A simple market-like allocation mechanism for public goods

We argue that since allocation mechanisms will not always be in equilibrium, their out-ofequilibrium 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. JEL codes: D820, H4, D5, C72. * [email protected] † [email protected] Corresponding author: Mark Walker, Economics Department, U. of Arizona, Tucson AZ 85721-0108 Telephone: 520-241-8868, Fax: 520-621-8450. There is a substantial literature analyzing the design of institutions, or “mechanisms,” for achieving efficient allocations in the presence of public goods. The pioneering paper by Groves and Ledyard (1977) introduced the first public goods mechanism with Pareto efficient Nash equilibria. Subsequently, Hurwicz (1979) and Walker (1981), building on the ideas in Groves & Ledyard, defined mechanisms that attain Lindahl allocations — allocations that are individually rational as well as Pareto efficient. Subsequent theoretical research has focused on developing mechanisms with additional desirable properties, or mechanisms that can be applied to economies with other kinds of externalities. A number of the mechanisms developed in this theoretical research have been the subject of experimental studies. The experimental results have been mixed at best. The mechanisms have variously failed to converge to equilibrium, or have exhibited slow convergence, or while out of equilibrium have suffered failures of individual rationality, failures of collective feasibility, or severely inefficient outcomes. These results are serious red flags for practical implementation. They suggest that in the case of public goods there remains a gap between implementation in theory and implementation in practice, and that perhaps a different approach might be fruitful. The failures when out of equilibrium are especially troubling. Even for mechanisms that have good stability properties, we can’t realistically expect to be in equilibrium very often (if ever!). And the failures when out of equilibrium are often unacceptable: outcomes that make some (or all) the participants far worse off than they would have been had they been simply left alone, or outcomes that are not well-defined, because they are not feasible for some individuals or for the economy as a whole. This suggests that a focus on just the equilibrium properties of mechanisms — asking whether the equilibria are Pareto efficient, or Lindahl allocations, etc. — and even expanding the focus to the mechanisms’ stability properties as well, is too narrow. It suggests that we also need to take into account some desiderata for mechanisms’ out-of-equilibrium properties. In this paper we take a very limited, preliminary step in that direction. Our objective is to devise a mechanism for public goods that always, whether in equilibrium or not, produces feasible and “acceptable” outcomes and still produces Lindahl allocations as equilibria. Along the way, we introduce a notion of acceptability that, as far as we know, has not appeared before. We’re partially successful in attaining this objective: the mechanism we introduce always produces feasible and acceptable outcomes, and does produce Lindahl allocations as Nash equilibria. Communication among the participants is via natural, market-like proposals involving quantities and Lindahl-like For example, Bagnoli and Lipman (1989), de Trenqualye (1989, 1994), Kim (1993), Varian (1996), Peleg (1996), Corchon and Wilkie (1996), Tian (2000), Chen (2002), Healy and Mathevet (2013), and Van Essen (2013, 2015). For example, see Chen and Plott (1996), Chen and Tang (1998), Chen and Gazzale (2004), Healy (2006), Van Essen (2012), and especially Van Essen, Lazzati, and Walker (2012).