A simple market-like allocation mechanism for public goods

doi:10.1016/j.geb.2016.02.002

Games and Economic Behavior

Volume 101, January 2017, Pages 6-19

https://doi.org/10.1016/j.geb.2016.02.002 Get rights and content

Abstract

We argue that since allocation mechanisms will not always be in equilibrium, their out-of-equilibrium properties must be taken into account along with their properties in equilibrium. For economies with public goods, we define a simple market-like mechanism in which the strong Nash equilibria yield the Lindahl allocations and prices. The mechanism satisfies critical out-of-equilibrium desiderata that previously-introduced mechanisms fail to satisfy, and always (weakly) yields Pareto improvements, whether in equilibrium or not. The mechanism requires participants to communicate prices and quantities, and turns these into outcomes according to a natural and intuitive outcome function. Our approach first exploits the equivalence, when there are only two participants, between the private-good and public-good allocation problems to obtain a two-person public-good mechanism, and then we generalize the public-good mechanism to an arbitrary number of participants. The results and the intuition behind them are illustrated in the familiar Edgeworth Box and Kölm Triangle diagrams.

Section snippets

The pure exchange allocation problem

There are two goods and two traders. Trader S wishes to sell good X in exchange for good Y, and Trader B wishes to purchase good X in exchange for good Y. It's convenient to think of Y as money.

The number of units of X the traders exchange will be denoted by q; the price at which the units are exchanged is denoted by p; and we write $m = p q$ for the amount of money exchanged. Thus, B pays $m = p q$ dollars to S in exchange for q units of X. Each trader $i \in {B, S}$ has a strictly quasiconcave utility

The public good allocation problem

Now we assume that the good X is a public good. We continue to think of the good Y as money, and we assume that it costs cq dollars to provide q units of the public good. The two-person allocation problem is to decide on the level q at which the public good will be provided, and how the cost of providing the q units, viz. cq, will be divided between two persons A and B. Allocations, or outcomes, are therefore triples $(q, t_{A}, t_{B})$ that satisfy the equation $t_{A} + t_{B} = c q$ ; the amounts $t_{A}$ and $t_{B}$ are in

The mechanism with more than two participants

So far, we've exploited the fact that the private-goods and public-goods allocation problems are identical in the two-person case to establish that a natural trading mechanism for private goods can be exactly duplicated when one of the goods is a public good, and that the mechanism has the same properties in both the private- and public-good problems. Here we extend the public-good version of the mechanism to an arbitrary number of participants.⁷

Discussion

We set out to devise a mechanism for allocating public goods in which the mechanism's participants would communicate via natural, market-like proposals involving quantities and Lindahl-like prices, and in which a transparent and natural outcome function would always turn the price-quantity proposals into balanced and acceptable outcomes that would be Lindahl allocations when in equilibrium. The necessary insights were provided by focusing first on the problem when there are only two parties

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A simple market-like allocation mechanism for public goods

Abstract

Section snippets

The pure exchange allocation problem

The public good allocation problem

The mechanism with more than two participants

Discussion

J. Public Econ.

Econ. Letters

J. Math. Econ.

J. Econ. Theory

J. Math. Econ.

Games Econ. Behav.

Acceptable points in general cooperative N person games

Provision of public goods: fully implementing the core through private contributions

Rev. Econ. Stud.

Coalition proof Nash equilibria I: concepts

J. Econ. Theory

Nash bargaining III

The Demand and Supply of Public Goods

Learning and incentive compatible mechanisms for public good provision: an experimental study

J. Polit. Economy

A family of supermodular Nash mechanisms implementing Lindahl allocations

Econ. Theory

When does learning in games generate convergence to Nash equilibria? The role of supermodularity in an experimental setting

Amer. Econ. Rev.

Double implementation of the ratio correspondence by a market mechanism

Econ. Design

Nash implementation of Lindahl allocations

Soc. Choice Welfare

Price quantity strategic market games

Econometrica

A solution to the “free rider” problem

Econometrica