the ith individual

and C

T

is the total cost.

5. Production costs can be split in a variety of ways among the 1,000

group members (that is, the group can define production units in a

variety of ways, and assign any number of group members to these

units), but the minimum number of people capable of producing the

good is two .

6. Finally, individual costs to prod uce the good are not retrievable. An

individual cannot recoup whatever he pays to drain the meadow

(e.g., monetary costs) before the good's production is completed.

We shall vary each of the last four features of the example in this and the

next section in order to reveal different types of free-rider problems in

the production of step goods. But supposing all six hold, what is the

game-theoretic structure of this situation?

Consider that., in order to get the meadow drained, Hume's people

must not only decide how many of their number shall participate in the

good's production (as we noted, it must be at least two), but they must

also decide who these producers will be if they choose a number below

1,000.

So they have potentially a two-pronged selection problem here:

they m ust determ ine the nu m ber of produce rs, and they mu st define th e

identity of these producers. Assuming people are largely self-interested,

what are their likely preferences in this sort of situation? We wou ld need






252

JEAN HAM PTO N

a 1,000-person matrix to represent them properly, but because I have as

little inclination to provide such a matrix as the reader has to see one, I

will simplify the situation by supposing there are only three people

involved, and then describe their preferences so as to reveal the game-

theoretic structure of this type of situation, whether there are three

people or 1,000 peop le involved .

5

Clearly each player would most prefer the outcome in which the

other two players drain the meadow and she languishes at hom e, eventu-

ally enjoying the good produced at no cost to her. Next best is the

situation where all of them share the work to be done, which is better

than the situation where she and only one other player split the work

between them (doing half of the work is worse than doing a third of it).

But this option is substantially better than the situation in which the

meadow isn't drained because none of them or only one of them is

willing to do it, and of course the worst situation for each of them is

where she puts in work almost equal to the benefit to be received from

the good to be pro duced , bu t is never assisted by anyo ne else, so that the

good never gets produc ed and she loses wh atever resources she put into

the attempt to produce it.

There is a nice sense in which each player in this sort of game wants

to ride free on the backs of the othe r players , insofar as each wants the

others to do the work involved in getting the good produced so that he

or she can enjoy the benefits of its production for free. Nonetheless, the

game is not a prisone r's dilemm a. A prison er's dilemm a is one in which

noncooperation dom inates over cooperation. But in this situation, nonco-

operation does not dominate. Although you should refuse to cooperate

if you think that the other two people will do so, you should not refuse -

that is, you sh ould vo lunteer to pay the cost of draining the m ea do w -if

you think that only one, and not the other, is willing to volunteer. It is

better for you to do the work to get the meadow drained than to let the

meadow go undrained. And of course you know that every other per-

son's preferences are the same as yours. Like you, they want to try to

get out of the wo rk, but like you , they also would rather do the work

than see the project a ban don ed.

This is a three-perso n, mixed-m otive or non-zero sum game

much discussed in game-theoretic literature. Luce and Raiffa (1957, pp.

90-94, and chapte r 6) call it the Battle-of-the-Sexes gam e after their

unfortunately sexist example of a husband and wife who each prefer

different evening activities (he prefers prize fighting and she prefers

ballet) but who would also rather go out with the other to his or her

favorite evening activity than to go to his or her own favorite alone. In

5. In Ham pton (1986, p. 151) I pres ent a 3-D matrix representin g preferences in a battle-of-

the-sexes gam e.







53

PERSON X

ACTION

A

ACTION

B

PERSON Y

ACTION

A

ACTION

B

1 . 2

3 . 3

3 , 3

2 , 1

FIGURE

4

order

to

facilitate

the

discussion

of

this game,

a

simplified two-person

version of it is given in the m atrix in Figure 4.

This type

of

interaction problem

is

still

on the

coordination side

of

the

game-theoretic spectrum since coordination of interest predominates and

there

is

more than

one

coord ination equilibrium (represented

by the

upper left and lower right cells) where this notion is stronger than a

Nash equilibrium

in

that

it

denotes

an

outcome

in

which

no one

would

be better off if any one player, either himself or another, acted differ-

ently.

6

In

this situation

the

parties are rational

to

reach

an

agreement

on

their actions so that o ne of these equilibria will be realized. However, the

relative advantages

of the

different coordination points introduce

con-

flict that mig ht prev ent them from coming to an agreem ent.

I have already hinted that there is ano ther battle-of-the-sexes prob-

lem that

can be

involved

in the

production

of

this type

of

good.

In the

meadow -draining example there appears to be a variety of ways of split-

ting costs such that considerably more than two people-maybe even

all

1,000 of the m -co uld participate in the good's production. A nd although

everyo ne will believe

it is in his or her

interest (as well

as in

the interest

of the group as a whole) to split the cost in some way, there might be

much disagreement among them about

the

way

to

split it. So

the

group

faces

a

battle-of-the-sexes problem not m erely over who will pay the cost

to produce

the

good

but

also over

how to

split those costs

in the

first

place. (Note that if they decide to split the costs equally among all the

members

of the

group, there will

be no

further battle-of-the-sexes prob-

6. This formulation is from David Lewis (1969, p. 14)






254 JEAN HA MP TO N

lem involved in selecting producers, although this outcome is not a

coordination equilibrium and so will not be stable.)

This analysis should illustrate

the

following point: free-rider problems

have

to do

with

the

relationship between

the

productive units

of the

good

and

individual costs

in

the comm unity.

Battle-of-the-sexes problems occur when

there is no one way to link individuals in the group to productive units

of the step good: either the units are fixed but the number of individuals

who would find it rational to join their fellows in producing these units

is greater than the number of units; or the units are not fixed, in which

case there are a variety of ways in which individual producers can be

linked to the (artificially defined) productive units.

7

The fact that

the

battle-of-the-sexes game

is a

type

of

coordination

game is critical in dete rmining w hat strategies are effective in solving it. I

have discussed the complicated issues involved in the solution of this

type

of

game elsewhere

(see

Hampton,

1986,

chapter

6.5.)

Suffice

it to

say here that the task of the players is to effect coordination on one

coordination equilibrium, where this

can be

done

via

explicit agree ment

or via the generation of a convention on a salient coordination equilib-

rium by the players. The latter non agre em ent solution to these dilem-

mas requires that the players determine the likelihood that the others

will pursu e

any of the

possible coordination equilibria,

and

clearly,

any

one playe r's estimation of probabilities h ere de pe nd s in part on what she

7.

Without actually presenting this battle-of-the-sexes analysis of free-rider problems in

step good production, the discussion of Frohlich et al. (1975) strongly sugg ests it. O ther

theorists whose discussion of free-rider problems suggests this game include James

Buchanan (1975, p. 37f) and Brian Barry (1982, p. 56). Taylor and Ward also come close

to presenting

it, but

they mistake

the

battle-of-the-sexes structure

of

this situation

for

the game of chicken, presented later in Figure 8. There is a big difference between the

game of chicken, w hich is a game of conflict, and the battle-of-the-sexes dilemm a, w hich

is a type of coordination game with some conflict of interest. The former has only N ash

equilibria, the latter has coordination equilibria; and whereas the former poses the

question, "Do we cooperate? , the latter poses the question, "How do we cooperate?

Taylor

and

Ward mistakenly assimilated

the two

because they defined (what they

called) the family of chicken games as games in which it is rational for a player to

attempt a pre-comm itment strategy, that is, one in which the player b inds himself to

his favorite outcome, thereby forcing the other player(s) to pursue that outcome (on

pain of irrationality) also. However, this strategy is advised not only for players in a

chicken game but also for players in a battle-of-the-sexes dilemma, each of whom

should

try to

bind himself irrevocably

to his

favorite coordination equilibrium, thereby

forcing

the

other player(s)

to

accept

it or

else lose

all

chance

of

realizing

a

desirable

coordination outcome. It turns out that one cannot define chicken gam es in terms of a

strategy that those who are in a significantly different game-theoretic situation would

also be rational to follow. Non etheless, as we shall discuss later, Taylor and Ward are

right to think that some free-rider problems are true chicken games. Our analysis will

show that these chicken games arise

not in the

context

of

getting

the

producers

of a

collective good selected, but rather in the context of getting previously selected produc-

ers of the collective good to pe rform.






FREE RIDERS

AN D

COLLECTIVE

GOODS

255

believes the others believe about which coordination equilibria she will

pursue.

This analysis sho w s tha t if, in the course of deliberating about being

one of the producers of a step good, I reason in the way that Rawls

describes, re gar di ng] th e collective action of othe rs as already given

one way or the oth er , then I am reasoning fallaciously. Because this is a

situation calling for coordination, it is what Elster (1979, pp. 18-19, 117-

23) calls a strateg ic situation . W hereas a param etric choice situation

is one in which the actor's behavio r is the sole variable in a fixed environ-

ment, a strategic situation is one in which an actor's behavior is but one

variable among others, so that his choice must take into account his

expectations of these others' choices even as they must take into account

their expectations of his and others' choices. The choice situation just

described qualifies as strategic because whether others will volunteer to

be the good's producers depends in part upon their expectations of

whether I or other members of the group are willing to do so. In this, as

in any coordination ga me , each person should make her decisions mind-

ful of her strategic situation, aware that her preferences will have an

effect on the other players, whose preferences will have an effect on

hers. If she reasons param etrically (as Rawls essentially suggests), she

is not trying to effect a coordination of all the players' actions; instead

she is treating the rest of the group as a single entity unmindful of her,

believing that their choices are fixed independently of what she will

choose (although she is not sure quite how) such that her choice is the

sole variable in the environment. The analysis in this section shows that

such reasoning is mistaken.

How ever, a reader might wonder w hether a parametric choice in this

situation will be not on ly justified bu t also inescapable if the actor does no t

have adequate information about what others' expectations and prefer-

ences are and thus has no easy way to coordinate his actions with them.

W henever such a lack of information exists, feature 3 of Hu m e's meadow-

draining case does n ot

hold:

that is , individual costs and benefits involved

in the good 's production are not commonly kno wn . And if there is no way

to persu ade som eone to provide that information, it

is

impossible to make

one's choice responsive to others' expectations, so that one must choose

parametrically, u sing an expected utility calculation in which one tries to

estimate the probability that one is necessary to the production of the

collective step good. There are a variety of ways in which this calculation

might go, but if one's estimate of the probability is sufficiently low, one

will conclude that it is not rational to contribute; and if everyone comes to

this conclusion, the collective good will not be produced.

But this lack of information does not make the battle-of-the-sexes

structure of the situation disappear, as Pettit (1986, pp. 369-70) has

argued; instead, it makes the achievement of coordination in this battle-






256 JEAN HA MP TO N

of-the-sexes situation virtually impossible because there is no way that

the players

can

develop

or

come

to

know

of a

salient coordination

equilibrium

at

which

to

aim. This point

is

im portant

not

merely

for the

sake of getting the game-theoretic structure of the situation right, but

also for the sake of understanding how to solve it. Whereas peop le fail to

cooperate in a prisoner's dilemma because it is individually irrational to

do so, in the situation just described people fail to cooperate because

there is a dearth of information enabling them to coordinate on a coopera-

tive outcome. If that information is supplied, cooperation is possible.

The economic geom etry of the situation is different, so that the prob-

lems preventing cooperation,

as

well

as the

remedies that will effect

it,

differ in

the

tw o cases.

Indeed,

the

fact that

we are not

dealing with

a

prisoner's dilemma

can explain why it is possible to credit the success of (what appear to be)

latent groups

in

providing collective goods

to the

work

of

political

en trep ren eur s. These are people willing to pay the cost of providing the

information necessary to produce public goods because they perceive

that this activity will pay off for them

individually

in a big way; e.g., it

might enhance their careers or increase their power. But political en tre-

preneurs couldn't, for example, organize the building of a bridge if

people really were

in a

prisoner's dilemma situation

in

which noncoop-

eration dominated. That

the

people face

a

coordination problem

in get-

ting the good produced, only lacking an organizer who can help effect

the coordination

by

obtaining

the

needed information,

is

something that

his organizational activity pres upp ose s.

Estimates of how often lack of information will attend the produc-

tion of step goods are hard to make from a philosopher's armchair.

Economists and other social scientists are in a better position to make

these estimates than I am. But one won ders w hether, even if the prob-

lem were common, political entrepreneurs would frequently be available

(or recruitable, if the gro up had the resources to pay them in some way)

8

to help resolve it, paving the w ay for voluntary cooperation.

Feature 3 also does not hold when information about the cost of

producing the step good is lacking. In this sort of situation, it would be

reasonable for the group to make an estimate of the cost, and then

proceed to try to find producers to pay it such that the good will be

produced.

But if I am

deciding wh ether

or not to be a

producer,

I

will

note that

as

long

as the

other p roduc ers pa y their share

of

the estimated

cost,

my

contribution might

not be

necessary:

if the

estimate

is

wrong,

then either it is too high, in wh ich case the good will be produced by the

others without my contribution, or the estima te is too low, in which case

8. Frohlich et al. (1970, p. 119) suggests that groups may find it rational to subsidize

voluntarily the pay of political entrepreneurs.






FREE RIDERS AND COLLECTIVE GOODS

257

the good will not be produced even if I do contribute. Of course, the

better the estimate and the higher my stakes in getting the good pro-

duced, the more likely an expected-utility calculation will dictate that I

produce. But w hen the estimate of the goo d's cost is poor, and/or wh en

one's stakes in getting it produced are low, an expected-utility calcula-

tion will likely dictate against pro duc tion. Perh aps the grou p might have

certain devices available to them that could remedy this situation; for

example, they might deliberately overestimate costs but then allow some

individuals whose contributions prove to be unnecessary to retrieve

them . But if such rem edies a re not possible, then the group is once again

faced with a s i tuat ion which, although still a battle-of-the-sexes problem, is

very difficult to solve coopera tively.

Finally, feature 3 doe sn 't hold if the step goods are themselves vague,

in the way tha t, for exam ple, a he ap of stones is vague. Such vague-

ness in the definition of these goods encourages people to reason in a

way that has been associated with wha t is called the Sorites paradox .

9

Each possible contribu tor may reason, My contribution to the hea p is

unnecessary; either the pile that exists already qualifies as a heap, in

which case my stone doesn't contribute anything to the heap's produc-

tion; or the pile is not a heap, in which case my adding one stone to it

won't suddenly cause it to be a heap, meaning that, once again, my

stone do esn 't contribute any thing to the hea p's production. Note that

this reasoning will be duplicated no matter

what

the e stimate of stones

needed to produ ce the he ap . In this situation, each member of the group

will believe she faces no t a single prisoner's dilemm a b ut wh at I will call

an ordered game set of prison er's dilemm as. For any estimate of wha t

is necessary to produce the good by some number

K +

1 producers

where K ranges from 0 to n - 1 (assuming there are n members of the

group), then Figure 5 shows how an individual will reason when deter-

mining w hethe r or not to join with

K

other producers to pay her sh are of

the estimated cost. Here it appears rational, no matter what the others

do, for her not to produce her share of the estimated cost. But Sorites-

like reasoning is supposed to be a

mistake,

so that the situation ought to

have a battle-of-the-sexes structure. There are, thus far, no uncon-

troversial proofs showing how it is fallacious, a lthoug h even were one to

be given, it still seems to be the kind of (fallacious) reasoning that people

would find te mp ting, to the detriment of the grou p.

Let me conclude this discussion of producer-selection problems in

step good p roduc tion by varying features 4 and 5 of Hu m e's example in

order to see how the production of the step good is affected.

9. See Tuck (1979, p. 152), who cites Crispin Wright's argu me nt (1976, pp . 223 and 247)

that this paradox arises out of the vagueness of our criteria for defining certain entities,

such as hea ps.






258

JEAN

H A M P T O N

THE COLLECTIVE

PRODUCE

NOT

PRODUCE

THE

INDIVIDUAL

PRODUCE

NOT

PRODUCE

2

1

4

3

FIGURE 5

Theorists have generally thought that if feature 4 doesn't hold and

the group charged with producing a collective good is privileged rather

than latent, th ere is no collective action problem in the produc tion of the

good. But this isn't true. Privileged groups can also face a battle-of-the-

sexes problem in their attempts to produce a collective good if there is

more than one person for whom the value to her as an individual is

greater than the total cost. In this case, the group must determine which

of these individuals will produce the good, or else work out a way for

them to share the production costs. Clearly it is in the interest of these

individuals to try to escape paying for the good unless doing so would

jeopardize its production . Theorists have tended to overlook the fact that

this kind of free-rider problem can exist in privileged groups because

they have concentrated only on problems involved in getting people to

pay the costs of production, rather than on problems involved in selecting

people to pay those costs. A privileged group will produce a collective

good only if it solves the selection problem .

Finally, sup pose w e change feature 5 of Hu m e's m eadow draining

case-the feature that costs can be split in a variety of ways among more

than o ne individual. If production un its of a good are fixed and uniquely

assignable to mem bers, the n there is no battle-of-the-sexes problem asso-

ciated with the selection of the good's producers; indeed, there is no free-

rider selection problem at all in this situation. Assuming tha t i t i s common

knowledge that only these members can produce the good by paying

only these units, they are rational to volunteer to produce it, because

they know it will not get produced unless they do so, and they know

that they are better off by paying their share of the cost of production

and producing the good than they are by not paying the cost and living






FREE RIDERS AND COLLECTIVE GOODS 259

PERSON A

PRODUCE DON T PRODUCE

PERSON B

1 .1

2 , 2

2 . 2

2 , 2

PRODUCE

DON T

PRODUCE

FIGURE 6

without it. Hirshleifer (1983) has suggested that this is actually the way

people perceive their situation in times of disaster: each of them believes

he or she is the weakest link in a fragile chain of produ cers necessary

to prev ent a public bad or create a public good.

My analysis in this section has demons trated that, in general, coordi-

nation problems, rather than conflict problems, attend the selection of

producers of these goods, so that it is not the individually rational pur-

suit of collectively irrational outcomes, but paucity of information's pre-

venting successful coordination, that threatens successful production of

these goods. However, before we can conclude that there are usually no

conflict problems involved in the production of collective goods, we

need to analyze the game-theoretic structure of the situation after indi-

viduals have been chosen to produc e the step goo d.

IV . FREE-RIDER PROBLEMS IN THE P R O D U C TI O N OF STEP

GOODS FOLLOWING THE SELECTION OF PRODUCERS

How we answer the question of what sorts of problems are involved in

producing go ods after their produ cers have been selected de pen ds upo n

whether or not production costs are retrievable.

10

In my reconstruction

of Hume's meadow case, they were not; this was feature 6 of that case.

But if feature 6 does not hold and production costs are retrievable, no

further free-rider problem prevents th e good 's production (see Figure 6).

In this gam e, the preference for paying is the same as the preference

10. I am told th at aspects of the following argu me nt are know n in some circles; I do no t

know of any place wh ere they have been p ublished.






260

JEAN HAMPTON

PERSON A


PERSON B

PRODUCE

DON T

PRODUCE

1 ,1

2 . 3

3 , 2

2 . 2

FIGURE 7

for not paying in the unilateral breach situation because any costs paid

can always be retrieved if the other produ cer fails to contribute. Thus th e

action of pay ing do minates weakly over the action of not paying .

However, there are interesting free-rider problems in the production

of these goods if feature 6 does not hold and costs are not retrievable.

One such problem is a variant of the assurance problem explored by Sen

(1973, pp. 96-9; 1967, pp. 112-24), presented in the matrix in Figure 7.

This dilemm a is a species of coordination problem with two equilibria

(the upper left and lower right cells) in which each player is rational to

cooperate if the other player coope rates, and each is rational not to do so

if the other does not cooperate. Thus, before cooperating each needs to

be assured in some way that the other player will also do so. Insofar as

the players are the designated producers (and insofar as they know that

no one who has not been designated producer will produce the good),

they cannot expect the realization of any of the outcomes represented in

the battle-of-the-sexes matrix in which they do not do the work but the

good is produced anyway. However, each knows that if all of the desig-

nated producers do their share of the work, the good will be produced

(the situation represented by the up pe r left cell of the m atrix in Figure 7),

and each also knows that if some of them don't do their share, then the

good will not be produced and those who have worked to produce the

good will lose their investment without getting any benefit from the

good (because it won't exist-this situation is represented by the lower

left and upper right cells of the matrix). Of course, it is rational for

everyone to work together to produce the good, but how can each pro-

ducer be assu red that th e othe rs will actually do so?

If, as they produce the good, they can watch one another working,

then each of them can be completely assured that the others are doing






FREE RIDERS

AN D

COLLECTIVE

GOODS

261

their share. But if such scrutiny is not possible, and if they cannot get

information about the extent to which the others are working, should

each of them do his/her share of the production work? Elster (1979, p. 20)

notes that the maximin rule dictates against doing so. But the maximin

rule-i f it is ever ap pro pri ate -w ou ld seem to be inappropriate in those

circumstances in which one is able to estimate the probability that the

others will do their shares. (And the principle of insufficient reason

could be used to estimate probabilities in situations of complete uncer-

tainty.) If the estimate is fairly high, e.g., if there is some way in which

the better coordination point is naturally salient, then it is likely that an

expected-utility calculation will dictate performance for each of them,

and the good will be produced. Moreover, any agreement among them

to do the work required would be a way to make doing the work the

salient action in the circumstances; each would estimate the probability

of the others' doing their tasks as fairly high. [I have argued (Hampton,

1986, chapters 6.2 and 6.5) that this is the most natural way to obtain

assura nce in any coord ination game,] In any case, it seems that th e

producers in this sort of situation would have a good chance of solving

the assurance problem.

However, if there exists what I call a critical cost po int, the produc-

ers face a far more difficult problem . Consider H um e's me adow -draining

example. Suppose the battle-of-the-sexes problem in the selection of

produce rs were solved, such that you and I are supposed to drain the

me adow , w here for each of us V

t

>

ViC

T

.

S uppo se further that each of us

will do so by digging irrigation ditches in the meadow that join together

and eventually drain into a nearby river. (Thus what we pay, i.e., our

labor, is irretrievable.) We both start to work, but after each of us has

done a quarter of the total work (so that half the work remains to be

done) I run off when you are not looking, leaving you alone to do the

rest of the work . Is it rational for you to do it?

Consider that you have paid your contribution, which is equivalent

to

V*C

T

and this is a sun k cost, since you cannot retrieve your time and

effort. So if you quit now, you are without the good and also without

ViC

T

,

so that your utility is

-ViC

T

.

But remember that half the work

remains and tha t for you V, >

V2C

T

.

If you continue to work and complete

the project, your utility is V, — ViC

T

- ViC

T

, which is clearly greater than

—ViC

T

.

So you are rational to com plete the job.

Thus, for any producer of the good, whenever the remaining cost of

producing a good can be split between all the

other

producers in the

group such that, for those other players, their benefit from the good

exceeds their share of the remaining cost, then tha t individual p roducer

is rational to cease work. This calculation dictates nonperformance at

what I call the critical cost point: that is, the po int at which it is rational for

only

some

of the selected p rodu cers of the good to pay the whole rem ain-

ing cost.






262

JEAN HAMPTON

PERSON A


PERSON B

PRODUCE

DON T

PRODUCE

2 , 2

1 , 3

3 , 1

4 , 4

FIGURE 8

If this critical cost point has been reached (and note that it might be

reached before anyone has paid any cost), what is the structure of the

game-theoretic situation faced by the producers? In a two-player game,

the matrix in Figure 8 describes the situation (e.g., in the meadow-

drainin g example) and as we see , it depic ts the game of chicken.

In this game there is no dominant action, which makes it impor-

tantly different from a prisoner's dilemma; nor are there any coordina-

tion equilibria, so that unlike the battle-of-the-sexes dilemma, it is not a

coordination game. Each player prefers the situation in which he is the

person rene ged upo n by the other, to the situation in which both renege,

whereas in a prisoner's dilemma, the latter is preferred to the former. So

in this game, if I believe you will pay the remaining share of the cost of

production, I am rational to renege, but if I believe you will not do so, I

should pay either the entire rema ining share or, as long as you continue

to put in your original share of the total cost involved, only the remain-

ing cost of my original share of the total cost. Indeed, in this sort of

gam e, if we

each

dis trust the othe r, the result will be that we will both do

the work required to get the good produ ced.

In any case, because th ere is no dom inant action in this sort of game ,

what is rational for either of us to do can depend upon a wealth of

contingencies. A nd as Taylor and Ward discuss (1982, pp. 354ff), we are

certainly well advised to try a precommitment strategy to force the oth-

ers) to cooperate while escaping that fate ourselves. So, in this kind of

situation each is trying to be a free rider, n ot in the sense that he is trying

to get out of being selected to be a producer, but in the sense that, as

someone who has already been selected, he is trying to get out of doing

some (or maybe even all) production work. Moreover, he is not (as in a







263

battle-of-the-sexes game) merely trying to score a "win" over the others

in the group, who will still "win" themselves as producers insofar as the

benefits they will get from the good exceed the cost to them of their

work; instead he is trying to score a win over others in the group who

will actually

lose

if he wins, insofar as they will end up by paying

more

for

the good produced than the benefit they will receive from it.

Note, however, that an individual's succeeding in being a free rider in

this second sense, thereby scoring a win in the chicken game, is not bad for

the collective. Of course it is bad for the loser, but the collective will still get

the good it desires. We have actually discovered a free-rider problem

which poses more difficulties for individuals than it does for groups

Nonetheless, the group will find it difficult to produce this sort of

step good if individuals realize before the producers are selected, that as

producers they run the risk of being exploited in this way. The possibil-

ity of exploitation changes the game-theoretic structure of the situation

from a battle-of-the-sexes coordination game to a prisoner's dilemma.

Each knows that if he contributes to the good's production, he stands a

high chance of being exploited by the others and paying more for the

good than he will receive from it; and he also knows that if he does not

pay anything for the good, either he will get the good for free or he will

at least not lose anything. Hence, no matter what the others do, it is

rational for this individual not to produce, since this action is both the

best defensive strategy and the best way to take advantage of an exploit-

ative opportunity. Every other individual's preferences will be symmet-

ric with his, so that no one will find it rational to produce the good.

11

What can members of a group do to change the structure of the

situation so that they can get the good produced?

1. The group can take steps to make production costs retrievable. If,

for example, paying the cost involves contributing money, the group can

make each producer pay into some kind of escrow account, such that

unless all the producers pay, the good will not be produced and the

individual's share of the cost will be returned. This strategy makes it

impossible for anyone to be an exploiter. (Note also that this strategy

solves any assurance problem involved in the good's production; I know

that I will pay to produce the good only when all the other producers

necessary to its production pay their share.)

2. Where retrievability isn't possible the group can try to destroy the

critical cost point. For example, they can use any time deadline for the

good's completion in the situation to accomplish this result. If the pro-

ducers start work at a point where each of them has just enough time to

11.

In

fact,

this is

what Pettit

(1986) calls a

"foul

dealer"

variant

of a

multiperson

PD

game,

because a lone defector makes one or more cooperators worse off than they would

have been had everyone defected.






264

JEAN HA MP TO N

complete his or her individual share of the productive efforts before the

deadline for the good's production but no time to take on anyone else's

share, then no one will be able to exploit the other workers: if one of

them ceases work, the others will not be able to take on this work and

complete the good's production before the deadline. So, because a re-

neger can gain nothing by his reneging action (indeed, he suffers a net

loss

equivalen t to the work he inve sted ), each producer is rational, as

long as he or she can be reasonably assured of the others' performance,

to work.

3. Selective incentives can be introduced to make the exploitative

option irrational.

However, the fact that the first two strategies can be used in a wide

variety of circumstances m ean s that m any step goods

can be made to be

(if

they are not already) goods whose production poses only coordination

problems (assurance and/or battle-of-the-sexes dilemmas) to the group.

An d these are problem s w hich it is quite possible to solve (if information

and mec hanism s for coordination exist) without the help of the state.

V. THE GAME-THEORETIC STRUCTURE UNDERLYING

THE

PRODUCTION OF INCREMENTAL GOODS

What about the production of incremental goods? Surely PD games

necessarily attend their production, so that the introduction of sanctions

will be required to get them produc ed at optimal levels?

To see if this is so, I want to discuss the production of these goods

using a nota tion that will facilitate precision. A nontechnical sum mary of

the results follows this discussion.

Let us define an inc remental g ood (G) as follows:

where v is the total num ber of incremen ts produced and Ag

a

is the ath

increment of the good.

12

To define the cost of production of a certain

amount of incremental good, let C

r

be the total cost of producing a

certain amount of that good. In order to simplify our problem and en-

sure that C

T

is well defined, let us as sum e tha t the cost of produ cing any

part of CT is the same for any individual

13

(e.g., suppose, as econo-

12. Recall that in the case of a continu ous public good th e definition wou ld go as follows:

G c) =

I dg(c ).

13. In the real world, the cost of producing Ag° would likely vary dep end ing upon which

individual w as asked to produce it, but w e ignore this complication h ere by assuming

that the cost of producing any increment is the same for any individual. However,

note that we are

no t

assum ing that produ cing each increment of the good costs the

same amount.






FREE

RIDERS AND COLLECTIVE GOODS

265

mists standardly do, that producing the good can be computed in

money, that the monetary cost of producing any part of the good is the

same for each individual in the group, and that individual utilities are

roughly proportional to amounts of money). We can define C

r

as 2 C,

(where

n

is the num ber of people in the group). H owever, C

T

can also be

defined as the sum of the costs

o f

each increment of the good p roduced . In

other words, there is a function relating any

Ag

to the cost

(AC)

of

producing that Ag; i.e., f Ag

a

) = AC . And C

r

can be defined as the sum of

the incremental costs involved in producing a certain amount of the

incremental good. Thus:

where

v

is the total number of increments produced. This notation al-

lows us to pick out the cost of the ath increment of the good produced

(which would be AC ).

Now the benefit that the individual receives from the production of

an incremental good is defined as a function of the good, i.e.,

/ '(O) = V,

where V, is the ind ividual's benefit received from the good 's provision

up to and including v. We must also define the individual's

incremental

benefit

AV,

from some increment of the good as a function of that incre-

ment of the good; i.e.,

f (Ag«) = AV,

where AV,

a

is the benefit the individual would receive from the ath

increment (only) of the good. Hence, we see that

0=1

where

v

is the num ber of increments of the good produce d.

Also recall that we have defined the total benefit of the good to the

group (

V

T

)

as the sum of the benefits to each individual in the group from

the good, i.e.: V

T

= J^V,, where n = the number of individuals in the

group.

Now, what is the precise nature of the problem that might arise in

the production of incremental goods? It is clear that a person is not

rational to contribute if

V ,

> AC

a

,

but rather if and only if

AV,

a

> AC ,

that is, she is rational to contribute only if the increment of benefit that

her contribution would bring to her exceeds the cost to her of providing

this increment.

14

H ence, in a situation where it is always true that AV,

V

<

AC , it is nev er rational for an individual in this group to contribute to the

good's production.

14. Again, in the con tinuo us case, the question is slightly different: Is dV/dc, 5 0?






266

JEAN HA MP TON

K OTHERS


INDIVIDUAL

PRODUCE

DON T

PRODUCE

\.

v

ac

v

- A C

V

0

FIGURE 9

One can present people's problems in this sort of situation as in-

volving a one-shot ordered-gam e set of prisoner's dilem m as- bu t

only if one clarifies how one's attention can turn from the production

of the good's increments to the productive efforts of others

in

the

group.

Thus far, the individual's calculations have concerned whether or not

to produce the ath increment of a collective incremental good. But if

the ath increment is not the first increment, these calculations assume

that one or more people in the group will cooperate to produce the

previous increments. Suppose the individual assumes that any individ-

ual in the group who contributes to the production of the good will

contribute no

more

than one increm ent of that good (her sha re ). Each

individual then deliberates about whether she should contribute to the

good's production, where K other people in the group do so by contrib-

uting one increment (so that

v

=

k +

1). Her payoffs (in cardinal

numbers) from the various possible outcomes are represented in the

matrix in Figure 9. But if we assume that AC

> AV,

V

,

then

V,

v

-

AC

<

V

1

. So the preference orders of the individual for these outcomes are

as follows in Figure 10. These preferences match those of an individual

in a prisoner's dilemma.

Nonetheless, it is a bit misleading to say that this dilemma is

a

prisoner's dilem ma. It is in fact

a

set of prisoner 's dilemm as. Each individ-

ual must determine for each possible number of fellow contributors (in

the case whe re each will produce one increm ent), whe ther she is rational

to pay the cost of producing the next increment of the good. Hence each

individual engages in not one calculation but a set of calculations, and if,

at every level of the good's production, the cost of the increment she

would provide exceeds the benefit to her from that increment, then she

is rational to conclude that she should not contribute to the good's






FREE RIDERS AND COLLECTIVE GOODS 267

K OTHERS

PRODUCE

DON T PRODUCE

INDIVIDUAL

PRODUCE

DON T

PRODUCE

2

1

4

3

FIGURE 10

production, no matter ho w m any other people cooperate to produce any

given level of that good.

It is importan t to appreciate that the individual m ust unde rgo a set of

calculations in this situation in order to appreciate why there can be a

very

different, non-PD -type problem involved a t some or even all levels of the incre-

mental good's production.

As we have seen, in her set of calculations, an individual must

dete rm ine the answ ers to a series of questions of the form: W hat is it

rational for me to do if x num ber of the group contribute? (And remem-

ber that her concern for the number of others contributing is simply an

indirect concern for what actually interests her, namely, the number of

increments of the good which will be produced by these individuals.)

Now it might be (as we discussed above), that at every contribution level

the cost of providing an additional increment of the good exceeds the

benefit to her from that increment. But it is also possible that at certain

levels of an incremental good's production (where a certain number of

others in the group cooperate to produce these increments) the incre-

ment of benefit produced for that individual really does exceed the cost

of that increment to her. (Indeed, this may be true at all levels.) The

graphs in Figures 11 and 12 indicate two ways of representing an incre-

mental good whose structure is such that at some levels of the good's

production, the incremental benefit to an individual exceeds her cost of

providing that increment.

15

15. Frohlich et al. (1975) also argue tha t, given certain produc tion functions of a collective

good , An individual could be induced to contribute voluntarily without the use of

selecting incentives if he could be persuaded that 'enoug h' others are contributing (p.

325). And to make this point they present a number of graphs, one of which (in their

Figure 7) almost exactly duplicates the graph in my Figure 12. However, in their






line representing

AC

f(Ag)

increments

of

good

Ag)

FIGURE

contribution region

(where

V? - AC >

v-l

V,

v

- AC

increments

of

good

Ag)

FIGURE 2






270 JEAN HA MP TO N

whether the cost

to

h er

of

doing so is greater than

or

less than the benefit

to her from that increment. If it is never the case that the cost of supplying

any increment

of the

good

is

exceeded

by the

benefit

to her

from that

increment, she is irrational to involve herself in the production of that

good, even if she would be better off with the good than without it. But

if there are som e levels of the good 's p roduction in which the benefit to

her from an increment exceeds the cost to her of providing it, she is

rational to produce it-as long as others find it rational to produce the

good up to the level of that increment, and as long as solutions have

been found

for any of the

(previously discussed) game-theoretic prob-

lems (e.g., battle-of-the-sexes, assurance, or chicken problems) involved

either

in

selecting produ cers

for the

good

or in

getting them

to

produce

that level of the go od.

I suspect that

the

complicated gam e-theoretic structure underlying

the production of incremental goods has been missed b ecause it is very

easy to believe tha t the appropriate way of reasoning in these situations

is: sup pose everyone contributes . . . suppose no one contributes -

assuming, in other words, that the actions of others are given when in

fact they are not. In particular, such reason ing will cause one to miss the

rationality of contributing to the production of a good in which benefit

exceeds cost only

at

m edium levels

of

the goo d's p roduc tion. Sorites-like

reasoning may also mislead one about the good's structure: one can

believe that

the

incremen t o ne will produce will

be

imperceptible

and

hence unnecessary. Of course, it would indeed be imperceptible in

one sense

if the

benefit

one

received from that increm ent

was so

small

that the cost of providing it exceeded one's benefit from it, but it is this

latter calculation one should be concerned to perform. Unless one does

so , dismissing the idea of contributing an increment of the good on the

basis of its smallness alone is irrational.

Empirical estimates

are

needed

in

order

to

determine

how

many

incremental goods do not pose prisoner's dilemmas at all levels of the

good's production.

But

even

if

there

are a

significant number, just

be-

cause it is utility-maximizing for individuals to pay the cost of producing

the incremental good

at a

certain level, doesn't mean that producing this

level of the good is optimal for the group. Hence, the group might still

find

it

necessary

to

introduce selective incentives into

the

situation

in

order to get an incremental good produced at optimal levels. So haven't

we finally discovered the area of collective good production which is, as

the traditional analysis suggests, plagued by PD games requiring sanc-

tions for their so lution?

Not necessarily; voluntary production at an optimal level of even

t hese goods

is

still possible

if their increm ents can be restructured in the right

way. That is, if the group desiring such a good is able to make certain

levels

of the

production

of the

good impossible, such that

it

can only

be






FREE

RIDERS AND COLLECTIVE GOODS

271

produced in one or more large ste ps , the production of the good at an

optimal level might pose only a battle-of-the-sexes problem. Suppose,

for example, that a security service approached a neighborhood haunted

by frequent burg laries and offered to provide pa trol service for the neigh-

borhood, with the number of hours of the patrol per week depending

upon the number of households paying for the patrol. If the security

service offered to make the num ber of ho urs strictly de pe nd en t up on the

number of households contributing (for example, each new contributing

household might pay for two more hours of patrol per week), the neigh-

borhood would be asked to produce an incremental collective good and

each household might find it individually rational not to pay for its two-

hour increment of patrol no matter how many other households did so

(i.e.,

each household might find itself facing a coordinated set of prison-

er's dilemmas). But suppose the security service said that it would, at a

minimu m, prov ide patrol for half of the hou rs (50%) of the week as long

as it got 40% of the households contributing, but that if less than 40%

contributed it would provide no hours of patrol (and any contributions

made would be returned to these households). In this second offer, the

security service has made an incremental good into a good with at least

one large step, and residents of the neighborhood would now have to

determine whether they would be better off paying a certain share of the

cost of producing this large step than they would be if they refrained

from d oing so. Supp ose tha t the security service asked each of the house-

holds making up the 40% to pay for the equivalent of one hour of the

half-week patrol. Each household would then calculate whether or not it

was rational to pay for this hour-its share of the cost of this half-week

patrol - b y determ ining w heth er or not the cost of doing so was exceeded

by the benefit to it of the half-week

patrol.

In other word s, instead of

compar ing the

cost of providing an increment

of security with

the benefit it

would get from that increment,

each househo ld would now compare

its

share of the cost of providing 50% of the incremental good,

wi th

the benefit it

would get from 50% of the incremental good.

An d w hi le cont r ibut ing on the

basis of the first comparison is likely to be irrational, contributing on the

basis of the second com parison could well be rational. So, by transform-

ing the situation into the produc tion of a good that has a very large initial

step,

the security service has ensured that only the (primarily coordina-

tion) problems involved in step good production will be involved here.

16

Recall at the outset that I said the distinction between incremental

goods and step goods was not sharp. The last example illustrates this

point. Those collective goods that come in more than one increment can

16. Although they do not explicitly purs ue this restructuring idea, Frohlich and O ppe n-

heim er (1978) sugg est it wh en they insist that successful political action based solely

on the individual's incentives to obtain the collectively supplied good requires mar-

ginal cost sharin g (p. 63).





FREE RIDERS AN D COLLECTIVE GOODS

273

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