Noussair, C.N.

Soo, C.

English

Research Papers in Economics

 Voluntary Contributions to a Dynamic Public Good: Experimental 
Evidence 
Charles Noussair
* and Cindy Soo
* 
 
Abstract 
Previous experimental studies indicate that voluntary contributions to a public good decline over 
time to near zero. We explore whether a similar decline of contribution rates occurs when the 
return to contributions is a function of contributions in previous periods. We find that, at least in 
one such environment, average contributions decline to low levels in only a minority of groups. 
 
1. Introduction 
Individual incentives exist to free ride on the provision of a public good when the good is 
supplied with voluntary contributions. Experimental evidence has largely confirmed such free 
riding as a behavioral principle. This result emerges primarily from the extensive and careful 
investigation of behavior in a game called the Voluntary Contributions Mechanism (VCM). In the 
VCM game, each member of a group of potential beneficiaries of the public good receives an 
initial endowment of money. They then decide simultaneously on a portion of their endowment to 
contribute to a group account. A contribution to the group account increases the total earnings of 
the group, benefiting each group member equally, while it reduces the earnings of the contributor. 
Thus, contributing to the group account constitutes a voluntary provision of a public good. 
Individuals’ average contributions, while initially positive, decrease to low levels with repeated 
opportunities to contribute (Isaac et al., 1985; Isaac and Walker, 1988a; Andreoni, 1988; Ledyard, 
1995), unless an additional instrument to promote cooperation, such as communication (Isaac and 
Walker, 1988b) or punishment (Fehr and Gaechter, 2000) is in place. 
The marginal per-capita return (MPCR) is the benefit each individual receives from each 
unit of money that any group member contributes, and can thus be interpreted as a return on 
expenditure on a public good. In all of the previous studies of which we are aware, the MPCR is 
independent of the history of prior expenditures on the public good. However, such dependence is 
a feature of many situations of interest in the field. For example, if individuals have failed to 
                                                 
* Department of Economics, Emory University. Correspondence to Charles Noussair, Department of 
Economics, Emory University, 1602 Fishburne Dr., Atlanta, GA 30322-2240, USA. E-mail: 
cnoussa@emory.edu. We thank Rob Moir, Chris Anderson, and participants at the 2005 World Economic 
Science Association Meetings for helpful comments. We thank the SIRE program at Emory College for 
financial support.   
  1maintain the cleanliness of a lake in the past, the cost of converting it into a recreational facility 
of a given quality is higher than if the lake had been well maintained. Similarly, a public park that 
is a popular destination because it has been well maintained in the past yields benefits to a greater 
number of users, and thus higher welfare for a fixed monetary expenditure, than a park that has 
been undermaintained. National defense readiness is less costly to maintain when large 
investments have been made in its provision in the past; investment in military equipment yields a 
higher return when the personnel operating it have been better trained previously. In this paper, 
we refer to public goods with the property that the value of the marginal product of current 
expenditure depends on past expenditures as “dynamic public goods”.  
We report here the results of an experiment that investigates the effectiveness of a system 
of voluntary provision of a dynamic public good. The principal issue we consider is the extent to 
which the free-rider problem, so evident in the studies described in the first paragraph, leads to 
underprovision of a dynamic public good. In the experiment, the production technology for the 
public good has the property that the MPCR is a simple increasing function of prior total group 
contributions. If the total contribution in period t was greater than 50% of total group endowment, 
the MPCR increases by .1 for period t+1. If period t contributions fail to reach the 50% threshold, 
the MPCR decreases by .1 for t+1. If period t contributions equal exactly 50% of endowment, the 
MPCR remains the same for t+1.  
It is plausible to hypothesize that the free rider problem might not be severe for dynamic 
public goods. Because the value of the public good is a function not only of current contributions, 
but of previous contributions as well, an “investment’ motive exists to contribute to dynamic 
public goods, and this motive might encourage high contributions. Furthermore, because higher 
contributions are generally associated with higher MPCR (Isaac and Walker, 1988a), it is possible 
that high contributions in early periods could create positive feedback that raises the MPCR and, 
in turn, contributions in later periods. Nevertheless, the logical argument leading to an outcome of 
free-riding and zero public good provision is highly compelling. Because of a restriction that the 
MPCR < 1 at all times, and the fact that the number of periods is finite and common knowledge, 
the only subgame perfect equilibrium of the game is for all players to contribute zero in each 
period. Thus, it is also reasonable to hypothesize that contribution levels would converge to close 
to zero, as in the case of non-dynamic public goods. 
 
2. The Experiment 
  The experiment was conducted in ten sessions at Emory University, located in Atlanta, 
Georgia, USA. At the beginning of each session, eight participants were separated into two 
  2groups of four on a random basis. Each session followed a “partner matching” protocol, in which 
group membership remained fixed for the entire session. Each session consisted of 10 periods of 
play of the voluntary contributions mechanism. At the beginning of each period, each subject was 
endowed with 10 tokens, where each token was to be converted to US$.1 at the end of the 
session. Communication between subjects was strictly prohibited at all times. 
During each period, subjects simultaneously chose the number of tokens from their 
endowment to keep for themselves, contributing the remainder to a group account. In each period, 
each individual earned $.1 for every token he did not contribute and $MPCR/10 for each token 
any member of their group contributed. There were two treatments, HM (High MPCR) and LM 
(Low MPCR). In HM, the MPCR in period 1 equaled .4. In LM, the MPCR in period 1 was .1. 
Ten independent groups participated under the conditions of each treatment. In both treatments, 
however, the MPCR in periods 2 and greater depended upon the level of contributions in the 
previous periods. If the total contribution of the group equaled more than 20 tokens (50% of the 
group’s total endowment) in period t, the MPCR would increase by .1 for period t+1. If the total 
group contribution equaled less than 20 tokens, the MPCR would decrease by .1, and if the total 
number of tokens contributed equaled exactly 20, then the MPCR would remain the same. The 
MPCR could not exceed .9 or drop below 0.  
  
3. Results  
Figures 1 and 2 display the total contribution levels for each of the ten groups as a 
percentage of the total endowment in treatments HM and LM, respectively, over the ten periods 
that comprised each session. Each time series represents the activity of one particular group. The 
bold line indicates the average over all groups comprising the treatment. The data indicate that 
contributions do not consistently exhibit the decline found in previous studies in either treatment. 
Rather, there is heterogeneity among groups. In both treatments, contributions of a considerable 
minority (30 – 40%) of groups increase over time to close to the maximum possible level. For 
another 30 - 40% of groups, contributions decrease to zero. For the rest of the groups, 
contributions decline over time but do not reach levels close to zero. Therefore, the strong 
tendency for contribution rates to decline observed in previous studies does not carry over to the 
dynamic public good environment that we study here.
1  
                                                 
1 The willingness to contribute in the early periods in LM is noteworthy because the MPCR in these periods 
is less that .25, and thus each token contributed yields less than one token in overall earnings to the four 
players in the current period. This means that short-term group gains from not contributing are foregone to 
achieve higher total payoffs over the 10-period horizon.  
  3 
 
        [Figures 1 and 2: About Here] 
 
  Contributions are high enough to allow the MPCR to exhibit an overall increase over the 
ten round horizon for a majority of groups. Figures 3 and 4 illustrate the MPCR in each period for 
each group in treatments HM and LM, respectively. The bold lines in the figures represent the 
average MPCR in each round for all groups in the treatment. 
 
  [Figures 3 and 4: About Here] 
 
Figure 3 shows that under HM, seven of the ten groups made sufficiently high 
contributions to increase MPCR by .1 each period and to reach the maximum level of .9 in either 
period 9 or 10. The MPCR for the three remaining three groups declined to a low level: zero in 
two of the sessions, and .1 by period 10 in the remaining session. Figure 4 indicates that five of 
the ten groups in LM converged to an MPCR of at least .8 by period 9, while 4 groups converged 
to zero.  
Contributions and final MPCR are not significantly different between the two treatments, 
suggesting that the properties of the provision patterns for dynamic public goods after several 
periods are fairly independent of the initial conditions. Contributions average 22.2 and 19.4 
tokens in the HM and LM treatments, respectively, over the complete 10-period horizon. They 
average 21.1 and 16.8 in the last five periods for HM and LM, respectively, and 21.0 and 16.7 in 
period 9. We conduct Wilcoxon rank sum tests for treatment differences, using each group’s 
activity as a unit of observation, yielding 10 observations in each treatment. These tests indicate 
that we cannot reject the null hypothesis at the 10-percent level that the median group 
contributions in the two treatments are equal in period 9, over the last five periods, or over the 
entire 10 periods (z = .68, 1.24 and .72, for the 10 periods, the last five periods, and period 9 
respectively). The final MPCR averages .62 in HM and .50 in LM. The difference between the 
two treatments is also not significant (z = .57). 
 
4. Summary  
The strong tendency for voluntary contributions to public goods to decrease over time, 
widely observed in previous studies, does not carry over to the particular environment studied 
  4here, in which the value of the public good depends on both previous and current contributions. 
Many groups in our experiment were able to reach levels of contribution close to the maximum 
possible and thereby achieve highly efficient outcomes over the course of ten periods. Only a 
minority of groups saw contributions decrease and fall to or close to zero. This was the case even 
when the initial marginal per-capita return equaled .1. There is no significant difference between 
the treatments in terms of average level of contributions or final MPCR. Thus the initial 
value/cost ratio for the public good appears to become largely irrelevant in determining long run 
outcomes for the dynamic public goods we have studied. 
    
References 
 
Andreoni, James (1988) “Why Free Ride? Strategies and Learning in Public Goods 
Experiments,” Journal of Public Economics, 37:3, 291-304.  
 
Fehr, E. and S. Gaechter (2000), “Cooperation and Punishment in Public Goods Experiments”, 
American Economic Review, 90(4): 980-994. 
 
Isaac, R. M, and J. Walker (1988a) “Group Size Effects in Public Goods Provision: The 
Voluntary Contributions Mechanism,” Quarterly Journal of Economics 103:179-99. 
 
Isaac, R. M, and J. Walker (1988b) “Communication and Free-Riding Behavior: The Voluntary 
Contributions Mechanism,” Economic Inquiry, 26:4 585-608.  
 
Isaac, R. Mark, Kenneth McCue, F., and Charles R. Plott (1985) “Public Goods Provision in an 
Experimental Environment,” Journal of Public Economics, 26(February), 51-74.  
 
Ledyard, John O. (1995) “Public Goods: A Survey of Experimental Research,” in A Handbook of 
Experimental Economics, edited by A. Roth and J. Kagel, Princeton: Princeton University Press, 
111-194. 
 
 
 
 
 
 
  5Figure 1. Group Contribution Levels as % of Optimum (High MPCR of .4)
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  6Figure 2. Group Contribution Levels as % of Optimum (Low MPCR of .1)
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  7 
Figure 3. MPCR Levels (High MPCR of .4)
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Groups 1, 5, 6, 7, 
and 8 follow the 
same trajectory 
Groups 9 and 10 follow 
the same trajectory 
 
 
  8  
Figure 4. MPCR Levels (Low MPCR of .1)
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Groups 7 and 10 follow the 
same trajectory 
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and 9 follow the 
same trajectory 
  9

Communication and Free-Riding Behavior: The Voluntary Contributions Mechanism,” Economic Inquiry,

Cooperation and Punishment in

Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism,”

Public Goods Provision in an Experimental Environment,”

Public Goods: A Survey of Experimental Research,”

Why Free Ride? Strategies and Learning in

Voluntary contributions to a dynamic public good: Experimental evidence.

Voluntary contributions to a dynamic public good: Experimental evidence.

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