On equity with public goods

Existence theorems for envy-free and efficient allocations are derived for economies with public goods. For economies with an arbitrary but finite number of private and public goods, an adaptation of the existence proof of Svensson for private good economies is used. For economies with one private and one public good, a case often studied in theory and applications, two more direct proofs are given, using different conditions and taking advantage of the particularly simple structure of the set of envy-free allocations in this case. These proofs are also shown to apply to the case of excludable public goods with congestion.I am grateful to William Thomson, Marcus Berliant, Robert Gilles, Hervé Moulin, Thomas Palfrey, Tomoichi Shinotsuka, Simon Wilkie, and two anonymous referees for their comments. This paper is a revised version of Chap. 1 of my doctoral dissertation submitted to the University of Rochester in July 1988. The financial support of the University of Rochester in the form of the Raymond N. Ball Dissertation Year Fellowship is gratefully acknowledged. All shortcomings of this paper are solely of my own creation.     

A characterization of strategy-proof social choice functions for economies with pure public goods

We characterize strategy-proof social choice functions when individuals have strictly quasi-concave, continuous and satiated utility functions on convex subsets of IR ^m , representing preferences for the provision of m pure public goods. When specialized to the case m=1, these assumptions amount to requiring that preferences are single peaked, and for such a domain there exists a wide class of strategy-proof social choice functions. These were studied by Moulin (1980) under strong additional assumptions. Our first results characterize the complete class, after an appropriate extension of the single-peakedness condition. The new characterization retains the flavour of Moulin's elegant representation theorem. For the general m-dimensional case, previous results have shown that there is no efficient, strategy-proof, nondictatorial social choice function, even within the domain restrictions under consideration (Border and Jordan 1983; Zhou 1991). In fact, Zhou's powerful result indicates that nondictatorial strategy-proof s.c.f.'s will have a range of dimension one. This allows us to conclude with a complete characterization of all strategy-proof s.c.f.'s on IR ^m , because restrictions of preferences from our admissible class to one dimensional subsets satisfy the slightly generalized notion of single-peakedness that is used in our characterization for the case m=1. We feel that a complete knowledge of the class of strategy-proof mechanisms, in this as well as in other contexts, is an important step in the analysis of the trade-offs between strategy-proofness and other performance criteria, like efficiency.This paper was written while both authors were visiting GREMAQ, Université des Sciences Sociales de Toulouse. We are thankful for its hospitality and good research atmosphere. Barberà's work is supported by the Instituto de Estudios Fiscales and by research grant PB89-0294 from the Secretaría de Estado de Universidades e Investigación, Spain. Jackson acknowledges the support of NSF grant SES8921409. We thank Jacques Crémer, Beth Allen, John Weymark and two anonymous referees for helpful comments on earlier drafts.     

Equilibrium and efficiency with property rights and local consumption externalities

There is no mechanism that guarantees existence and Pareto optimality of equilibrium in all situations if each individual has limited property rights and a utility function that depends upon his neighbour's consumption. This is true under virtually any assumption about coalition formation. Therefore, Sen's paradox of the Paretian liberal is confirmed in an economic exchange setting with limited externalitities, and Coase's conjecture on the efficiency of bargaining with complete information is denied.David Austen-Smith, Michael Peters, and Jonathan Riley provided helpful comments at various stages. I am grateful for their suggestions and for the financial support of the Social Sciences and Humanities Research Council (Canada). Responsibility for the paper's deficiencies rests with the author, of course.     

Social capital and public goods

Previous literature suggests positive relationships between social capital, pro-social behavior and subsequent economic development. We analyze the relationship between social networks and trust (two measures of social capital) and self-reported charitable contributions of time and/or money (pro-social behavior) using data collected from two ethnically distinct, low-income neighborhoods. We find that large social networks are positively related to charitable contributions, but that the effects of trust are less robust. We also find that social networks that are more geographically dispersed tend to be larger. Our results indicate that the social capital in a neighborhood is more important than ethnicity, ethnic diversity, or other demographic information in understanding public goods contributions.     

Trade-off between equity and efficiency in a general economy with indivisible goods

In most of the recent literature on fair allocation in economies with indivisible goods and a single infinitely divisible good, it is assumed that each agent can consume at most one indivisible good. In this paper, we show that if this assumption is dropped, there do not necessarily exist envy-free and Pareto efficient allocations. However, envy-free allocations still exist and so do Pareto efficient allocations. Hence, a trade-off between equity and efficiency arises.     

Distribution-neutral provision of public goods

The paper describes a normative approach to budget incidence, given the provision of a public good. The objective is to balance the budget by an income tax such that the budget is distribution-neutral. This property requires that every consumer’s net welfare gain, i.e. the benefit from consuming the public good and the tax burden in financing it, does not change the inequality inherent in the income distribution. The properties of the distribution-neutral tax are investigated and completely determined. The marginal willingness to pay for the public good is decisive for the degree of progression of the tax schedule. My co-author Georg Tillmann passed away in March 2006, much too soon. He was my friend, more than a colleague. I dedicate this paper to his memory.     

Embeddedness and cohesion: regimes of urban public goods distribution

Theory and Society - Why do some urban governing regimes realize a more equal distribution of public goods than others? Local government interventions in São Paulo, Brazil, have produced...     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

Linear cost sharing in economies with non-Samuelsonian public goods: Core equivalence

 We consider an economy with non-Samuelsonian public goods and we focus on linear cost sharing. In a linear cost sharing equilibrium all agents in the economy optimize given a certain fixed cost share to be contributed towards the provision of public goods in the economy. Hence, each agent pays a certain fraction of the total establishment costs of public goods and these cost shares are common knowledge. We show that for a certain fixed contribution scheme the resulting linear cost share equilibria are equivalent to corresponding core allocations, in which the core is based on the integral of the individual cost shares. We also show that there is no equivalence of the Foley core with cost share equilibria, even in well-behaved large economies. Received: 16 August 1995/Accepted: 29 July 1996     

Equal factor equivalence in economies with multiple public goods

We reconsider the problem of provision and cost-sharing of multiple public goods. The efficient equal factor equivalent allocation rule makes every agent indifferent between what he receives and the opportunity of choosing the bundle of public goods subject to the constraint of paying r times its cost, where r is set as low as possible. We show that this rule is characterized in economies with a continuum of agents by efficiency, a natural upper bound on everyone's welfare, and a property of solidarity with respect to changes in population and preferences. Received: 3 August 1995 / Accepted : 29 April 1997     

When in Rome: conformity and the provision of public goods

We ask whether conformity, copying the most observed behavior in a population, affects free riding. Our model suggests that, if sufficiently frequent at the start of a public goods game, conformity will increase the growth rate of free riding. We confirm this prediction in an experiment by showing that free riding grows faster when players have the information necessary to conform. As a stricter test, we econometrically estimate the dynamic on which the model is based and find that, controlling for the payoff incentive to free ride, players react significantly to the number of free riders in their groups.     

Binary participation and incremental provision of public goods

This paper presents a comprehensive analysis of voluntary binary participation in the provision of public goods in a full information setting where the marginal product of participation is positive but decreases with the number of participants. Our study extends Palfrey and Rosenthal's (1984) binary model. It deals with an important special case of uniform multi-person prisoner's dilemma, Schelling (1978), that might be conceived of as the discrete counterpart of the continuous model where both players' contributions and the production function of the public good are continuous, Olson (1965), Chamberlin (1974), McGuire (1974). For pure strategies, we find that as in the continuous setting, Nash equilibria are inefficient and the public good is underprovided. Surprisingly, for mixed strategies, the symmetric equilibria are inefficient, however, even in expected terms, the public good can be overprovided. The concurrence between inefficiency and underprovision of the public good reemerges, provided that one of the following holds: (i) the number of potential participants is sufficiently large, (ii) the marginal product of participation is sufficiently stable, (iii) the costs of participation are sufficiently low or sufficiently high, or (iv) the identical players are constrained to select identical strategies.We would like to thank Howard Rosenthal and two anonymous referees for very helpful comments and suggestions.     

Strategy-proof rules for two public goods: double median rules

We consider the problem of selecting the locations of two (identical) public goods on an interval. Each agent has preferences over pairs of locations, which are induced from single-peaked rankings over single locations: each agent compares pairs of locations by comparing the location he ranks higher in each pair. We introduce a class of “double median rules” and characterize it by means of continuity, anonymity, strategy-proofness, and users only. To each pair of parameter sets, each set in the pair consisting of $(n+1)$ parameters, is associated a rule in the class. It is the rule that selects, for each preference profile, the medians of the peaks and the parameters belonging to each set in the pair. We identify the subclasses of the double median rules satisfying group strategy-proofness, weak efficiency, and double unanimity (or efficiency), respectively. We also discuss the classes of “multiple median rules” and “non-anonymous double median rules”.     

Network public goods with asymmetric information about cooperation preferences and network degree

We propose a game theoretical model of one-shot network public goods formalizing the ‘closure argument’ that cooperation is more frequent in denser groups or networks. Equilibrium analyses show that (i) an ‘inefficiency problem’ exists: players all preferring mutual cooperation need not all cooperate; (ii) in dyads, groups and networks with degree independence, first order stochastic dominance shifts of the distribution of cooperation preferences or the degree distribution (weakly) increases cooperation, and (iii) the latter result does not hold for networks with degree dependence. Hence the closure argument always holds in networks satisfying degree independence but not in other networks.     

Sanctioning as a social norm: Expectations of non-strategic sanctioning in a public goods game experiment

Sanctioning increases cooperation in public goods games, but not indiscriminately under all conditions and in all societies, and the mechanisms by which sanctioning exercises its impact on behavior are yet to be studied in detail. We show experimentally that in the presence of sanctioning, our experimental subjects adjust their behavior in order to avoid being a free rider. They do this not only in the STANDARD sanctions treatment, where they directly experience any sanctions assigned to them, but also in our main treatment, the SECRET sanctions treatment, where no information on sanctions received is available until the end of the experiment. We observe no such free riding avoidance in the treatment without sanctioning. The mere knowledge that sanctions might be assigned increases cooperation among the members of our subject pool; subjects expect that non-strategic sanctioning occurs against the free riders. Moreover, these expectations are correct as we observe a similar pattern and extent of sanctioning in both treatments. We propose that sanctioning in itself is a social norm and may be culturally dependent, as suggested in the literature.     

Multilevel public goods game: Levelling up,substitution and crowding-in effects

In an online multilevel public goods experiment, we implement four treatments where we gradually increase the marginal per capita return of the global public good. First, we find evidence of an increase in the contribution to the global good (levelling-up effect). Secondly, subjects fund their higher contribution to the global good by reducing their contribution to the local good (substitution effect) rather than by increasing total contribution, i.e., the sum of their contributions to the local and the global good (marginal crowding-in effect). Moreover, we observe that total contribution increases as a consequence of the mere introduction of the global good (categorical crowding-in effect). Finally, we observe that subjects continue to contribute to both public goods even when they are dominated in terms of costs and returns.     

Private provision of public goods under price uncertainty

In this paper, price uncertainty is introduced into the model of voluntary provision of public goods. The analysis is carried out depending upon whether individuals make real or nominal contributions. We highlight the significant factors that determine the complex effects of changes in uncertainty on the level of provision, the level of welfare, and the gaps between equilibrium and optimal values of these variables. In particular, we show that in some situations it would be desirable to introduce artificial randomness in prices in order to alleviate the free rider problem and to increase welfare.We are indebted to two referees for their comments and suggestions.     

On increased risk and the voluntary provision of public goods

This paper examines the impacts of increased risk on the voluntary provision of public goods. I strengthen the view that uncertainty ameliorates free riding even given negative non-Nash conjectures. This result holds since the change in the perceived free riding (i.e., the magnitude of the conjecture) drives voluntary contribution to public good supply. The result has two main implications. First, the traditional model of the rational self-interested individual can explain voluntary contributions. Second, a public policy to encourage volunteerism would maintain private information of private contributions to the supply of public goods. However, risk as a public policy instrument is limited by ethical concerns and behavioral responses to risk.U.S. Environmental Protection Agency provided support for this research. Garey Durden, Todd Sandler, Fred Sterbenz, Robert Sugden, and Joe Kerkvliet provided useful comments. I owe tanks to Peter Bohm, Hans Wijkander, and Charles Mason for encouraging my work in this area. Two referees provided detailed suggestions that greatly improved the paper.