SOCIAL ORGANISATION, CIVIC RESPONSIBILITY AND COLLECTIVE ACTION:
GAME THEORY MODELS OF COMMUNITY PARTICIPATION IN DEVELOPMENT
PROJECTS
Howard White*
Institute of Development Studies
University of Sussex
(e-mail: [email protected])
Abstract
Why do people participate in community projects? Game theory approaches based
on the prisoners’ dilemma suggest that people will not participate even if they
would have been better off had they all done so. This paper adapts an argument of
Bates to show how a system of enforceable fines can ensure full participation. It
then goes on to present a model in which individuals have differing degrees of
civic responsibility, so that some will participate whilst others free-ride. But the
size of the initiating group has to be above a threshold level for the project to take
place at all. External agents can encourage collective action by lowering the costbenefit ratio facing individuals.
1.
Introduction
Community participation in projects is now well established on the development agenda. But in
recent years economists have paid little attention to the conditions under which participation will
occur.1 This paper presents game theory models addressing this issue. Part 2 discusses the
prisoners’ dilemma, which would suggest there would be no participation, and how enforcing
fines can bring about full participation. In practice there are usually some free riders in
community initiatives. The model of Part 3 presents a model which achieves this result by
assuming differing degrees of civic responsibility amongst community members. This model has
implications for how external agents may support community participation. Part 4 concludes.
2.
Social organisation and collective action
Hardin’s “Tragedy of the Commons” is a pessimistic perspective on the possibility for collective
action. He argued that there was little incentive to act collectively to preserve common resources,
but a considerable disincentive in the form of free-riding. Common resources, such as pasture,
*
Thanks are due to Jan Kees van Donge for suggesting the importance of civic responsibility in analysing
community participation and to Amirah El-Haddad for discussion of the model in Part 3.
1
The expression “in recent years” is necessary, since Olson (1971) was concerned with precisely this issue.
However, the models presented here do not follow from that earlier work.
are thus consumed by individuals to maximise their own return, eventually exhausting the
resource. This argument, and those put forward to counter it, may be presented in terms of the
prisoners’ dilemma, which shows that individuals acting to maximise their own individual
welfare may result in a sub-optimal equilibrium.
The dilemma is this. Two prisoners are being held before trial for a crime that they committed.
They are kept apart, and are being interrogated separately before trial. Each one faces the choice
of confessing the crime or of not confessing. If prisoner 1 confesses and 2 does not then 1 goes
free whilst 2 receives a 20 year sentence. If they both confess they receive 15 years each.
However, if neither confesses there will be insufficient evidence to bring all the charges against
them and they will only get 5 years each. These choices are summarised in the pay-off matrix
shown in Table 1. The numbers in each cell represent prisoner 1’s sentence and prisoner 2's
sentence respectively.
Table 1 The pay-off matrix for the prisoners’ dilemma
Prisoner 2
Prisoner 1
Don’t confess
Confess
Don’t confess
5,5
20,0
Confess
0,20
15,15
Consider the problem from the point of view of prisoner 1. If prisoner 2 is not going to confess
then the best thing prisoner 1 can do is to confess. Similarly, if prisoner 2 is going to confess then
1 will receive the least possible sentence by confessing. That is, no matter what prisoner 2 does,
the best option for prisoner 1 (i.e. that which, given prisoner 2's actions, leads to the minimum
possible sentence) is to confess. But exactly the same analysis will apply in the case of prisoner 2.
So the outcome is that both prisoners will confess and both receive 15 years. Clearly they would
be better off had neither confessed (only 5 years each) but this is not an equilibrium. Equilibrium
in this context is called Nash equilibrium, which is that situation in which, given the other
player’s choice, a player cannot make him or herself better off by changing his or her strategy.
The strategy of neither player (prisoner) confessing is not a Nash equilibrium since if, Prisoner 2
say, is not confessing then 1 can improve his pay-off (reduce his sentence) by confessing. Once 1
is confessing 2 can improve his pay- off by confessing. When both confess neither can improve
their pay-off by a change in strategy. It is therefore a Nash equilibrium.
This approach may be applied to analysing community participation in development projects. The
analysis here is based on Bates’ (1983) discussion of grazing associations, which is thus a more
direct rebuttal of Hardin’s argument. Imagine a project which yields a benefit of 30 to each
2
person (of which there are only two in this example) in the village. These benefits are nonexcludable, meaning that everyone gets them regardless of whether they participated in project
implementation. This will be the case either because it is something everyone can use, such as a
road, or a conservation activity which preserves a communal resource, or if the project is a
facility such as a school, which children may attend whether or not their parents assisted with the
project. Suppose the total project cost is 40, which is spread equally amongst all those who
participate.
Table 2 Pay-off matrix from participation in a development project
Villager 2
Don’t participate (N)
Participate (P)
Villager 1
Don’t participate (D)
0, 0
30, -10
Participate (P)
-10, 30
10, 10
The resulting pay-off matrix is shown as Table 2. The Nash equilibrium is the situation in which
the project does not take place (N, N), although both villagers would be better off had they
participated (P,P). The project makes sense if both participate since individual benefits (30)
exceed individual costs (20). But if the other villager is going to participate then it makes sense to
free-ride. And if they are not going to participate, then participating means bearing the whole
project cost (40), which exceeds the individual benefit. Hence there will be no project.
A number of possibilities may be advanced as to why the argument of the preceding paragraph
may not be correct, so that (P,P) can be achieved after all. One criticism may be of the
assumption of the individual pursuing self-interest regardless of consideration for others, though
this is a standard assumption in economics. But if the well-being of villager 2 affects the wellbeing of villager 1,2 then villager 1 may choose to participate. Certainly, if villager 1’s objective
is to maximise villager 2’s well-being (and vice versa) then the outcome is (P,P). Bonds of trust
and loyalty may also change the outcome. In the case of the prisoners’ dilemma, if the prisoners
trust one another then both will feel safe in not confessing. Or it may be that individuals have a
sense of civic responsibility, the implications of which are pursued in the next section. Finally,
action may be taken to change the pay-off matrix to ensure a participatory outcome. It is this last
possibility, advanced by Bates (1983), that is considered here.
2
More formally, the utility of villager 2 enters the argument of the utility function of villager 1.
3
The co-operative solution can be attained when a system of fines is in force. Suppose that a fine
of 21 units is levied on a villager who does not participate and that the proceeds are passed onto
the participating villager. The pay- off matrix becomes as in Table 3. There are no fines when
neither participate as there is no project. Equilibrium is now (P,P).
Table 3 Pay-off matrix with fines
Villager 1
Don’t participate (D)
Participate (P)
Villager 2
Don’t participate (N)
Participate (P)
0, 0
9, 11
11, 9
10, 10
Bates suggests that such a system of fines can enforce co-operation in so-called “stateless”
societies, such as Nuer pastoralists. But social organisation is required in order for fines to be
enforceable. This lesson is clear from Wade’s analysis of co-operation for managing irrigation
schemes in southern India (1988). The critical insight from Wade’s work is that participation
works best if rooted in existing social organisation, which provides the framework for cooperation and the legitimacy for a system of fines to be accepted. Hence, for example, range
management schemes should work within the social structure provided by traditional tenure
arrangements rather than try to impose a more “logical structure”.
This argument is well-illustrated by social funds in Malawi and Zambia. These funds are demanddriven, meaning that communities must apply to the social fund agency for financial support for a
project such as building a school or clinic (see Carvalho et al., 2002 for more discussion). The
community must provide a contribution, which in rural areas is provided in the form of moulding
bricks and bringing building sand to the project site. This community labour is organised by
village headmen, who divide the tasks amongst the villages (e.g. each village must mould 20,000
bricks) and are responsible for ensuring that each household sends the requisite labour. Fines are
imposed on households who do not provide labour (see Gupta Kapoor and White, 2002 for more
discussion of the nature of participation in these projects). These procedures are not to be found
in the social fund manuals, but are the way in which rural communities across both countries have
adapted to the requirements of the social fund. Similar mechanisms do not exist in urban areas,
which lack the traditional social organisation to mobilise labour and enforce fines. Projects in
urban areas levy cash contributions rather than labour and project committee members complain
of the difficulty in getting beneficiaries to meet their obligations.
4
Whilst social organisation can change the pay-off to ensure that collective action takes place,
examination of the pay-off matrix shows that the value of the fine must exceed the cost of
participating in order for the fine to change incentives. This makes sense from the point of view
of the literature on the economics of crime, according to which people will commit a crime if the
benefits from doing so exceed the costs of being caught, where the costs of being caught combine
the penalty if caught and the probability of detection. In the case considered above, nonparticipation is detected with certainty (the probability of being detected is unity), so the penalty
must be just marginally greater than the cost.3 One problem with the model is that it results in a
symmetric solution in which all or none participate. In reality, projects take place, but there are
some free-riders. A solution to this problem come from accepting that people may not commit
crimes on other grounds than simply fear of being caught. Similarly, people may engage in
collective action for reasons other than the direct benefits it brings to them. That is, they have a
sense of civic responsibility. The implications of including civic responsibility are the subject of
the next part of the paper.
3.
Individual civic responsibility and collective action
The model
Consider the case of a project which yields a non-excludable benefit of B per person in the
community.4 The total cost of the project is NxB, where N is the number of people in the
community. Since the total value of benefits is NB, x is the cost-benefit ratio.5 Each individual, i,
has a sense of civic responsibility yielding them a value of ϕi from engaging in collective action.6
Table 4 shows the two person case. The costs of participation to each individual are greater the
fewer people participate as costs are spread less thinly. Where only one person undertakes the
project their cost is 2xB, compared to xB if both villagers participate. If villager 1 pursues a
strategy of non participation (N), then villager 2 will participate (P), if (1-2x)B + ϕ2 > 0 ⇒ B + ϕ2
> 2xB (i.e. benefits exceed costs). If villager 1 participates then villager 2 also does so if (1-x)B
+ ϕ2 > B ⇒ ϕ2 > xB. Two conclusions can already be drawn. Since villager 1 and 2 have different
3
In the case of social funds in Malawi and Zambia, the fines do exceed the costs, since they are either
longer or more arduous labour or charged in livestock (a chicken). But, whilst non-participation is detected,
it is not clear if fines are always imposed, so that the system of fines is probably insufficient to explain the
high rates of participation (in excess of 80 per cent) observed in these projects.
4
B should be thought of as the present value of the future benefits stream.
5
Fines for non-participation are ignored for convenience, but may be added without difficulty or changing
the argument.
6
The variable ϕ may simply reflect individual utility or kudos within the community.
5
values of ϕ, the pay-off matrix is non-symmetric, so that solutions off the leading diagonal can be
observed (unlike the examples in the Part 2). Hence we may get, say, (P, N), in which villager 2 is
free-riding. The second conclusion is that such free-riding is likely, as relatively high values of ϕ
are needed amongst all community members for it to be avoided.
Table 4 Pay-off matrix for two person co-operative project
Villager 1
Villager 2
Don’t participate (N)
Participate (P)
0,0
B, (1-2x)B+ϕ2
(1-2x)B+ϕ1, B
(1-x)B+ϕ1,
(1-x)B+ϕ2
Don’t participate (N)
Participate (P)
Generalisation to the M person case requires an M-dimensional matrix. However, this
generalisation can be made without resorting to such a matrix, but noting that (1) the “bottomright” cell of such a matrix is that in which every-one co-operates; and (2) if only n people cooperate the cost to each person who is co-operating is MxB/n. Consider the case in which
everyone else is co-operating, then villager i will also co-operate if ϕi > xB. Supposing the
distribution of ϕ is such that there exist some ϕi < xB then there will be some (at least one) freeriders. In the case when at least one person does not co-operate, then villager i decides to cooperate, if (1-Mx/n)B + ϕi > 0 ⇒ B + ϕi > MxB/n. For algebraic convenience, transform ϕ, so
that ϕi = (1 + εi ) B. The condition for participation becomes (2 + εi ) / x > 1/np, where np is the
proportion of the population who participate (n/M). It can be seen that someone is more likely to
participate (1) the lower the cost-benefit ratio, (2) the greater the proportion of the community
also engaging in the collective action (since costs are then spread more thinly), and (3) the higher
their individual sense of collective action.
To see how the model works it is best to consider a numerical example, shown in Table 2.7 The
values of ε are generated randomly from an approximately normal distribution with a mean of
zero. The solution is iterative, given an initial value of the number of people who decide to cooperate. The story here is intuitively appealing. A group get together to undertake a collective
activity. Other community members observe this, and based on that value of np, all community
7
The model is in Excel. The initial number of participants is entered manually, and the resulting number of
participants derived by summing the final column, which is based on the comparison of the third and fourth
columns. Iteration is carried out by entering the resulting rate as the initial rate and so on until equilibrium
is found.
6
members (including those in the initial group) decide whether to participate.8 The group can
enlarge, as a result, setting off a snow-ball effect, with increasing participation through successive
rounds of iteration. Alternatively if the initial group is too small it can “melt away” so that the
activity does not take place.9 In the case shown, when x is 1.0, then if 3 or less people form a
group then participation falls to zero and there is no project.10 However, if 4 people form the
initial group this is a low-level equilibrium. And if five people form the initial group (the case
shown in Table 2), the resulting participation rate of 50 per cent, leads 6 of the 10 people to want
to join. This higher value entices 7 to do so, and the value of 7 results in a value of 8, which is the
equilibrium level. If the whole community had formed the initial group then some would have
decided to free-ride after all, so that the participation rate falls to 80 per cent.
Table 5 Model simulation with community of 10 people
Parameter
X
1.0
Model solution
Person
εi
1
2
3
4
5
6
7
8
9
10
-0.30
0.05
-1.47
-1.25
0.77
1.66
0.28
-0.57
1.72
0.72
Initial number of
participants
Resulting number of
participants
5.0
(2 + ε ) / x
1/np
1.70
2.05
0.53
0.75
2.77
3.66
2.28
1.43
3.72
2.72
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
Participate?
(Yes = 1)
0
1
0
0
1
1
1
0
1
1
6.0
Re-solving the model with a cost-benefit ratio of 0.5, one person alone is still not sufficient to
motivate collective action. But a group of 2 is, resulting in an equilibrium of 9. With the decision
rule used here 10 is also an equilibrium. But, in the case when everyone co-operates then the
person with the lowest εi will free-ride, so that participation will never be 100 per cent. With a
8
It is being assumed that the distribution of ε (or, equivalently, ϕ) is known. The story told here provides a
rationale as to why this may be so.
9
This model thus provides an example of frequency dependent equilibrium (Diamond, 1989) in which a
person’s pay-off is dependent upon the decisions of others, which in this case depend on the distribution of
ϕ. Communities with higher levels of ϕ (e.g. a right-ward shift of the distribution) are more likely to
undertake community projects and to have higher rates of participation when they do so.
10
If three initially decide to participate the group, one person melts away, leaving a group of two, which
then disbands.
7
lower cost-benefit ratio there is a lower threshold for the initial participation rate required to set
off the snowball effect, and the resulting participation rate is higher.
Figure 1 Results of model simulation against the cost-benefit ratio (x)
100
Participation rate falls
to high level equilibrium
90
80
Participation rate
70
Participation rate rises to
60
to high level equilibrium
50
40
30
20
Participation rate falls to zero
10
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Cost benefit ratio
Low level equilibrium
High level equilibrium
Fuller analysis was conducted using a larger number of community members, the results of which
are shown in Figure 1. The same points as above emerge and may be stated more formally as
follows. There is a low-level equilibrium, which is unstable. If the initial participation rate (the
group that get together to promote the activity) is less than this threshold level, then the
participation rate falls to zero and no activity occurs.11 But if the initial participation rate exceeds
the low level equilibrium then the snowball effect occurs and participation rises to the high-level
equilibrium.12 This high-level equilibrium is stable, so that if initial participation exceeds this rate
11
A participation rate of zero is also a stable equilibrium. If initial participation is greater than zero but
below low-level equilibrium then participation falls back to zero. Negative values can of course not be
observed.
12
If the initial group happens to equal the low-level equilibrium then the participation rate gets stuck at that
level.
8
1.0
some community members decide to free-ride after all and participation falls to that equilibrium
level.
The figure also shows the impact of the cost-benefit ratio on the participation rate. The higher the
cost-benefit ratio then the higher the low-level equilibrium, which acts as the threshold for the
level of initial participation required to set off the snowball effect. Over half the community (53
per cent) have to form the initial group for the activity to take place when the cost-benefit ratio is
1, compared to 16 per cent when the ratio is 0.5.13 And the higher the cost-benefit ratio then the
lower the high-level equilibrium participation rate. If the ratio is one, then only 75 per cent of the
community participate, compared to 90 per cent when it is 0.5.
Interpretation
The main insight of this model is intuitively straight-forward. Getting more people involved in a
project reduces the per capita cost of involvement. A snowball effect can be created, if enough
people express an interest, drawing in an even greater number, and so on, until most of the
community are involved, though there will always be at least one free-rider; and, on realistic
values of the cost-benefit ratio, rather more.
The model also provides insight as to how to encourage participatory activities. The traditional
approach of “mobilisation” is one route, if this is taken to mean a way of increasing the initial
participation rate so that it lies above the threshold (low-level equilibrium). The model suggests
that this should indeed then enable the community to establish a high-level equilibrium, though it
may be that some are wary of the temporary enthusiasm created by an external visitor and not
trust the revealed values of ϕ. Changing the distribution of ϕ is thus more likely to be effective
than a “one-shot” mobilisation. But it is also much more difficult. There is a third option, which is
to lower the cost-benefit ratio. The cost-benefit ratio is the private, not social, ratio. If an external
agent bears some of the costs, the relevant x is lowered.
This discussion is very relevant in the light of current debates regarding social funds; see, for
example, White (2002) and the other papers in that collection. Specifically, should social funds
invest in social infrastructure or social capital? There is a growing feeling from some quarters that
13
The figure is drawn up to an x of 1.00. Since participating individuals get a benefit from participating (ϕ)
in excess of B, they will still undertake projects for which x exceeds unity. With the values of ε used in this
simulation a project can take place with a x up to 1.16.
9
there should be increased emphasis on the latter, which may be seen as an attempt to shift the
distribution of ϕ. But it is not easy for external agents to affect such a cultural change. It is far
easier from them to bring about a reduction in the cost-benefit ratio by meeting project costs.
Social funds do this by paying for purchased construction materials (window frames, roofing
material, doors etc.) and the cost of skilled labour. The model presented here shows why doing so
can bring about a high degree of community participation.
A final insight from the model is that it is the proportion of the population who participate that
matters, not the absolute number. A group of six friends who want to engage in some collective
activity will manage to get this activity underway if it involves a group of just themselves or, say,
a dozen people. But they will not be able to mobilise a larger group of, say, 100. In settings in
which there is not the social framework for large scale mobilisation it is more likely that smallscale efforts at collective action will be observed rather than community-wide ones. Support for
this view comes from resettlement schemes in Zambia. Whilst these schemes are rural, the
inhabitants are drawn from around the country and live outside of the authority of local traditional
authorities. The social mechanisms described above thus do not operate, so that they experience
difficulty in mobilising to access the social fund, and the ,in the words of one settler, cooperatives “do not co-operate”. But smaller groups do operate for common activities such as
animal husbandry.
4.
Conclusion
This paper has presented some simple game theory models of participation in development
projects. Part 2 begins with the tragedy of the commons, cast in the framework of the prisoner’s
dilemma, which sought to show that people will not co-operate (participate) even though they
would have been better off had they all done so. Utilising the approach of Bates (1983) it is
shown that a system of fines can change behaviour to bring about full participation. But such
fines cannot exist in a social vacuum. There need be social structures to ensure their
enforceability.
The models in Part 2 assume that people act solely out of self-interest, with no sense of civic
responsibility. People may engage in collective action from a sense that they ought to do so, or
because of the kudos it gives them. But the sense of civic responsibility is not uniformly
distributed, it varies between individuals. The model in Part 3 shows that some are very likely to
participate, whereas others will usually choose to be free-riders. The model also shows that higher
10
levels of participation spread costs more thinly, which may generate a snow-ball effect resulting
in yet higher levels of participation. But if the initial group proposing the project is too small the
initiative melts away.
External actors may support community participation by three channels. First, mobilisation to get
the initial group above the threshold. But this may not be sustained once the mobiliser disappears
from the scene. More effective would be to shift the distribution of ϕ, but this is a cultural change
which is difficult for an external agent to bring about. Finally, they may lower the cost-benefit
ratio by paying implementation costs.
References
Bates, Robert (1983) "Essays on the Political Economy of Rural Africa" [Berkley: University of
California Press].
Carvalho, Soniya, Gil Perkins and Howard White (2002) Social Funds: assessing effectiveness
[Washington D.C.: OED, World Bank].
Diamond, P (1982) “Aggregate Demand Management in Search Equilibrium” Journal of Political
Economy 881-894.
Gupta Kapoor, Anju and Howard White (2002) “Participation, social capital and sustainability in
social funds: case Studies of Malawi and Zambia”, mimeo [Washington D.C.: OED, World
Bank].
Olson, Mancur (1971) The Logic of Collective Action: Public Goods and the Theory of Groups
[Cambridge, Mass., Harvard University Press].
Wade, Robert (1988) "Village Republics: Economic Conditions for Collective Action in South
India" [Cambridge: Cambridge University Press].
White, Howard (2002) “Social Funds: a review of the issues” forthcoming in Journal of
International Development.
11