Global public goods and unilateral matching mechanisms

While conventional agreements on international public goods require bilateral or multilateral cooperation, we show that unilateral action through matching mechanisms with a self‐commitment device can possibly generate Pareto‐improving outcomes. Even without commitment, unilateral matching may also benefit both players at corner situations. We further characterize the conditions under which this desirable outcome is achieved, particularly highlighting the role of the income distribution and its interplay with the preferences. Moreover, we propose a variant of unilateral matching that can generate Pareto‐improving outcomes regardless of the preferences and the income distribution, indicating that income inequality may not be an obstacle for improving public good provision through unilateral matching.     

Global public goods and coalition formation under matching mechanisms

This paper links coalition theory with matching mechanisms in the presence of global public goods among heterogeneous players. This matching coalition may achieve Pareto‐improving outcomes while avoiding side payments. The paper characterizes conditions of coalition profitability and stability at both interior and corner equilibria. It is generally much harder to satisfy stability conditions than profitability conditions. A matching coalition is more profitable but less stable with a larger matching rate. Empirically there is no stable coalition but this can be overcome by introducing reputation mechanisms. There always exists a stable grand matching coalition if players value their reputation. The matching coalition faces a trade‐off between matching depth and breadth.     

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.     

On the voluntary provision of “weakest‐link” public goods: The case of private information

We characterize equilibria in a private‐provision public‐good game where individuals are allowed arbitrary contribution levels and the level of the public good equals the least contribution made by an individual. Equilibrium comparative statics are derived for the interim Pareto‐dominant equilibrium. First, improvements in the cost distribution of even only one player benefit all. Second, even with such “weakest‐link” public goods, for which greater similarity of preferences would seem to facilitate coordination, decreased heterogeneity can actually decrease payoffs. Indeed, increasing the riskiness of cost distributions has an ambiguous effect on welfare. Two mechanisms are provided for improving equilibrium payoffs: Technology transfer and cheap‐talk communication. While substantial welfare gains are possible, examples show that (a) technology transfer may be futile if a “regularity” condition is not satisfied and (b) cheap talk may be useless if the language for communication is not sufficiently rich.     

Budget Balancedness and Optimal Income Taxation

We make two contributions to the theory of optimal income taxation. First, assuming conditions sufficient for existence of a Pareto optimal income tax and public goods mechanism, we show that if agents' preferences satisfy an extended notion of single crossing called capacity constrained single crossing, then there exists a Pareto optimal income tax and public goods mechanism that is budget balancing. Second, we show that, even without capacity constrained single crossing, existence of a budget balancing Pareto optimal income tax and public goods mechanism is guaranteed if the set of agent types contains no atoms.     

Existence of an equilibrium with arbitrary tax schemes for financing local public goods

The existence of a public competitive equilibrium for any arbitrary (nondistortive) tax schemes (in particular, proportional taxes) for economies with local public goods, is proved. Allowing preferences to be both nontransitive and noncomplete enables an explicit introduction of the government as an (additional) agent in the economy. Moreover, we allow for “spillovers” of the public goods among localities, and for the production sets to depend on the amount of public goods produced in the economy. The only restriction on the tax system is that every individual is able to afford it and that the government's budget never runs a surplus. Since every equilibrium allocation is a Pareto optimum, every tax scheme is optimal (in the sense that its equilibrium allocation is a Pareto optimum).     

On the evolution of conditional cooperation

A long series of laboratory and field experiments, as well as conventional empirical studies, has established that (1) individuals voluntarily provide themselves with public goods at levels exceeding those predicted by the Nash voluntary contributions mechanism, and (2) agents reciprocate increases in the contributions of their counterparts in such settings (conditional cooperation). This paper presents a simple model of the evolution of preferences for conditional cooperation in the presence of a public good, which explains these two empirical findings without employing reputational or group selection arguments. In this model, individuals inherit preferences to match other agents' contributions to the provision of a public good, at some specified “matching rate.” Agents whose preferences induce them to be relatively successful – in material terms – increase in number, from one generation to the next. Under complete information and with randomly matched groups of N agents who have quasilinear preferences over the public good and a private good, the unique evolutionarily stable matching rate is 1, leading to Pareto optimal voluntary provision of the public good, regardless of group size N. The evolutionarily stable matching rate can be viewed as an endogenous social norm.     

Commitment and matching contributions to public goods

We study multi-stage processes of non-cooperative voluntary provision of public goods. In the first stage, one or more players announce contributions that may be conditional on the subsequent contributions of others. In later stages, players choose their own contributions and fulfill any commitments made in the first stage. Equilibrium contributions are characterized under different assumptions about the commitment ability of players, the number of public goods and whether players commit to matching rates or to discrete quantities. We focus on contribution mechanisms that can emerge and be sustainable without a central authority, and that may be particularly relevant for international public goods. Efficient levels of public goods can be achieved under some circumstances, while in others commitment is ineffective.     

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.     

A voting model for the allocation of public goods: Existence of an equilibrium

It is well known that equilibria may not exist for majority voting over multidimensional policy spaces. This paper shows that certain institutional constraints can be imposed upon the voting process to ensure existence of a restricted equilibrium. A restricted equilibrium point must defeat only those points connected to it by one of an exogenously given set of linearly independent voting vectors. Using this procedure in a general equilibrium model to determine demands for public goods, existence of a general political equilibrium is proven. The equilibrium need not be Pareto optimal and may be manipulated by changing the vectors.     

Public goods,voting, and growth

We study a parametric politico‐economic model of economic growth with productive public goods and public consumption goods. The provision of public goods is funded by a proportional tax. Agents are heterogeneous in their initial capital endowments, discount factors, and the relative weights of public consumption in overall private utility. They vote on the shares of public goods in gross domestic products (GDP). We propose a definition of voting equilibrium, prove the existence and provide a characterization of voting equilibria, and obtain a closed‐form solution for the voting outcomes. Also we introduce a “fictitious” representative agent and interpret the outcome of voting as a choice made by a central planner for his benefit. Finally, we undertake comparative static analysis of the shares of public goods in GDP and of the rate of balanced growth with respect to the discount factors and the preferences for public consumption. The results of this analysis suggest that the representative‐agent version of our model is capable of capturing the interaction between many voting heterogeneous agents only if the heterogeneity is one‐dimensional.     

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.     

Efficiency, monotonicity and rationality in public goods economies

Summary. In economies with public goods, we identify a necessary and sufficient condition for the existence of cost monotonic, Pareto optimal and individually rational mechanisms. These exist if and only if the preferences of the agents satisfy what we call the equal ordering property. We also show that when this condition holds the egalitarian equivalent correspondence is the only cost monotonic selection from the core of the economy. Furthermore, it is unambiguous in the sense that the agents are indifferent among all the allocations in it. Received: February 26, 1996; revised version: January 31, 1997     

The strategic Marshallian cross

We prove existence and uniqueness of non-autarkic equilibria in bilateral oligopoly assuming only that preferences are binormal and satisfy a weakened version of gross substitutes. We permit complete heterogeneity of preferences and our analysis exploits the fact that payoffs depend only on own strategy and two universal aggregates. This allows us to define strategic versions of supply and demand curves such that non-autarkic Nash equilibria are in 1–1 correspondence with intersections of these curves. The same approach can be used to establish comparative statics under the assumptions above. As examples, we focus on adding players and changing endowments. This competitive approach also allows us to conclude that much of conventional Marshallian analysis is robust to strategic manipulation.     

On the set of Pareto efficient allocations in economies with public goods

Summary We examine the set of Pareto-efficient allocations in economies with public goods. We show that even if preferences are continuous and strongly monotonic, it need not coincide with the set of weakly efficient allocations. We then study topological properties of the Pareto set. We show that it is neither connected nor closed in allocation space. Furthermore, if the public goods are local, the image of the Pareto set in utility space need not be closed or connected. We provide two independent sufficient conditions for the closedness of the Pareto set. The results are directly applicable to private goods economies with joint production. Our results should be of interest for general equilibrium and mechanism design theory; where for example, the properties of the efficient set are important for proving the existence of an equilibrium and for the study of the properties of monotone-path social choice correspondences.We thank Hideo Konishi, Tomoichi Shinotsuka, Nicholas Yannelis and an anonymous referee for valuable comments on previous drafts of this paper.     

The strategic Marshallian cross

We prove existence and uniqueness of non-autarkic equilibria in bilateral oligopoly assuming only that preferences are binormal and satisfy a weakened version of gross substitutes. We permit complete heterogeneity of preferences and our analysis exploits the fact that payoffs depend only on own strategy and two universal aggregates. This allows us to define strategic versions of supply and demand curves such that non-autarkic Nash equilibria are in 1–1 correspondence with intersections of these curves. The same approach can be used to establish comparative statics under the assumptions above. As examples, we focus on adding players and changing endowments. This competitive approach also allows us to conclude that much of conventional Marshallian analysis is robust to strategic manipulation.     

Leadership and motivation for public goods contributions

Results from a leader–follower public goods game are presented. An individual, when randomly selected to make a contribution knowing others will observe the selection, gives more than in the simultaneous‐move public goods game. Followers adopt a quasi‐matching strategy where they systematically donate less than the leader, but contribute more when the leader does and contribute less when the leader free rides. The net result is increased provision of a public good when contributions are sequential. The results highlight that psychological preferences, rather than solely social preferences, can explain behavior.     

Competition between asymmetrically informed principals

Summary. This paper derives the set of equilibria for common agency games in which the principals compete in piece rates and lump sum payments and one principal has incomplete information about the agent's preferences. We show that the uninformed principal's expected payoff function is discontinuous with respect to the identity of the marginal agent type. This discontinuity is shown to support an open set of equilibria. For games in which the first-best equilibrium strategies are measurable with respect to the uninformed principal's information partition, this result implies the existence of an open set of Pareto inefficient equilibria. Received: December 5, 1995; revised version August 18, 1996     

The Efficiency of Direct Public Involvement in Environmental Policymaking: An Experimental Test

In collaborative negotiation, stakeholder representatives are charged with the development of a mutually acceptable set of public policies. Although this approach has become popular in environmental negotiations, little is known about the characteristics of the outcomes that are reached. In this paper, we employ an Edgeworth box framework to investigate the nature of bargaining over public goods (environmental policies) that have multiple attributes. We then design and conduct laboratory experiments within this framework to test whether negotiated outcomes satisfy standard axiomatic bargaining predictions under a variety of conditions. Specifically, we test whether two parties with Pareto inefficient endowments of two goods will trade to Pareto improving and Pareto efficient outcomes, and to the Nash bargain in particular. We vary whether the Nash bargain coincides with or diverges from the outcome that maximizes the joint payoff, or the outcome that equalizes payoffs, and whether subjects are provided full or partial information. We find that bargainers reach Pareto improving and efficient outcomes across treatments, but withdraw support for the Nash bargain when it generates unequal payments or when payoff information is private. We conclude that this experimental framework offers a promising method for studying multi-attribute negotiations.     

Collective decisions with interdependent valuations

Many collective decision problems have in common that individuals’ desired outcomes are correlated but not identical. This paper studies collective decisions with private information about desired policies. Each agent holds private information which mainly concerns his own bliss point, but private information also affects all other agents. We concentrate on two specific mechanism, the median and mean mechanisms establish the existence of symmetric Bayesian Nash equilibria of the corresponding games and compare the performance of the mechanisms for different degrees of interdependencies. Applications of our framework include the provision of public goods and the design of decision processes in international organizations.