Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

Coordination and the Provision of Discrete Public Goods by Correlated Equilibria

The strategic analysis of the private provision of a discrete public good has shown the existence of multiple Nash equilibria with the efficient number of players voluntarily contributing. However the coordination issue is left unexplained by this literature. The experimental evidence shows that communication among players is helpful in achieving cooperation. We claim that, from the theoretical point of view, this is equivalent to playing correlated equilibria in an extended public good game with communication, modeled as Chicken. We characterize such equilibria as feasible coordination mechanisms to achieve public goods provision in the general contribution game. We further introduce a second kind of game characterized by payoff externalities that may persist after the minimal threshold of contributors is achieved. While it is easy to show the existence of Pareto efficient correlated equilibria in the first game, in the second one players face incentive problems such that a first best cannot always be an equilibrium. Nevertheless there exist correlated equilibria that can qualify as incentive efficient mechanisms, once free riding is seen as a moral hazard issue. Finally, with an example, we discuss the impact of coalition formation in our framework.     

An Experimental Investigation of Excludable Public Goods

This paper extends the research on incentive compatible institutions for the provision of public goods by imposing a minimum contribution that must be met in order for an individual to enjoy the benefits of the public good. Excluding individuals who do not contribute at least the minimum transforms the linear n-player pure public goods game to an n-player coordination game with multiple, Pareto-ranked Nash equilibria. The experimental results show that exclusion increases contributions to the public good in most cases. However, an increase in contributions may not be sufficient to increase social welfare because there is a welfare cost to excluding individuals when the good is non-rival. Furthermore, exclusion can decrease both contributions and welfare in environments in which individuals fail to coordinate their contributions. The results are sensitive to the minimum contribution requirement and to the relative returns from the public and private alternatives.     

Threshold uncertainty in the private-information subscription game

We introduce threshold uncertainty, à la Nitzan and Romano (1990), into a private-values model of voluntary provision of a discrete public good. Players are allowed to make any level of contribution toward funding the good, which is provided if the cost threshold is reached. Otherwise, contributions are refunded. Conditions ensuring existence and uniqueness of a Bayesian equilibrium are established. Further restricting the threshold uncertainty to a uniform distribution, we show the equilibrium strategies are very simple, even allowing for any number of players with asymmetric distributions of values. Comparative statics with respect to changes in players' distributions are derived, allowing changes in both the intensity and the dispersion of values. For example, increased uncertainty, in the sense of mean-preserving spreads of players' distributions of values, increases equilibrium contributions. Finally, we show the equilibrium is interim incentive inefficient. The sharpness of our results greatly contrasts with the more qualified insights of earlier private-values models with known cost threshold, which relied on there being two symmetric players and generally exhibited multiple equilibria.     

Local public goods, inter-regional transfers and private information

Suppose that the centre wishes to make transfers between member states of a federation to reduce inequality. However, it lacks precise information concerning the cost differences that are responsible for the initial income inequality. We examine the implications of asymmetric information for the design of the transfer scheme. We show that if member states’ inherent cost levels as local public good providers take discrete values, the first best, or ‘complete information’, transfer scheme may or may not violate incentive compatibility. If inherent cost is a continuous random variable, such a scheme certainly violates incentive compatibility. We also explore the possibility of binding participation constraints. In our model, a binding incentive compatibility constraint leads to a reduction in effort devoted to cost reduction, and a binding participation constraint will also lead to a violation of Samuelson's optimality condition for public good provision.     

Playing monopoly in the creek: Imperfect competition, development, and in-stream flows

Land ownership and control of development in new and frontier cities is often concentrated. Local public goods, such as wetlands and riparian habitats, can be adversely affected by development. Regulatory pressure to protect these local public goods may not emerge until after some development has occurred. When development rights are insecure, an incentive exists to accelerate early development, an incentive that increases with the number of firms. Further, multiple equilibria may exist, which can result in large increases in development for small increases in the number of firms. When firms are uncertain about how the regulator values the local public good, development may be further accelerated and there may be even more equilibria.     

VOLUNTARY CONTRIBUTIONS TO A PUBLIC GOOD: NON-NEUTRALITY RESULTS

Abstract.  We show that the well-known neutrality theorem (that a small redistribution of wealth does not affect the aggregate private provision of a public good) no longer holds if agents take into account the effect of their individual supply of the public good on the relative price of private goods.     

Efficient Equilibria in the Voluntary Contributions Mechanism with Private Information

We characterize generally the Bayesian Nash equilibria of a voluntary contributions public goods game for two consumers with private information.The two consumers simultaneously make voluntary contributions to the public good, and the contributions are refunded if the total falls short of the cost of the public good. Several families of equilibria (step‐function, regular and semi‐regular) are studied. Necessary and sufficient conditions for regular and semi‐regular equilibrium allocations to be interim incentive efficient are derived. In the uniform distribution case we prove (i) the existence of an open set of incentive efficient regular equilibria when the cost of production is large enough and (ii) the existence of an open set of incentive efficient semi‐regular equilibria when the cost of production is low enough. Step‐function equilibra are proved to be interim incentive inefficient.     

Exchange Rules and the Incentive Compatibility of Choice Experiments

The incentive properties of stated-preference surveys continue to be a central debate in the valuation of public goods. The majority of empirical studies have focused on incentive properties of contingent valuation questions in relation to situations where answers have monetary consequences. This research explores the incentive properties of repeated, attribute-based choice questions when subjects are provided with an explicit connection between choices and outcomes. Two market/provision-rules are investigated: a posted-price market and a plurality-rule vote. These two provision rules are contrasted to treatments in which no provision rule is discussed—subjects are simply asked to choose their preferred alternative. These three hypothetical choice treatments are compared with a binding choice treatment. While none of the public good treatments are theoretically incentive compatible, we include a comparison of hypothetical and binding choices for a private-good that is incentive compatible. The private good experiments indicate that marginal willingness to pay (WTP) estimates from the hypothetical treatment are larger, but not statistically different than corresponding estimates in the binding choice treatment. Results for the public good experiments indicate that marginal WTP estimates from the hypothetical treatments are much larger, and statistically different than corresponding estimates in the binding choice treatment. The bias is largest when no provision rule is discussed. The bias is reduced with the inclusion of a provision rule, but surprisingly, there was no difference across provision rule treatments. Overall, our results indicate that choice experiments involving a public good should include a provision rule to reduce bias, but the resulting marginal WTP estimates may still be more biased, on average, than those arising from contingent valuation survey formats.     

Optimal democratic mechanisms for taxation and public good provision

We study the interdependence of optimal tax and expenditure policies. An optimal policy requires that information on preferences is made available. We first study this problem from a general mechanism design perspective and show that efficiency is possible only if the individuals who decide on public good provision face an own incentive scheme that differs from the tax system. We then study democratic mechanisms with the property that tax payers vote over public goods. Under such a mechanism, efficiency cannot be reached and welfare from public good provision declines as the inequality between rich and poor individuals increases.     

Constrained public goods in networks

This paper analyses the private provision of public goods where agents interact within a fixed network structure and may benefit only from their direct neighbours’ provisions. We generalise the public goods in the networks model of Bramoullé and Kranton [J. Econ. Theory 135 (2007), pp. 478–494] to allow for constrained provision. In so doing, we characterise Nash equilibria with no intermediate contributors.     

USING COMMERCIAL DISCIPLINE TO IMPROVE AUSTRALIAN DEFENCE PROCUREMENT: MISPLACED ENTHUSIASM?

Australia, like other democracies, has long sought to improve the efficiency and effectiveness of procurement for national defence. A recent review exhorted Defence procurement managers to exert greater “commercial discipline.” Similar calls have been made in other countries. This paper tests such public sector emulation of commercial practice by comparing the relative effectiveness of procurement via in‐house arrangements; a public procurement agency detached from Defence; and privatized provision. We show that what matters is not public or private ownership but how ownership and management are integrated and what incentive structures are applied. (JEL H44)     

Optimal Income Taxation and Public Good Provision with Endogenous Interest Groups

This paper studies public goods provision when agents differ in earning abilities as well as preferences. Heterogeneity in skills makes redistribution desirable and generates an equity-efficiency trade-off. If tax revenues are devoted to a public good, this trade-off is affected in such a way that income transfers are less desirable. High-skilled individuals thus have an incentive to exaggerate their preferences for public goods. Analogously, low-skilled individuals lobby against public good provision. A requirement of collective incentive compatibility eliminates these biases. It implies that income transfers are increased whenever a public good is provided and are decreased otherwise.     

Finitely Repeated Voluntary Provision of a Public Good

This paper theoretically explores the voluntary provision of a public good when either one of the following holds: (i) agents’ utility is the sum of their monetary earnings and a nonmaterial component, or (ii) agents’ exhibit satisficing behavior. We show that a small degree of either nonmaterial payoffs or satisficing behavior can generate large contributions in a finitely repeated game, even if the incentive to free‐ride on others’ contributions calls for negligible public good provision in the static game. The equilibrium is characterized by a sharp decline in contributions toward the end of the game. Several comparative results regarding group size and technology are consistent with laboratory data obtained in experimental studies. The model also predicts the restart effect observed in previous experiments.     

Best-shot network games with continuous action space

This paper presents a model of public good provision in networks where the level of public good that an agent has access to depends on the maximum of contributions by the agents in her neighbourhood. Our analysis shows that the game always has an equilibrium in pure strategies and all equilibria are specialised and stable. Welfare analysis shows that formation of new links in a prevailing network may not always be useful.     

Chores

We analyze situations where the provision of each of c public goods must be voluntarily assumed by exactly one of n private agents in the absence of transfer schemes or binding contracts. We model this problem as a complete information, potentially infinite horizon game where n agents simultaneously wage c wars of attrition. Providing a public good commits an agent not to take on the provision of another public good for a fixed period. We explore the strategic trade-offs that this commitment ability and the multiplicity of tasks provide. Subgame perfect equilibria (SPEs) are characterized completely for games with two agents and two public goods. For games with two identical agents and c > 1 identical public goods, we establish that an equilibrium that yields a surplus-maximizing outcome always exists and we provide sufficient conditions under which it is the unique equilibrium outcome. We show that under mild conditions, the surplus-maximizing SPE is the unique symmetric SPE. Journal of Economic Literature Classification Number: H41, C72, D13.     

Kantian Equilibrium

Consider a game whose strategies are "contributions". A strategy profile is a Kantian equilibrium if  no  player would like  all  players to alter their contributions by the  same multiplicative factor.  Kantian equilibria are Pareto efficient. We characterize the allocation rules on several domains of environments that can be implemented as Kantian equilibria. The concept unifies the  proportional solution  on production economies and the  linear cost-share equilibrium  on public-good economies. We study Kantian equilibrium in the prisoner's dilemma, in a voting problem, and in a political economy where redistribution is the issue. The Kantian dictum engenders considerable but not unqualified cooperation.     

Public sector motivation and development failures

This paper provides a theoretical analysis of the relationship between public sector motivation and development. In the model the public sector produces a public good and workers are heterogeneous in terms of public sector motivation (PSM). Wages in the private sector increase with the quality of the public good. In this context, public sector wage premia (PSWP) have two opposite effects: low PSWP helps screen workers with PSM into the public sector, while high PSWP helps motivate workers to be honest. Raising PSWP may not improve the quality of governance and multiple equilibria might arise. The model highlights that the relative importance of workers selection and provision of ”on the job” incentives in the public sector varies in systematic ways with wages in the private sector. We provide anecdotal and original empirical evidence consistent with the theoretical predictions and discuss some policy implications for public sector reforms in developing countries.     

A general characterization of interim efficient mechanisms for independent linear environments

We consider the class of Bayesian environments with independent types, and utility functions which are both quasi-linear in a private good and linear in a one-dimensional private-value type parameter. We call these independent linear environments. For these environments, we fully characterize interim efficient allocation rules which satisfy interim incentive compatibility and interim individual rationality constraints. We also prove that they correspond to decision rules based on virtual surplus maximization, together with the appropriate incentive taxes. We illustrate these techniques with applications to auction design and public good provision.     

Unequal Contributions from Symmetric Agents in a Local Interaction Model

The main findings of the theory on the private provision of public goods under the assumptions of symmetric agents and normality are that (1) there exists a unique Nash equilibrium in which everybody contributes the same; and (2) this pattern is stable. We show that these findings no longer hold in a context characterized by local interaction. In this context, it is always possible to find preferences satisfying the assumption of normality such that the symmetric Nash equilibrium is unstable, and there exist asymmetric Nash equilibria which are locally stable.