Conjectural Variations and Voluntary Public Good Provision in a Repeated Game Setting

The purpose of this paper is to show how conjectural variations can be derived as a reduced form in an infinitely repeated game of private provision of public goods. We obtain explicit closed forms of conjectural variations associated with maximal sustainable equilibria in which the sum of the utilities of all of a community's members is maximized for both quadratic and Cobb–Douglas preferences, provided that the resulting sequence of contributions can be sustained as a Nash (or subgame perfect) equilibrium in the underlying repeated game. We also show that positive conjectural variations will emerge as long as people place positive weight on the future, and that those conjectures are positively related to the discount factor.     

Improving Voluntary Public Good Provision Through a Non-governmental,Endogenous Matching Mechanism: Experimental Evidence

Social norms can help to foster cooperation and to overcome the free-rider problem in the private provision of public goods. This paper focuses on the endogenous establishment of an average-oriented norm which sanctions deviations from average public good contributions. In a laboratory experiment, we analyse whether subjects are willing to implement a punishment and reward scheme at their own expense by applying the theory of non-governmental norm enforcement put forward by Buchholz et al. (J Public Econ Theory 16(6):899–916, 2014). Based on their theory, which omits a central authority but introduces an endogenously determined enforcement mechanism, we implement a two-stage public good game. In the first stage, subjects determine the strength of the sanctioning mechanism on their own. In the second stage, they decide on their personal contributions to the public good based on the established mechanism. In line with comparable pool punishment experiments, we find that subjects are apparently willing to contribute funds in order to establish a norm enforcement mechanism. Groups over-invest in the mechanism, but this over-investment decreases over time. These investments seem to be driven by the subjects’ previous individual contributions and partly by a number of strategic considerations, i.e. the previous average contribution made to the public good lowers the investment in the sanctioning mechanism. In the second stage of our experiment, higher norm enforcement parameters tend to lead to higher public good contributions. The earnings with the mechanism are on average higher than without.     

Voluntary Participation and Spite in Public Good Provision Experiments: An International Comparison

This paper studies voluntary public good provision in the laboratory, in a cross-cultural experiment conducted in the United States and Japan. Our environment differs from the standard voluntary contribution mechanism because subjects first decide whether or not to participate in providing this non-excludable public good. This participation decision is conveyed to the other subject prior to the subjects' contribution decisions. We find that only the American data are consistent with the evolutionary-stable-strategy Nash equilibrium predictions, and that behavior is significantly different across countries. Japanese subjects are more likely to act spitefully in the early periods of the experiment, even though our design changes subject pairings each period so that no two subjects ever interact twice. Surprisingly, this spiteful behavior eventually leads to more efficient public good contributions for Japanese subjects than for American subjects.     

Inefficient Public Provision in a Repeated Elections Model

We consider a dynamic setting with no policy commitment. Two parties that compete for election must choose the level of provision of a public good as well as the tax payment needed to finance it. The cost of producing the good may be high or low and this information is not known to the voters. We show that there exists an equilibrium in which the party that does not want much of the public good uses the inefficient (high cost) technology even though the efficient one is available. Using the low cost technology would, by informing the voters about the cost parameter, force it to produce an excessively high level of the good in the future. Interestingly, this equilibrium is not symmetric, suggesting that a party with a strong taste for the public good is less likely to adopt a wasteful policy.     

Uncertainty and the Voluntary Provision of a Pure Public Good in a Two‐Moment Decision Model

In this paper, we explore the potential benefits of uncertainty that may arise in a two‐moment model of the voluntary provision of a pure public good. We find that an increase in a given contributor i’s risk associated with the aggregate contribution level of the other contributors (i.e., an increase in social uncertainty) induces that contributor to increase his own contribution level if and only if the uncertainty's incremental effect on the expected value of his net marginal utility is negative. Contributor i’s welfare likewise increases when a closely related condition is met, namely that the uncertainty's marginal effect on his expected marginal utility value of the public good exceeds its countervailing effect on the numeraire. Further, the corresponding aggregate contribution to the public good increases in the presence of free‐riding if and only if the incremental effect of contributor i’s contribution on the aggregate expected value of all other contributors’ net marginal utilities is small‐enough positive. We derive similar conditions for the case of private uncertainty, where the increase in contributor i’s risk is associated with his own marginal valuation of the public good. A simple example illustrates these conceptual results. Numerical analysis demonstrates that an increase in private uncertainty can have a nonmonotonic impact on contributor i’s welfare.     

Voluntary Provision of Public Goods and Technology

This paper highlights issues in the theory of voluntary provision of public goods, building on the investigation by Peacock in connection with the contributions by Coase and Buchanan. Our goal is twofold. We first draw attention to the early literature investigating the provision of public goods and to the successive theoretical analysis. We then focus on the impact of technology on supply and demand. Examples of different types of public goods are provided, with special attention to the cultural sector, to investigate whether and how technology affects the efficiency and the effectiveness of the related public goods provision. The implementation and exploitation of technological advancements are investigated in view of the role of different actors (public, private) at different levels of government.     

Public Good Provision Under Monopolistic Competition

This paper presents a model of voluntary private provision of public good under monopolistic competition following Pecorino. Consumers prefer product varieties and a public good. Marginal utility of income depends inversely upon the aggregate consumption of private goods in this model. As population size increases, aggregate consumption of private goods goes up and marginal utility of income falls. This explains the positive relationship between population size and public good provision. Any technological changes in the production of private goods are shown to be neutral to the aggregate provision of public good. These results are in contrast to Pecorino.     

Heterogeneity and the Voluntary Provision of Public Goods

We investigate the effects of heterogeneity and incomplete information on aggregate contributions to a public good using the voluntary contribution mechanism. The non-linear laboratory environment has three-person groups as partners under varying conditions of information and communication. Bergstrom, Blum and Varian predict that increasing heterogeneity will have no effect on aggregate contributions in a no-communication environment. Ledyard conjectures a positive effect of incomplete information, a negative effect of heterogeneity, and a positive interaction of heterogeneity and incomplete information. We find that incomplete information has a small but significant negative effect. Heterogeneity has a positive effect on aggregate contributions, but its effects interact unexpectedly with communication. In a no-communication environment, heterogeneity in two dimensions (endowment and preferences) increases contributions substantially while heterogeneity in a single dimension (endowment or preferences) has little effect. In the communication environment we find the reverse. We also find a positive interaction between heterogeneity and incomplete information. Thus we reject the Bergstrom, Blume and Varian invariance result and provide mixed evidence on Ledyard's conjectures.     

Non‐Governmental Public Norm Enforcement in Large Societies as a Two‐Stage Game of Voluntary Public Good Provision

In small groups, norm enforcement is achieved through mutual punishment and reward. In large societies, norms are enforced by specialists such as government officials. However, not every public cause is overseen by states, for instance those organized at the international level. This paper shows how nongovernmental norm enforcement can emerge as a decentralized equilibrium. As a first stage, individuals voluntarily contribute to a nongovernmental agency that produces an incentive system. The second stage is the provision of a public good on the basis of private contributions. The incentive system increases contributions by means of public approval or disapproval of behavior. It is shown that, even in large populations, nongovernmental norm enforcement can be supported in a noncooperative equilibrium of utility‐maximizing individuals. This result is in sharp contrast to those obtained in the standard situation of voluntary provision of an intrinsic public good which—without altruism or related motives—is eroded by free‐riding. Reliance on altruistic behavior is not required in supplying the second‐order public good “norm enforcement” in large societies.     

公共品私人自愿提供决策的实验研究

本文利用实验数据对公共品私人自愿提供机制的多个经典特征事实进行了实证检验,其结论基本支持诸如"公共品私人自愿供给的存在性"、"捐献率随重复捐献次数的增加而有下降的趋势"和"公共品投资的私人边际回报率和交流的正效应"等特征事实.同时,实验还得到了一些新的发现,如"期初平均捐献水平较低"、"口头协议效果显著"、"经验分享存在积极作用"和"小组的合作程度存在巨大的差异"等.这些结论说明通过合理的制度设计和安排可以达到部分公共品由私人自愿提供的目的.     

The Asymptotic Voluntary Provision of the Pure Public Goods

This paper analyzes the voluntary provision of the pure public good in a sequence of finite economies. The boundedness of this provision is established under very weak conditions. The Cournot–Nash provision of the public good is bounded. In contrast, the Lindahl provision is unbounded but the proportion of private good devoted to its production may be infinitesimal. Several examples are provided to relate this paper to the literature.     

Collective Choice and Voluntary Provision of Public Goods*

Some public goods are provided entirely with private contributions, others with a mixture of public and private funding, and still others are entirely publicly funded. In order to study this variation, a model of dual provision is developed that endogenizes public and private funding. Households vote over an income tax that finances public supply of the good and on whether to permit private contributions. While permitting private contributions may lead to a reduction in total provision, a majority always favors permitting private contributions. Results are developed for small and large economies, and the relevance of nonexcludability and noncongestion are investigated.     

Dynamic Voluntary Provision of Public Goods: A Generalization

In this note we examine if the proposition offered by Fershtman and Nitzan (1991) and Wirl (1996) in the context of a dynamic voluntary provision model with a linear production function can be generalized to a more general CES formulation. By comparing the steady-state stocks of a public good in open-loop and feedback Nash equilibria with that under the cooperative solution, we demonstrate that their ranking among the steady-state stocks is indeed preserved under the CES framework.     

Private Provisions of a Discrete Public Good with Voluntary Participation

This paper studies the mechanism that a profit-making principal should adopt to provide a discrete public good when the values of the consumers are their private information and their participation is voluntary. The free-riding issue is resolved through threatened nonprovision of the good by the provider. Every bidder is asked to announce his or her virtual value as defined in Myerson (1981) . The public good is provided if and only if the sum of the bidders' announced virtual values exceeds the provision cost. When a provision decision results, each bidder pays an amount that is determined by the announcement of other consumers. No one pays when a nonprovision decision results. We find that this mechanism is implementable through an all-pay auction. A restricted profit-maximizing mechanism that implements efficient allocation is also characterized. As in Gradstein (1994) , when provision is always efficient, that is, the sum of consumers' values always exceeds the provision cost, efficient allocation is achievable through a profit-maximizer. However, this is not the case when provision is not efficient.     

Repeated Interaction and the Public Provision of Private Goods

The literature suggests that governments can use in-kind transfers to design efficient and targeted redistribution schemes if individual incomes are not directly observable. We investigate the extent to which the self-selection property of in-kind transfers carries through if redistributive transfers are made repeatedly. In a two-period setting, the government may gain information about the individuals' incomes in the first period and exploit this information for making targeted transfers in the second-period. This, however, also triggers changes in the individuals' behavior. If the government can commit to its future policy, the least cost policy may involve randomization between cash and in-kind transfers. Without commitment, the dynamic setting works against the government's interest. It may no longer be able to use in-kind transfers to generate information about the individuals' types.
JEL classification : H 42; H 2     

Income Heterogeneity in the Voluntary Provision of Dynamic Public Goods

This paper explores the effect of income inequality on the voluntary contributions to a dynamic public good. We find that income heterogeneity has a significant impact both on contributions and welfare. The results show that the often observed decay of cooperation does not carry over to the asymmetric environment considered in this study. Our results also suggest that subjects in each income class make different contribution amounts in an absolute sense and give the same percentage of their income. Moreover, we find that contributions of individuals with the same endowment are sensitive to how heterogeneous the environment is.     

Dynamic Voluntary Provision of Public Goods and Optimal Steady-State Subsidies

This paper examines a differential game model of voluntary provision of a public good in which private agents' contributions accumulate over time and derives subsidy rules that achieve the socially efficient steady state. It is shown that the optimal subsidy rule is a simple one when agents use the open‐loop strategy, while under Markovian strategies it intricately depends on the parameters of the economy.     

Ambiguity and Public Good Provision in Large Societies

In this paper, we consider the effect of ambiguity on the private provision of public goods. Equilibrium is shown to exist and be unique. We examine how provision of the public good changes as the size of the population increases. We show that when there is uncertainty, there may be less free‐riding in large societies.     

Reducing Inefficiency in Public Good Provision Through Linking

We characterize the optimal mechanism for the provision of n public goods in an economy with m agents, binary valuations. The mechanism “links” the n problems together because decisions and transfers are based on the whole vector of valuations of the agents. In particular, the decision on whether or not to provide a public good depends not only on the valuations of the agents for that good but, in some cases, also on the valuations for the other goods reported by the low‐valuation agents. For the two‐agent case, we show that the mechanism is asymptotically efficient and we provide an example that compares its relative efficiency with optimal separate provision and with another asymptotically efficient mechanism in the literature.     

Beliefs and Public Good Provision with Anonymous Contributors

We analyze a static game of public good contributions where finitely many anonymous players have heterogeneous preferences about the public good and heterogeneous beliefs about the distribution of preferences. In the unique symmetric equilibrium, the only individuals who make positive contributions are those who most value the public good and who are also the most pessimistic; that is, according to their beliefs, the proportion of players who most like the public good is smaller than it would be according to any other possible belief. We predict whether the aggregate contribution is larger or smaller than it would be in an analogous game with complete information and heterogeneous preferences, by comparing the beliefs of contributors with the true distribution of preferences. A trade‐off between preferences and beliefs arises if there is no individual who simultaneously has the highest preference type and the most pessimistic belief. In this case, there is a symmetric equilibrium, and multiple symmetric equilibria occur only if there are more than two preference types.