Lindahl Allocations Research Articles

Continuous and Feasible Implementation of Rational-Expectations Lindahl Allocations

In this paper we consider Bayesian implementation of rational-expectations Lindahl allocations for economic environments with public goods when agents are incompletely informed about environments. We construct a continuous and feasible mechanism whose Bayesian equilibrium allocations coincide with rational-expectations Lindahl allocations. We not only allow the types of individuals to be unknown but also allow both the preferences and the initial endowments to be unknown to the designer. In addition, we allow some types of boundary equilibrium allocations and a continuous information structure.Journal of Economic LiteratureClassification Number: C72, D71, D82, H41.

A STABLE NASH MECHANISM FOR QUASI-ADDITIVE PUBLIC-GOOD ENVIRONMENTS

In this paper we present a simple game form implementing Lindahl allocations as Nash equilibrium outcomes, which has nice stability properties. we show that if the preferences of eaach consumer are representable by a utility function of the form a(y)xi+bi(y), where xi(y), where xi is the amount of private good and y, the amount of public good, then the Nash equilibrium of our geme is locally stable under the gradient adjustment process. This restriction on the preferences has been known in hte literature as the necessary and sufficient condition for the Pareto optimal amount of pukic goods to be independent of the private goods distribution. This type of preference includes quasi-linear preferences as a special case. but unlike quasi-linearity, this allows a non zero income effect of demand for public goods as well as private goods, which is often supported by empirical evidence. Our result shows how an equilbirium can be achieved over time by a decentralized strategy adjustement process for a fairly general class of environments, even in the absence of a dominant-strategy equilibrium.

On Nash-Implementation in the Presence of Withholding

In this paper we construct a completely feasible and continuous mechanism whose Nash allocations coincide with Lindahl allocations when both preferences and initial endowments are unknown to the designer and unreported endowments are withheld. This mechanism extends the mechanism of Hong by allowing for semi-positivity of endowments for private goods economies and the mechanism of Tian by allowing for any number of private goods for public goods economies. Thus our mechanism improves all the existing mechanisms that implement Walrasian or Lindahl allocations. Journal of Economic Literature Classification Numbers: C72, D6l, D78, H41.

Nash-Implementation of the Lindahl Correspondence with Decreasing Returns to Scale Technologies

This paper considers the problem of designing 'well-behaved' mechanisms whose Nash allocations coincide with Lindahl allocations in the presence of decreasing returns to scale technologies. The mechanism presented here is individually feasible, balanced, continuous, and differentiable around Nash equilibria. Further, the mechanism has a message space of minimal dimension. Moreover, the authors show that, in contrast to mechanisms dealing with constant returns to scale, an important characteristic of mechanisms implementing the Lindahl correspondence with decreasing returns to scale technologies is that at least one individual's personalized prices depend on his own messages, provided the mechanisms are balanced and smooth. Copyright 1995 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Sequential contributions to public goods

I examine games involving private contributions to a public good and show that less of the public good will be supplied if agents move sequentially than if they move simultaneously. If the agents bid for the right to move first, the agent who values the public good least will win. If each agent chooses the rate at which he will subsidize the other agent's contributions, the subsidies that support the Lindahl allocation are the unique equilibrium outcome. I also describe two related subsidy-setting games that yield Lindahl allocations in n-person games with general utility functions.

Convergence Theorems on the Core of a Public Goods Economy: Sufficient Conditions

It is shown if all consumers are either asymptotically satiated or strictly nonsatiated in public goods, then the core converges to the Lindahl allocations as the economy grow without bound. Asymptotic satiation implies that only a vanishing fraction of the private good is devoted to public goods production as the economy gets large. Strict nonsatiation, on the other hand, implies that essentially all of the private good is devoted to public goods production in the limit. It is interesting that these two conditions are independently sufficient for core convergence despite their completely opposite implications for the asymptotic nature of the Lindahl allocations. Journal of Economic Literature Classification Numbers: H41, D51, C71.

Nash implementation of Lindahl allocations

We define a class of Nash based mechanisms that implement Lindahl allocations in standard public good economies. As those that first proved Nash implementation of Lindahl allocations, defined by Hurwicz (1979) and Walker (1981), the mechanisms provided here are continuous, feasible, and independent of agents' characteristics. In economies with two agents (e.g., bilateral monopolies, duopolies, principal-agent models), our mechanisms are also applicable, in contrast to the well-behaved mechanisms in the literature, and they satisfy favourable stability properties.

Implementing Lindahl allocations by a withholding mechanism

This paper investigates the problem of designing mechanisms whose Nash allocations coincide with Lindahl allocations for public goods economies when initial endowments are private information and unreported endowments are consumed (withheld) but are not destroyed. It will be noted that the mechanism presented here is individually feasible, balanced, and continuous. Besides, we allow preferences of agents to be nontotal-nontransitive and discontinuous.

A stable Nash mechanism implementing Lindahl allocations for quasi-linear environments

A new simple game form implementing Lindahl allocations as Nash equilibrium outcomes is presented. Under the assumption of quasi-linear preferences, the gradient adjustment process of the new game form stabilizes the Nash equilibrium of the game form. Moreover, this adjustment process is globally stable. This shows how an equilibrium can be achieved over time by a decentralized strategy adjustment process, even in the absence of a dominant strategy equili- brium. In addition, the game form is auctioneerless.

Implementation of Lindahl allocations with nontotal—nontransitive preferences

The purpose of this paper is to present a mechanism the Nash allocations of which coincide with the Lindahl allocations even when preferences are nontransitive or nontotal. This extension to include nontotal–nontransitive preferences is potentially very important since preferences of agents are nontransitive–nontotal in many cases — in particular in the case where the players are groups of individuals. Besides, the mechanism presented here uses outcome functions that are individually feasible, balanced (not merely weakly balanced), continuous, differentiable around Nash equilibria and, furthermore, almost everywhere differentiable. Moreover, the mechanism has a message space of minimal dimension.

Completely feasible and continuous implementation of the Lindahl correspondence with any number of goods

This paper deals mainly with the problem of designing mechanisms whose Nash allocations coincide with the Lindahl allocations for public goods economies with any number of private and public goods. The mechanism presented here improves the previous mechanisms by introducing two new features. One is that the mechanism is balanced (not merely weakly balanced). The other is that the level of public goods is provided with the marginal cost pricing rule for both equilibrium and disequilibrium messages so that the single-valued input demand outcome function is obtained by the Shephard lemma and the prices of public goods equal the minimum-unit-cost functions. Besides, the mechanism is single-valued, individually feasible, and continuous.

Completely feasible and continuous implementation of the Lindahl correspondence with a message space of minimal dimension

This paper deals mainly with the problem of designing mechanisms whose Nash allocations coincide with the Lindahl allocations. It goes beyond the previously existing literature in that it uses outcome functions that are individually feasible, balanced, and continuous, and further, has a message space of minimal dimension and thus is informationally efficient.

Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism

This paper considers the problem of designing mechanisms whose Nash allocations coincide with the Lindahl allocations for public goods economies with more than one private good. Unlike previous mechanisms, the mechanism presented here has a single-valued, feasible, and continuous outcome function. Furthermore, when there are no public goods in economies, feasible and continuous implementation of the (constrained) Walrasian correspondence can be obtained as a corollary of our Theorem 1.

A ‘fair share’ model of public good provision

Many voluntary or non-profit organizations produce outputs that are best characterized as public goods. These organizations are financed, at least in part. by donations from individuals. Only models which incorporate internal (psychic) rewards for donating appear to be consistent with actual donor behavior. A simple ‘fair share’ model is proposed as an example. It is shown that under weak restrictions on demand, the donation process is locally stable about the Lindahl allocation. The process therefore converges to an efficient level of public good provision entirely without government intervention.

Stable implementation of Lindahl allocations

The resource allocation mechanisms using Nash equilibrium as the solution concept in economies with incomplete information rely on the assumption that agent's disequilibrium messages converge to a Nash equilibrium. The mechanisms implementing Lindahl allocations are, however, extremely unstable under the most used process to represent disequilibrium behaviour in games of incomplete information: the Cournot process. We provide a new mechanism overcoming the instability difficulty in the case of quasi-linear preferences.

An Incentive Compatible Price Mechanism For Attaining Lindhal Allocation

A mechanism operated by price signals of individuals that yields Lindahl allocation as an outcome is studied. This mechanism incorporates producers as players as well as consumers. The mechanism is valid when there are two or more consumers. A stable allocation rule exists when two consumers are present, and a stable operation of the mechanism through parameter for the more general environment is analized. [020]

On Bayesian Implementable Allocations

This paper identifies several social choice correspondences which are and are not fully implementable in economic environments when agents are incompletely informed about the environment. We show that in contrast to results in the case of complete information, neither efficient allocations nor core allocations define implementable social choice correspondences. We also identify conditions under which the Rational Expectations Equilibrium correspondence is implementable. We extend the concepts of fair allocations and Lindahl allocations to economies with incomplete information, and show that envy-free allocations and Lindahl allocations are implementable under some conditions while fair allocations are not.

Voluntariness and efficiency in the provision of public goods

This paper presents a characterization of Lindahl allocations which makes no reference to personalized prices. Lindahl equilibria are characterized here by two conditions: Pareto efficiency and a voluntariness condition. Voluntariness requires that no consumer may benefit from a reduction in his contribution if this means that the vector of public goods must be reduced in the same proportion. The intersection of the (large) set of voluntary allocations and that of efficient ones turns out to be (under differentiability) the set of Lindahl allocations.

A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations

A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations

Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points

In this paper we shall present balanced outcome functions . These are functions which, for any given set of messages by individual agents in the economy, determine as their outcome an economic allocation satisfying the resource balance constraints of the economyi.e. the constraints that, for any good, total demand must not exceed total supply. Now, it has been known for a long time that outcome functions realizing the Walrasian (or Lindahl) equilibrium correspondence can easily be constructed provided an auctioneer is permitted and balance not required. In unpublished work, Schmeidler has presented a balanced outcome function without an auctioneer which realizes the Walrasian correspondence when there are at least three traders; a later variant (in a forthcoming paper by the Author) appears also to work for two traders. As he himself noted, his outcome function is not individually feasible. It is also discontinuous. Groves and Ledyard (1977) proposed balance outcome functions whose equilibrium correspondences yield allocations which are Pareto optimal but not individually rational (in the sense that traders can be worse off than if they refused to trade at all), and hence not Lindahl allocations. Here again it is required that there be at least three traders. The outcome functions used by Groves and Ledyard are quadratic, and so smooth. For the pure exchange economy with at least three traders Hurwicz (1976) has constructed analogous balanced outcome functions which are Pareto optimal but not individually rational, as well as non-balanced outcome functions which are Pareto optimal (but not individually rational) when there are two traders. Shapley, Shubik, Schmeidler, Pazner and Postlewaite have also constructed feasible outcome functions that can yield allocations outside the Pareto optimal set. Either the outcome functions or the message spaces depend, however, on the initial endowment vectors, so that agents have to know one anothers' endowments. Thus, these outcome functions are not informationally decentralized. In the present paper we show balanced outcome functions that are smooth and, without employing an auctioneer, yield equivalence between Nash and Walrasian (or, where appropriate, Lindahl) allocations, for three or more traders. Our outcome functions are smooth, but not individually feasible away from equilibrium.